Trapping and Manipulation of Laser-Cooled Metastable Argon Atoms at a Surface

Home , Atomic mirror

Dissertation

zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.)

an der Universität Konstanz Mathematisch-Naturwissenschaftliche Sektion Fachbereich Physik

vorgelegt von

Dominik Schneble

Tag der mündlichen Prüfung: 20. Februar 2002

Referenten: Prof. Dr. T. Pfau Priv.-Doz. Dr. C. Bechinger Prof. Dr. G. Ganteför Abstract

This thesis discusses experiments on the all-optical trapping and manipulation of laser- cooled metastable argon atoms at a surface. A magneto-optical surface trap (MOST) has been realized and studied. This novel hybrid trap combines a magneto-optical trap at a metallic surface with an optical evanescent-wave atom mirror. It allows laser-cooling and trapping of atoms in contact with an evanescent light ﬁeld that separates the atomic cloud from the surface by a fraction of an optical wavelength. Based on this work, the continuous loading of a planar matter waveguide has been demonstrated. Loading into the waveguide, which was formed by the optical potential of a red-detuned standing light wave above the surface, was achieved via evanescent-

ﬁeld optical pumping from the MOST in sub-mdistancefromthesurface. In subsequent experiments, several light-induced atom-optical elements have been demonstrated in the planar waveguide geometry, including a continuous atom source, a switchable channel guide, an atom detector and an optical surface lattice. The source, the channel and the detector have been combined to form the ﬁrst, albeit simple, atom- optical integrated circuit. Contents

1 Introduction 1 1.1 General Context ...... 1 1.2 This Thesis ...... 5 1.3 Outlook ...... 6 1.4 Outline ...... 7

2 Basic Issues 9 2.1 Theoretical and Experimental Concepts ...... 9 2.1.1 Light Forces in the Dressed-Atom Picture ...... 9 2.1.2 Laser Cooling and Trapping ...... 15 2.1.3 Reﬂection of Atoms from an Evanescent Wave ...... 23 2.1.4 Generating Evanescent Waves with Surface Plasmons ...... 26 2.2 Experimental Apparatus ...... 29 2.2.1 Argon ...... 29 2.2.2 Beam Machine and Laser System ...... 32 2.2.3 The Surface ...... 36

3 Surface-Assisted Detection of Ar£ 39 3.1 Introduction ...... 39 3.2 Experimental Scheme ...... 39 3.3 Characterization of the Detector ...... 43

3.3.1 Focusing, Length Calibration and Spatial Resolution ...... 43

½× ½× ¿ 3.3.2 Detection Efﬁciencies for the 5 and States ...... 45 3.3.3 Sensitivity to Magnetic Fields ...... 48 3.4 Application: 3D Time-of-Flight Measurements ...... 49 3.5 Conclusion ...... 52

4 Magneto-Optical Surface Trap 53 4.1 Introduction ...... 53 4.2 Conﬁguration of the MOST ...... 54 4.3 Simple Model for Properties of the MOST ...... 55 4.4 Experiment ...... 60 4.4.1 Experimental Setup ...... 61

i ii CONTENTS

4.4.2 Properties of the Atom Cloud far from the Surface ...... 62 4.4.3 Behavior of the Trap for Varying Magnetic-Field Zero Position .. 66 4.4.4 Evanescent-Wave Bichromatic Atom Mirror ...... 68 4.4.5 Combined MOT–Atom Mirror ...... 73 4.5 Conclusions ...... 75

5 Continuous Loading and Manipulation of Atoms in a Surface Waveguide 77 5.1 Introduction ...... 77 5.2 Basic Concepts ...... 78 5.2.1 Overview ...... 78 5.2.2 The Waveguide ...... 80 5.2.3 Continuous Loading ...... 82 5.2.4 Surface-Sensitive Detection...... 84 5.3 Experiment ...... 85 5.3.1 Experimental Setup ...... 85 5.3.2 Continuous Loading ...... 85 5.3.3 Integrated Atom Source and Switchable Channel Guide ..... 92 5.3.4 Integrated Atom Detector and Simple Integrated Circuit ..... 94 5.3.5 Optical Surface Lattice ...... 95 5.4 Conclusions ...... 98

A Dressed Atom in a Bichromatic Light Field 101

Bibliography 103

Zusammenfassung 119

Danksagung 121 List of Figures

1.1 Trapping and manipulation of metastable argon at a surface ...... 5

2.1 Dressed atom ...... 12 2.2 Model of the 1D MOT ...... 17 2.3 3D 6-beam MOT conﬁguration ...... 18 2.4 Sisyphus cooling ...... 22 2.5 Evanescent-wave optical atom mirror ...... 24 2.6 Total potential of an evanescent-wave optical atom mirror ...... 26 2.7 Surface-plasmon evanescent-wave mirror ...... 27 2.8 Level scheme of argon ...... 30 2.9 Clebsch-Gordan coefﬁcients ...... 32 2.10 Schematic of the beam machine...... 33 2.11 View into the beam machine lab...... 34 2.12 The laser system for experiments with metastable argon...... 35 2.13 The surface ...... 36 2.14 Characterization of the surface-plasmon resonance ...... 37 2.15 Characterization of the straylight distribution above the surface ..... 38

3.1 The surface atom detector ...... 40 3.2 Surface deexcitation mechanisms ...... 41 3.3 Creating a test object for the atom detector ...... 44 3.4 Detection efficiency profile ...... 46 3.5 Measurement of the electron yield ...... 47 3.6 Switching the detector with a magnetic field ...... 48 3.7 Experimental 3D TOF spectrum for a cloud of laser-cooled atoms .... 51

4.1 General concept for the MOST ...... 55 4.2 3D conﬁguration of the MOST ...... 56 4.3 Model for a MOT near a surface ...... 57 4.4 Light ﬁeld distribution at the mirror surface ...... 59 4.5 Experimental setup for the MOST ...... 62 4.6 Fluorescence image of a trapped cloud ...... 63 4.7 Temperatures of the trapped cloud ...... 65

iii iv LIST OF FIGURES

4.8 Method for shifting the position of the magnetic ﬁeld zero ...... 66 4.9 Shifting the cloud toward the surface ...... 67 4.10 Properties of the trapped cloud for different heights ...... 69 4.11 Characterization of the bichromatic atom mirror ...... 72 4.12 Lifetime of the MOST ...... 74

5.1 Experimental schematic and transitions for the waveguide experiments .79 5.2 The waveguide potential ...... 81 5.3 Scheme and model for continuous loading ...... 83 5.4 Surface-sensitive detection ...... 85 5.5 Experimental conﬁguration for the waveguide ...... 86 5.6 Experimental setup for the waveguide ...... 87 5.7 TOF signal of the CW loaded waveguide ...... 88 5.8 Sequence for measuring the loading curve ...... 89 5.9 Loading curve of the waveguide ...... 89 5.10 Parameter dependence of the loading process ...... 91 5.11 Integrated atom source and channel guide ...... 92 5.12 Propagation of atoms in the channel guide ...... 93 5.13 Integrated atom detector and atom-optical integrated circuit ...... 95 5.14 A quasi-1D optical surface lattice ...... 96 5.15 Localization of atoms in the surface lattice ...... 97 Chapter 1

Introduction

1.1 General Context

The development of laser cooling and trapping [1, 2, 3] and atom optics [4]overthe last two decades has stimulated and contributed to a wide range of fundamental and applied research including optical lattices as model systems for solid-state physics, ultracold collisions, nano lithography, atom interferometry, precision sensing and metrol- ogy, and quantum information processing [5, 6, 7, 8, 9, 10, 11, 12]. In particular, it has also paved the way to the achievement of Bose-Einstein condensation in dilute, weakly interacting atomic gases [13,14,15]. Laser cooling and trapping exploits the mechanical effects of light on atoms which can be described in terms of spontaneous and dipole forces [16, 17, 18]. The spontaneous force arises when an atom scatters photons from a laser beam. While the absorption of photons is directed, the momenta of spontaneously emitted photons average to zero and so the atom experiences, averaged over many cycles, a nonzero momentum transfer from the beam. Since the emission is irreversible the resulting net force (also called radiation pressure) is dissipative. The dipole force, on the contrary, arises from the coherent interaction of an inhomogeneous laser field with the induced atomic dipole moment. It is conservative as no spontaneous emission is involved, and can be written as the gradient of an optical potential. These forces can be used to cool the motion of atoms and confine and manipulate them in traps. Radiation pressure on free atoms was observed as early as 1933 [19] yet remained without experimental relevance until after the advent of lasers in the 1960s. The idea of laser cooling, based on the high spectral intensity of lasers, was introduced in 1975 [20,21], and in the 1980s the first demonstration of a slowed thermal atomic beam [22] led to the development of optical molasses [23] and of the magneto-optical trap (MOT) [24]. The MOT has been intensely studied and improved in the last decade [25] and today is a standard initial step for experiments that involve trapping and cooling of neutral atoms. The usual design consists of three mutually orthogonal pairs of counterpropagating laser beams that intersect at the zero of a quadrupole magnetic field. In MOTs and molasses

the equilibrium temperature can reach down to the Krange[26, 27, 28] correspond-

1 2 CHAPTER 1. INTRODUCTION ing to a few photon recoils, and special laser cooling schemes have been demonstrated that allow to cool even below the one-photon recoil limit [29, 30]. Based on the optical dipole force, which was first observed for an atomic beam [31] in 1978, optical traps and microscopic optical lattices have been realized and studied [32, 5, 33, 34]. In optical lattices, the atomic de Broglie wavelength [35] typically is of the size of the confinement, such that these lattices can also be considered atom-optical cavities with a mode structure. Laser cooling and trapping got public attention in 1997 when the physics Nobel prize was awarded to S. Chu, C. Cohen-Tannoudji and W. Phillips for their contributions to the field. In atom optics [4], methods and elements for reflection, focusing, diffraction and interference of atoms have been demonstrated much in analogy to “photon optics”, based on optical and magnetic potentials as well as material structures. In analogy to “photon optics”, one can distinguish de Broglie wave atom optics (e.g. in an atom interferometer [36,37]),fromthespecialcaseofgeometricalatomopticsinwhichthe motion of atoms follows classical trajectories. An important atom-optical element for our experiments is the atom mirror. One type is based on the reflection of atoms at a repulsive optical dipole potential [38]. Such a mirror was first demonstrated in 1987 [39] in an experiment with a blue-detuned evanescent light wave at a surface from which a grazing-incidence thermal beam was reflected. In later experiments, laser-cooled atoms were employed [40, 41, 42, 43, 44] and recently the coherent reflection of an atomic Bose-Einstein condensate from an optical atom mirror was reported [45]. The second type of atom mirror is based on the repulsive interaction of an atom with a magnetic field via its magnetic moment. Over recent years, magnetic atom mirrors with exponentially decaying magnetic fields above a surface have been realized, using sinusoidally magnetized tapes [46, 47], arrays of alternating permanent magnets [48] and lithographically patterned current-carrying wires [49]. A third type of atom mirror exploits the quantum reflection of slow atoms from the attractive van der Waals potential at a solid surface [50] (atom-surface interactions also play an important role in evanesent-wave optical atom mirrors [44]). Ultracold atoms have proven powerful tools for the study of quantum degenerate

gases. In a dilute, ultracold atomic gas of density Ò, quantum degeneracy sets in when

½= Ì Ì

the thermal de Broglie wavelength £ (which scales as ,where is the tempera-

¿ >

£ ½

ture of the gas) becomes comparable to the average interatomic distance, Ò ,such that the atomic wavepackets overlap. For bosonic atoms this leads to Bose-Einstein condensation (BEC) [51,52], resulting in the macroscopic population of a single quantum state. BEC in a dilute, weakly interacting trapped atomic gas was first achieved in 1995 for rubidium, sodium and lithium [13, 14, 15] and very recently for metastable helium [53, 54] by combining laser cooling and trapping techniques with magnetic trapping [55] and evaporative cooling [56]. In evaporative cooling, the hottest atoms in a conservative atom trap are allowed to escape while the remaining atoms rethermalize at a lower equilibrium temperature via elastic collisions. In 1998, BEC was achieved in atomic hydrogen by evaporative cooling from a cryogenically loaded magnetic trap [57]. Over the last years, a wealth of fundamental phenomena in trapped 1.1. GENERAL CONTEXT 3 atomic BEC have been studied such as coherence, excitations, spinor condensates, Feshbach resonances, superfluidity and solitons [58, 59, 60, 61, 62, 63, 64]. BECs have been transferred from magnetic traps into purely optical traps [65, 66, 45], and very recently the first all-optical BEC was achieved by evaporative cooling from an optical dipole trap [67]. The way to the study of low-dimensional quantum degenerate gases [68, 69, 70, 71, 72, 73] has been opened in with a cryogenically cooled, degenerate 2D atomic hydrogen gas at a surface [74] and with the very recent realization of 2D and 1D BECs in highly anisotropic optical and magnetic traps [75]. For a trapped fermionic atomic gas, quantum degeneracy was first observed in 1999 [76].

One of the major implications of BEC for atom optics is the advent of atom lasers as sources of coherent atomic matter waves. Their impact on the field can be expected to be comparable to that of the laser on optics. In the laboratory, coherent matter- wave pulses and beams have already been created by coupling atoms out of a trapped BEC [77, 78, 79, 80, 66], and bosonic stimulation [81] and matter-wave amplification in BECs [82, 83] have been investigated as crucial elements of an atom laser. As one of the first applications, four-wave mixing of coherent matter waves has been demonstrated [84], opening the way to nonlinear atom optics. The major issue that is still open experimentally is a method to replenish a BEC from a reservoir in order to realize a continuous-wave atom laser [85, 86]. A number of CW pumping schemes based on collisional dissipation [87, 88, 89, 90, 91] and laser cooling [92, 93, 94, 95, 96, 97] have been proposed (a third possibility based on molecule dissociation was proposed in Ref. [98]). In the laser-cooling schemes for reaching BEC, an atom is optically pumped from a reservoir into the bound levels of a trap under the spontaneous emission of a final photon. Ideally this photon leaves the system, dissipating the excess energy. How- ever, it can also get reabsorbed by other atoms in the pumped level, which excites those

atoms to higher energy and thereby thwarts the effect of the pump. Photon reabsorp-

¿ £ tion thus limits the achievable phase-space density Ò [99]. In particular, it has been

shown that in macroscopic 3D traps (having linear extensions that are large compared

¿ £

to the optical wavelength), Ò cannot reach the critical value for BEC if the recoil

energy Ê imparted on the atom by the absorbed photon is larger than the trap level !

spacing ~ [94]. Several scenarios for getting around this problem have been worked

! !

out, including planar traps [100], tightly conﬁning 3D traps with Ê [101], and

the so-called festina lente regime for which ! is much larger than the pumping rate

[102]. the reabsorption. A recent proposal employs a pumping-laser induced Autler- Townes level splitting in the region of the thermal component of a BEC cloud to turn the emitted photons out of resonance with the atoms in the BEC [96]. Another recent scheme is based on a lambda level conﬁguration with large branching ratio, for which the reabsorption on the weak transition is suppressed [97]. This scheme is currently being investigated for chromium, for which the ﬁrst continuous loading of a magnetic trap from an overlapped MOT has recently been demonstrated [103]. Experimentally, the highest phase-space density in laser-cooling schemes has so far been achieved by cooling strontium on an optically forbidden transition, only one order of magnitude below quantum degeneracy [104]. 4 CHAPTER 1. INTRODUCTION

Over recent years, several proposals have been made for the realization of planar atom traps, based on tightly conﬁning optical and magnetic potentials at surfaces [105,106,107,108]. In these systems, which can also be considered planar atom- optical waveguides, the atomic motion is quasi-free parallel to the surface, while normal to it only a few bound states (ideally: one) are populated. Besides their relevance for reaching BEC with laser cooling, planar atom traps are of interest for the study of atomic gases in low-D and close to surfaces [109]. One of the schemes [107, 100]for such a trap has so far been demonstrated experimentally [110]. In this experiment, which was performed by us in 1998, laser-cooled metastable argon atoms released from a MOT were transferred into a single (anti-)node of a standing light wave above

a mirror surface. The optical trapping potential had five bound states and was separated from the surface by less than ½ m. Atoms were loaded into the waveguide by combining evanescent-wave reflection with a single dissipative optical pumping step in a second, overlapped evanescent field [111]. A related scheme is currently being

pursued for rubidium [112]. In another experiment, a laser-cooled cesium gas with a barometric thickness of ¾¼ m has been prepared in a weakly confining gravito- optical potential above a planar surface [113]. Here the loading scheme is based on motion-induced pumping between unequally shifted hyperfine states in the potential of an evanescent-wave atom mirror (evanescent Sisyphus cooling) [114, 106], and ef- forts are under way to achieve BEC in this system [115]. In restricted geometries,experimental methods have furthermore been demonstrated to guide ultracold atoms in hollow-core optical fibers and laser beams [116,117,118,119,45], and close to current- carrying wires [120, 121, 122, 123], using axially symmetric optical and magnetic potentials, respectively. The wire concept has been extended to the use of microfabri- cated wires on substrates, for which over the last two years several weakly confining

linear [124, 125, 126] and (switchable) Y-branch atom guides [127, 128] in a distance in the range 10 to ½¼¼ m from the substrate surface have been demonstrated. Micro- fabricated wires have also been used for the realization of magnetic traps [129]and a conveyor belt [130]. In these experiments, “mirror MOTs” [131, 111, 129] close to the reflecting surface were used for the loading of atoms into the confining potential. Recently, the first guiding of a BEC in a hollow laser beam was demonstrated [45], and the first creation of BECs in magnetic potentials above wire microstructures was reported [132,133].

The manipulation of atoms in tightly confining structured potentials close to substrate surfaces, both magnetic and optical, opens the way to integrated atom optics. This nascent field may be defined as the realization and combination of miniaturized atom-optical elements to form atom-optical integrated circuits in substrate-based geometries. This is in analogy to integrated optics, where optical integrated circuits have been built that combine a number of miniaturized, interconnected optical components on a common substrate [134]. An example for a future atom-optical integrated circuit might be a high-sensitivity integrated atom interferometer consisting of a (coherent) atom source, a large enclosed area between two waveguide beamsplitters, and a detector. By bringing ”established” atom optics down to a small scale, integrated atom 1.2. THIS THESIS 5 optics should allow for improved, cheap and easily reproducible setups. Many aspects accessible with integrated atom optics are currently being discussed, such as quantum information processing [135,136], atom-surface interactions [137], cold collisions and nonlinear atom optics [138].

1.2 This Thesis

In this thesis I present and discuss experiments performed with metastable argon on the all-optical trapping and manipulation of laser-cooled atoms at a metallic surface. In these experiments the ﬁrst continuous loading of a planar atom-optical waveguide was demonstrated, which as discussed above is of conceptual interest for schemes [92, 100, 112] to reach quantum degeneracy with laser cooling. The loading of the waveguide was achieved via evanescent-ﬁeld optical pumping from a novel magneto- optical surface trap that was used as a reservoir of pre-cooled atoms. This work was extended to the manipulation of atoms in the waveguide, which allows for a novel implementation of integrated atom optics. Several light-induced atom-optical elements

in the planar waveguide geometry in sub-m distance from the surface were demonstrated and were combined to form the ﬁrst, albeit simple, atom-optical integrated circuit. 1.5 mm WG

Detection MOST 1s e- 5 1s3 820 nm Ar* (1s3)

EWM OP WGD

Figure 1.1: Principle of trapping and manipulation of metastable argon in a planar waveguide

½× at a surface. A planar waveguide for ¿ metastable argon atoms is formed by a single layer of the periodic optical potential of a standing light wave (WG). Atoms are loaded into the

waveguide with evanescent-wave optical pumping (OP) from the magneto-optical surface trap ½

(MOST) for 5 atoms, which combines a modiﬁed MOT at the surface with an evanescent-wave

½× atom mirror (EWM). The optically pumped ¿ atoms propagate along the waveguide and are subsequently detected (WGD) via secondary electrons released upon impact on the surface.

The magneto-optical surface trap (MOST) is a combination of a modified MOT with an optical atom mirror above a gold-coated prism surface. The trapped atoms are in contact with an evanescent field that separates the atomic cloud from the surface by a fraction of an optical wavelength. The evanescent field is generated by the resonant

6 CHAPTER 1. INTRODUCTION

:¿ ¦ ¼:4µ ¢ ½¼

excitation of surface plasmons in the gold ﬁlm. In the experiment, up to ´½

¦ ¿¼µ atoms could be trapped with a lifetime of up to ´¿9¼ ms. The properties of the MOT were investigated for decreasing distances of its center from the surface and a drastic decrease of the lifetime due to losses to the surface was observed. The atom mirror was investigated in the presence of the MOT light and a a strong influence of the bichromatic light field on its performance was found. Combining the atom mirror with a MOT whose center was located on the surface, it was shown that the evanescent field of the atom mirror can increase the lifetime of the trapped atom cloud by at least one order of magnitude by suppressing losses to the surface. The properties of the MOST are explained in a simple model. The planar waveguide for ultracold metastable argon atoms is formed by the periodic optical potential of a red-detuned standing light wave above the surface. In this system the atomic motion is quasi free parallel to the surface while normal to it only a few bound states exist. A continuous, surface-sensitive loading mechanism for the lowermost waveguide layers was demonstrated and characterized experimentally. The mechanism is based on the MOST as a reservoir of laser-cooled atoms at the surface,

from which atoms are optically pumped into the waveguide in the short range of a ¿

second evanescent light ﬁeld. A loading rate on the order of ½¼ /s was achieved, which

5 ¾ corresponds to a ﬂux of ½¼ /(s cm ). The evanescent loading mechanism led to a rel-

ative population of around ¿¼± for the lowest confining waveguide layer centered at 820 nm above the surface, orders of magnitude closer to the surface than achieved in the work on atoms trapped in magnetic potentials at surfaces. Based on the continuous loading scheme for the planar waveguide, a local atom source in the planar waveguide geometry was implemented. A switchable channel guide connected to the source was realized and the propagation of atoms in this guide was directly observed. An atom detector in the channel guide was realized via a local deformation of the confining waveguide potential with another evanescent light field. The source, the guide and the detector were combined into an integrated circuit for a simple atomic beam experiment in the lowest waveguide layer. Also, the localization of atoms in a quasi-1D surface lattice (realized by retroreflecting the waveguide laser beam) was demonstrated. The atom detection in the experiments was largely based on the imaging of secondary electrons released from the surface upon impact of single atoms. The sur-

face atom detector was characterized with atom-optical methods, and the detection

½× ½× ¿ efﬁciencies for the metastable 5 and states of argon used in the experiments were determined. A method for 3D time-of-ﬂight spectroscopy of ultracold atoms was demonstrated that exploits the spatial and temporal resolution of the detector.

1.3 Outlook

The manipulation of atoms in a structured optical potential close to a substrate surface opens the way to integrated atom optics. The waveguide as the fundamental element provides a planar geometry above a substrate surface into which atom-optical compo- 1.4. OUTLINE 7 nents can be subsequently incorporated, and transverse guiding can be achieved by laterally structuring the waveguide potential (the shutterable channel guide and the quasi-1D lattice are simple examples). This scheme is extremely flexible since the confining optical potential of the waveguide can be modulated easily both in space and time – in future applications, one might envision using addressable liquid crystal pixel arrays as transmission masks in the waveguide beam that are combined with a high- resolution imaging system to ”write” arbitrary light fields onto the surface. In this way, miniaturized and time-dependent atom-optical setups could be realized, paving the way to novel integrated elements and complex integrated circuits. In addition, the extreme closeness to the surface makes our system interesting for probing atom-surface interactions in such applications. Continuous loading of planar atom waveguides has been discussed in connection with schemes to reach quantum degeneracy in open systems [92, 100, 112]. With our work, we have shown for the first time that such a continuous scheme can indeed be realized. In the present proof-of-principle realization the loading flux into the waveguide is comparable to that achieved with our previously realized pulsed scheme [110], being three orders of magnitude short of what would be required for a scenario for degeneracy in bosonic ground-state argon [100,111]. Our data suggest, however, that significant improvements in the flux might still be possible in an optimized experimental setup in which the loading rate of the MOST and the pumping rate of the evanescent pumping field are increased. Our work therefore might also encourage further studies in this direction. Finally, our scheme for bringing a magneto-optical trap near a mirror surface is of universal interest when laser-cooled atoms are desired in the vicinity of surfaces. In fact, adaptions of this kind of MOT have already been employed recently as starting points for loading atoms into magnetic potentials [129, 126] and reaching BEC near surfaces [133]. The additional combination of these surface MOTs with an atom mirror should allow to minimize initial losses to the surface and thereby allow for a significant increase in the starting phase-space density.

1.4 Outline

This thesis contains five chapters and one appendix. In this first introductory chapter, a general overview of the current status of the field and the scope of this particular work has been given. The second chapter contains an introduction to important aspects of atom-light interactions and to more general concepts related to the experiment, with a focus on the magneto-optical trap and the evanescent-wave optical atom mirror (as constituents of the magneto-optical surface trap). The chapter also summarizes important properties of argon and shortly describes the beam machine and laser system and its modifica- tions as compared to that used in previous experiments. Finally the properties of the coated prism surface for the generation of evanescent fields with surface plasmons are discussed. 8 CHAPTER 1. INTRODUCTION

The third chapter deals with our work on the surface atom detector as a crucial part of the experimental apparatus. A short overview of the detection principle and the present improved setup is given, and our experiments to characterize the performance of the detection scheme with laser-cooled atoms and an evanescent wave mirror are discussed. The fourth chapter and the appendix are devoted to the magneto-optical surface trap. The trap conﬁguration and a simple model picture for the behavior of the MOST are discussed, and the experimental study of the MOST and its constituents is presented. The ﬁfth chapter focuses on the continuous loading of the planar waveguide and the manipulation of atoms in the waveguide potential. Basic issues for the waveguide and a simple model for the loading process are discussed, and the experiments and results on continuous loading and the realization of light-induced atom-optical elements are presented. Chapter 2

Basic Issues

2.1 Theoretical and Experimental Concepts

2.1.1 Light Forces in the Dressed-Atom Picture

In laser cooling and trapping the external degrees of freedom of a free atom are ma- nipulated and controlled by exploiting the coupling of the atom to a quasi-resonant laser ﬁeld. The following subsections shortly review the concept of optical forces in the so-called dressed atom picture, following the description in Refs. [17,16,139].

Dressed states for the two-level atom. Consider a free two-level atom A at rest

interacting with a monochromatic laser mode Ä. The total Hamiltonian of the system

is given by

À = À · À · Î :

A Ä AÄ

AÄ (2.1)

À À Ä

The ﬁrst two terms describe the state of the atom A and the laser ﬁeld ,andthe Î

third term AÄ describes the atom-ﬁeld coupling. The coupling of the atom to the vacuum ﬁeld is neglected for the moment; instead it will be introduced below via the

spontaneous decay rate , which is the linewidth of the excited state of the atom.

À À · À

A Ä

The non-interacting part of the Hamiltonian ¼ is given by

½ ½

À = ~! jeihej ~! ; À = ~! ´a a · µ;

¼ ¼ Ä Ä

A (2.2)

¾ ¾

! jg i jei

where ¼ is the transition frequency between the internal states and of the atom,

´aµ

and a is the creation (annihilation) operator for a photon in the laser mode with

! À ji; Æ i i = e; g ¼

frequency Ä . The eigenstates of are given by the bare states ,where

= ha ai and Æ is the photon number. For a small detuning of the laser ﬁeld with

respect to the atomic transition frequency

Æ ! ! ! ;

Ä ¼ ¼ Ä (2.3)

10 CHAPTER 2. BASIC ISSUES

g; Æ ·½i je; Æ i

the states j and are quasi-degenerate with a small energy difference of

~Æ E ´Æ µ=fjg; Æ ·½i; je; Æ ig

Ä and can be grouped into manifolds . Î

In the semiclassical dipole approximation, the interaction Hamiltonian AÄ is given

Î = d ¡ E´Êµ d E

by AÄ ,where and are the operators for the electric dipole and ﬁeld

at the classical position Ê of the atom:

jeihg j · jg ihej d = d

ge (2.4)

E = Ù ´a · a µ Ù ~! =´¾" Î µ ¯

¼ Ä

with Ä (2.5)

d hg jdjei ¯ Ä Here, ge is the atomic dipole matrix element, is the unit vector repre-

senting the polarization of the laser ﬁeld, and Î is a normalization volume. In the Î

rotating-wave approximation [16] only the quasi-resonant terms in AÄ for the cou-

´Æ µ

pling within E are considered such that

Î = d ¡ Ù jg iheja · jeihg ja : ge AÄ (2.6)

For a sufficiently intense coherent laser field the field can also be described classi-

E = E cÓ× ! Ø E =¾Ù hÆ i

Ä ¼

cally by its expectation value ¼ ,where .Inthatcasethe

´Æ µ

interaction, expressed in the bare state basis of E , is simply given by

Î = he; Æ jÎ jg; Æ ·½i = ~ ! =¾;

AÄ Ê

Æ (2.7) !

where Ê is the (on-resonance) Rabi frequency

! d ¡ E =~ = Á=´¾Á µ :

eg ¼ Ë

Ê (2.8) !

The last equation relates Ê to experimentally accessible quantities using the

Weisskopf-Wigner theorem [140] that connects the dipole matrix element to the Á

linewidth of the excited state of the atom. The ﬁeld intensity is given by

Á = " cjE j =¾ ¼

¼ ,and

¾ ¿

µ Á ¾ ~c =´¿ =¾c=!

¼ ¼

Ë with (2.9) ¼

is the so-called saturation intensity.

À À Î

Ä AÄ

Using the contributions A , and thus determined, the total Hamiltonian

À E ´Æ µ

AÄ can now be diagonalized in the basis of the bare states of . This leads to

stationary eigenstates of the atom+ﬁeld system

j½´Æ µi = ×iÒ jg; Æ ·½i ·cÓ× je; Æ i

¾´Æ µi = cÓ× jg; Æ ·½i ×iÒ je; Æ i; j (2.10)

the so-called dressed states, with corresponding energy eigenvalues

E = ´Æ ·½µ~! · ~ª=¾;

½ Ä

Æ; (2.11)

E = ´Æ ·½µ~! ~ª=¾:

¾ Ä Æ; (2.12) 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 11

The mixing angle is deﬁned by the condition

ØaÒ ¾ = ! =Æ ´=4 ¿=4µ; Ä Ê (2.13)

and the quantity

¾ ¾

Æ · !

ª (2.14)

Ä Ê is the off-resonance Rabi frequency.

Spontaneous emission and transitions between dressed states. In the discussion of the dressed atom the coupling of the atom to the vacuum has not been included so far. This section describes how this coupling inﬂuences the population of the dressed

states; subsequent sections then address the issue in the context of light forces.

e; Æ i jg; Æ i

In a spontaneous emission process the state j decays into , thereby lead-

´Æ µ E ´Æ ½µ

ing to a transition from the manifold E to . The next emission then leads to

´Æ ¾µ ª E , etc. in a radiative cascade. As long as the Rabi frequency is large compared

to the decay rate , the decay will not perturb the dressed-state coupling which builds

½ up on the time scale ª . The populations of the dressed states and the coherences between them can be

derived from the master equation [16]

" #

d i ½

= [À ;] ´Ä Ä · Ä Ä µ Ä Ä ;

· · ·

AÄ (2.15)

dØ ~ ¾

where is the density operator of the dressed atom and AÄ is deﬁned as in the last

Ä jeihg jª½ Ä jg ihejª½ section, and the term containing · , describes the coupling to the vacuum. This operator equation leads to equations of motion for the reduced

matrix elements

= hi´Æ µj jj ´Æ µi;

ij (2.16)

obtained by summing up over the ladder of dressed states. Since ª , the coupling

¾¾ ½¾ ¾½ between the populations ½½ , and the coherences , can be neglected [16]

(secular limit), and the populations are then described by

_ = ·

½½ ½½ ½¾ ¾¾ ¾½

_ = · ;

¾¾ ¾½ ½½ ½¾

¾¾ (2.17)

where the transition rates ij (see ﬁgure 2.1)aregivenby[16]

¾ ¾

= = cÓ× ×iÒ ;

½½ ¾¾

= ×iÒ

¾½

= cÓ× :

½¾ (2.18)

12 CHAPTER 2. BASIC ISSUES

! ! ¦ ª ¼ The transition frequencies are ¼ , , give rise to the Mollow triplet [141]in

the emission spectrum. The steady-state populations are determined by the stationary

_ =¼µ

solution ( ii

×iÒ cÓ×

×Ø ×Ø

= =

and (2.19)

½½ ¾¾

4 4

´×iÒ ·cÓ× µ ´×iÒ ·cÓ× µ

= ·

¾½ ½¾

which build up with the rate ÔÓÔ that is on the order of the decay rate.

×Ø ×Ø

= =¼ = · =¾ ¾¾

The coherences vanish, , with a comparable rate cÓh .

½¾ ¾½

j½´Æ µi

{ jg; Æ ·½i

~Æ

E ´Æ µ

~ª´Êµ

je; Æ i

j¾´Æ µi

Ä ½¾

¾½

¾¾

½½

j½´Æ ½µi

{ jg; Æ i

~Æ

Ä E ´Æ ½µ

~ª´Êµ

je; Æ ½i

j¾´Æ ½µi

´Æ µ E ´Æ ½µ

Figure 2.1: Two manifolds E and of the dressed atom. With increasing coupling !

Ê to the ﬁeld, which in this example increases exponentially from left to right starting from

zero, the uncoupled bare states (at left) couple to dressed states (at right) with energetic sepa-

~ª Æ > ¼ ration . The example is for blue detuning Ä (for red detuning the energetic order of the bare states within a manifold is reversed). Transitions arise as a result of spontaneous decay, leading to a radiative cascade over the manifolds.

Optical dipole force and dipole potential. If the laser ﬁeld possesses a spatial variation of the ﬁeld intensity, the energies of the dressed states become spatially dependent,

giving rise to the conservative optical dipole forces

F = ÖE =´ ½µ Öª Æj

j (2.20) ¾

2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 13 E

as a gradient of the optical potentials (also called light shifts) Æi acting on the dressed

j =½´Æ µi jj =¾´Æ µi states j and , respectively.

The transitions between the states discussed in the previous section now lead to

F F ¾ random jumps between ½ and which in the steady state can be expressed by the

mean force

¢ £

×Ø ×Ø ×Ø ×Ø

hF i = F · F = Öª :

½ ¾

diÔ (2.21)

½½ ¾¾ ½½ ¾¾ ¾

which is the gradient of the potential [16]

~Æ ! =¾

Í = ÐÒ ½· :

diÔ (2.22)

Æ ·´ =4µ Ä

As a function of detuning, the force has the shape of a Lorentz dispersion curve: For

Æ > ¼ j½´Æ µi jg; Æ ·½i

Ä (blue detuning) the state contains the larger admixture of and

j¾´Æ µi > ¾¾

is therefore more stable against spontaneous decay than such that ½½ . F

In that case the contribution of ½ dominates and the atom is therefore repelled from

Æ =¼ Æ < ¼ Ä high intensity regions. On resonance, Ä , the force vanishes and for it takes

the opposite sign such that the atom is attracted to high-intensity regions.

¾ ¾

An important special case is the case of large detunings Æ for which the

Ä Ê transition rates tend to zero, such as for optical dipole traps and evanescent-wave atom

mirrors. The light shift is then given by

~ ~

Í !§ ´ª jÆ jµ § ; Ä

diÔ (2.23)

¾ 4 jÆ j

j¾´Æ µi · j½´Æ µi

where the sign is for the state and the sign is for the state.

Ä k

Scattering force. For the case of a homogeneous light ﬁeld with wave vector Ä ,

the optical dipole force on the dressed atom discussed so far vanishes. However there

e; Æ i jg; Æ i

are still transitions between j and as a result of absorption and spontaneous

emission that are themselves connected to momenta Ä . While the momentum transfer from spontaneous emission averages to zero, the absorption is unidirectional and is therefore connected to a net momentum transfer to the atom. Averaged over many absorption and emission cycles this gives rise to the so-called scattering force which is dissipative and can be used for laser cooling. The scattering force can be described easily using the so-called optical Bloch equa-

tions which are obtained by expressing the master equation 2.15 in the basis of

e; Æ i jg; Æ i the bare states j and and summing up over the radiative cascade, i.e.

eliminating the laser ﬁeld from the model [16]. By deﬁning the reduced elements

^ = hi; Æ j jj; Æ i

ij , i.e. by eliminating the laser ﬁeld, and introducing the quanti-

Ù =´^ ·^ µ=¾ Ú =´^ ^ µ=´¾iµ Û =´^ ^ µ=¾

eg ge eg ee gg ties ge , and ,eq.2.15 takes the

form

½ ½ ¼ ½ ¼ ½ ¼ ¼

¼ Ù =¾ Æ ¼ Ù_

A A @ A @ A @ @

¼ Ú Æ =¾ ! Ú_

¡ = Ê

Ä (2.24)

=¾ Û ¼ ! Û_ Ê 14 CHAPTER 2. BASIC ISSUES

This describes, in the reduced bare-state basis, a damped Rabi oscillation of the coher-

¾Û ences Ù; Ú and the population difference , in analogy to the Bloch equations known from nuclear magnetic resonance.

The population of the excited state, from which spontaneous transitions occur, is

= Û ·½=¾ · =½µ

gg ee

given by ee (since . In the steady state, it takes the value

! =¾

× ½

×Ø

× = ;

= with (2.25)

¾ × ·½

Æ · =4

×Ø

where s is called the saturation parameter (for small saturations, ). Since sponta-

ei neous decay from j occurs at the rate , the steady-state rate for absorption-emission

cycles is then given by

×Ø

×c (2.26) ee

which ﬁnally leads to the scattering force (also called radiation pressure)

! =¾

×~ ~

hF i = ~k = k = k :

×c Ä Ä Ä

×c (2.27)

¾ ¾

¾´× ·½µ ¾

=¾ · =4·! Æ

Ê Ä

´~ =¾µ k × !½

The scattering force, which takes a maximum value of Ä for , is a non- conservative force that cannot be derived from a potential. As a function of detuning, it has the shape of a Lorentzian centered about the atomic resonance frequency. It follows already from the discussion of the optical dipole force that transitions

between the states, i.e. the scattering force, can be made arbitrarily small compared

jÆ j! Ê

to the dipole force by increasing the laser detuning such that Ä .Inthatcase,

F =F » ½=Æ

×c Ä diÔ .

Force fluctuations. The spontaneous transitions not only influence the dipole force and give rise to the scattering force, but they also lead to fluctuations of these light

forces which are connected to random momentum kicks. In this section, a simple 1D

´Øµ = F ´Øµ hF i situation is assumed. The force ﬂuctuations ÆF are characterized

by [139]

ÆF ´Øµi = ¼

h (2.28)

¼ ¼

ÆF ´ØµÆF ´Ø µi = ¾Dg´Ø Ø µ; h (2.29)

The quantity D in the autocorrelation function of eq. 2.29 is called the momentum

diffusion coefﬁcient. The function g has unit area and a width that is given by the

correlation time c . Because of the random nature of photon emission, this time is

simply given by the photon scattering time, c . ×c

Consider the case of the scattering force, then integration of the autocorrelation

¾ ½

¾D hF ´¼µ i

function yields ×c ,suchthat,byusingeq.2.27,

×c

D ´~k µ :

Ä ×c ×c (2.30) 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 15

For the case of the dipole force, eq. 2.21, the diffusion coefﬁcient can be estimated

×Ø ×Ø

hF i ¼

similarly as above for ,i.e.forthecaseofsaturation diÔ at which

½½ ¾¾

=¾

×c :

¾ ½

D ¾´~Ö ªµ

diÔ (2.31)

The ﬂuctuations are connected to heating and limit the temperatures achievable in laser cooling. This is discussed further in section 2.1.2.

Multilevel atoms. The two-level atom picture can be extended to atoms with magnetic Zeeman substructure by taking the angular dependence of the induced dipole

moment and the polarization state of the light ﬁeld (with respect to the quantization

jg; Ñ i je; Ñ i e

axis) into account. For an atom with states g and , the dipole moment is

hg; Ñ jdje; Ñ i e

given by g . For light with the correct angular momentum to drive the

~´Ñ Ñ µ g

transition, i.e. with e , the connection to the two-level atom picture is then

! ! ! C C

Ê Ñ ;Ñ Ñ ;Ñ

made by the substitution Ê in eq. 2.8,where is the Clebsch-

g e g e Gordan coefﬁcient of the transition.

For multilevel atoms with a branching in the excited state the linewidth is given

= A A A i

as i ,wherethe are the Einstein coefﬁcients for the different transitions

jg i°jei Ä jg i° i

. For the case that the laser mode interacts with a single transition k

jei Æ

(detuning Ä;k ), the system can be described in the two-level dressed atom picture

! A

by substituting k in eqs. 2.8 and 2.9, which yields a corresponding on-resonance

! Á ×;k Rabi frequency Ê;k and (effective) saturation intensity . These direct analogies to the two-level atom generally break down when spontaneous decay is involved, being connected to a continual loss of population from the

effective two-level atom via decay to the other ground states. For the effective two-level

fjg i; jeig jg i = A

i ×c;i i ee

atom j , the optical pumping rates to the states are given by .

For the case of weak coupling Ê;k with slow pumping, it can be shown that the

¾ ¾ ¾

! =´ ·4Æ µ ee

population ee takes a quasi-stationary value given by [107].

Ê;k Ä;k

2.1.2 Laser Cooling and Trapping For a moving atom, the Doppler frequency shift can be exploited to dissipate the kinetic

energy of the atom by means of the scattering force. Consider an atom moving against

´Æ < ¼µ

a red detuned laser beam Ä . In the atom’s rest frame the frequency of the beam

Æ = Ú ¡ k : Ä

is shifted closer to resonance due to the Doppler shift D In the ideal case,

= Æ · Æ ¼ = Æ D

the light ﬁeld is shifted into resonance, Ä . Intherestframeofthe Ä

atom, the photons are then isotropically scattered with the maximum scattering rate

=¾ . Due to the Doppler effect, photons that are not re-emitted in the direction of the laser beam are shifted towards higher energies. The energy balance is maintained by a reduction of the kinetic energy of the atom. Since the photon scattering is also connected to an increase in entropy the effect is irreversible. This principle of laser cooling was suggested in 1975 by Hänsch and Schawlow [20] and independently by Wineland and Dehmelt [21]. 16 CHAPTER 2. BASIC ISSUES

Slowing of an atomic beam. For a thermal atomic beam the Doppler shift can exceed

the natural linewidth by orders of magnitude. To use the scattering force efﬁciently, the atoms therefore have to be kept on resonance as they slow down to small velocities. The two most common techniques for the preparation of slow atomic beams consist of sweeping the frequency of the counterpropagating laser beam accordingly (chirp- slowing, 1985 [142]) or by varying the transition frequency along the trajectory via a Zeeman shift of magnetic sublevels in a static magnetic ﬁeld, while keeping the light

frequency constant (Zeeman-slowing, 1982 [22] ). This creates a continuous beam of

g i jei slow atoms. The Zeeman shift of a transition between states j and in a magnetic

ﬁeld B is given by

Æ = ´g Ñ g Ñ µ B=~ =: B=~;

e e g g B

Z (2.32)

g Ñ

g;e B where g;e are the Landé factors, the magnetic quantum numbers, and is the Bohr magneton.

Optical molasses configuration. Atoms can be trapped in momentum space in the so-called optical molasses configuration, which was first realized by Chu et al. [23]in 1985. This configuration can best be illustrated in a 1D model. Consider a slow atom

at velocity Ú in a laser ﬁeld conﬁguration consisting of counterpropagating laser beams

Ä ;Ä Æ < ¼

¾ Ä ½ with uniform intensities and red detunings . For an atom at rest, the

two mean scattering forces balance each other and no net force is exerted. Suppose Ä

now that the atom moves in the direction of propagation of ½ and therefore against

Ä jkÚjjÆ j Ä

Ä ¾

¾ . This produces a small Doppler shift that brings closer to resonance, Ä

and at the same time shifts ½ further away from resonance. As a consequence the scattering forces of the two beams become unbalanced, and the total scattering force

opposes the motion of the atom. In eq. 2.27 for the scattering force the detuning has

Æ ! Æ ¦ Úk hF i = hF i´Æ ¦ Úk µ

Ä Ä ×c ×c Ä Ä

to be replaced by Ä such that . For small saturation

× , the effects of the beams can be treated independently, such that

hF i´Ú µ=hF i´Æ · Úk µ hF i´Æ Úk µ Ú

×c Ä Ä ×c Ä Ä ×c;ØÓØ (2.33)

with [143]

Á ¾Æ =

= 4~k > ¼:

(2.34)

¾ ¾

Á [½ · 4´Æ = µ ]

Ë Ä

hF i

×c is a velocity dependent friction force that damps the atomic motion with a rate

5 ½

Å ½¼ = which typically is on the order of s (M is the mass of the atom). The 1D model can easily be extended to 3D by setting up three orthogonal beam pairs. For large saturation, the effects of the forces from the beams can no longer simply be added; however the model remains qualitatively valid.

Magneto-optical trap configuration. A configuration that provides spatial confinement as well as cooling in momentum space is the so-called magneto-optical trap 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 17

(MOT), ﬁrst realized by Raab et al. in 1987 [24]. The MOT is illustrated in ﬁgs. 2.2

and 2.3. The underlying mechanisms are most easily explained in the 1D model shown

Â = ¼ ° Â = ½ Â ° Â ·½ e

in ﬁg. 2.2 for a g transition (this can be extended to any

Þ =¼

transition). The magnetic ﬁeld B has a zero crossing at and increases linearly to

= jdB=dÞ j

either side, with a constant gradient b . Then as a function of position the

= ½ Zeeman sublevels of the excited state of the atom split up energetically, with Ñ

having the highest energy when choosing the local direction of B (cf. ﬁg. 2.2)asthe quantization direction. Suppose the atom is situated in a pair of counterpropagating,

red-detuned laser beams (as in the discussion of the 1D molasses) that now are right- =¼

handed circularly polarized. The “inbound” beams propagating towards Þ are then

jÂ =¼;Ñ =¼i°j½; ½i

beams, driving only the transition because of angular mo-

= ¼

mentum selection. After passing Þ and becoming “outbound” beams, they revert

j¼; ¼i ° j½; ½i Ñ = ½

to , now driving . Because of the Zeeman shift, the level is

always closest to resonance. As a result the scattering force from the beam exceeds ·

the one from the beam and the atom is pushed towards the center. In addition to

=·½ Energy Ñ

·½

Ñ =¼ Â = ½

¼ {

Ñ = ½

rhc

Ñ =¼

Â =¼

B B

=¼° Â =½

Figure 2.2: One-dimensional MOT model for a Â transition. The large arrows

represent a pair of right-handed circular (rhc), red detuned laser beams ( Ä )whosepolar-

ization changes from to with respect to which is chosen as the quantization axis.

¦Æ

the above limits for saturation and atomic velocity, the Zeeman shifts Z (eq. 2.32)

jÆ j

with the limit Z must also be included. Now the mean scattering force in the

MOT is given by1

hF i´Þ; Úµ = hF i´Æ · Úk Æ ´Þ µµ hF i´Æ Úk · Æ ´Þ µµ

×c Ä Ä Z ×c Ä Ä Z

×c;ØÓØ (2.35)

Ú Þ; (2.36)

with [144]

¬ ¬

(2.37)

¬ ¬

k dÞ Ä

Â =¼ ° Â =½ e For g all Clebsch-Gordan coefﬁcients are equal to 1.

18 CHAPTER 2. BASIC ISSUES ¼ which is the force of a damped harmonic oscillator ( is deﬁned in eq. 2.32). The

damping constant is the same as for the molasses in eq. 2.34. The spring constant

¾ ½

=Å ½¼

is connected to an oscillation frequency which typically is of order s . Å

Since this is much smaller than the damping rate = the motion of atoms in the Þ

potential is strongly overdamped. The spatial capture range c within which atoms can

jÆ ´Þ µj < jÆ j Ä be trapped is deﬁned by the condition Z and is typically in the mm range.

The depth of the trap, i.e. the capture range in velocity space, can be estimated by Ú

considering that atoms with the maximum allowable velocity c must be slowed down

Þ ~k =¾ Ä

in a distance c while experiencing the maximum scattering force of the Ú

counterpropagating beam. Typical values for c are a few m/s, corresponding to trap depths around 1 K. The 1D configuration of a MOT can be extended to 3D. The configuration of the most commonly used 6-beam MOT is shown in figure 2.3. A quadrupole field with constant field gradients near the center is generated by a pair of coils with equal but opposite currents, and three orthogonal laser beam pairs provide for 3D cooling and

conﬁnement. Due to the rotational symmetry of the coils (and Maxwell’s equation

Ö¡B =¼ dB =dÜ =dB =dÝ = ´½=¾µ dB =dÞ:

Ý Þ ), the ﬁeld gradients are Ü

rhc

lhc

B Á

lhc Á rhc

rhc Ü

Figure 2.3: 3D 6-beam MOT conﬁguration. All beams traveling towards the trap center are

beams (the direction of B is chosen as a quantization axis). The situation in the radial plane corresponds to the 1D model; for the axial direction, the beams are left-handed circular (lhc)

because of the opposite direction of B

Momentum diffusion and Doppler temperature. The ﬂuctuations of the scattering force discussed in section 2.1.1 are connected to a heating process that counteracts the produced by the net friction force. Considering a 1D molasses, eq. 2.33,theforce

acting on a single two-level atom including ﬂuctuations is then given by

F ´Øµ= Ú´Øµ·ÆF ´Øµ ×c;ØÓØ ×c;ØÓØ (2.38) 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 19

Using the deﬁnition of the force ﬂuctuations, eq. 2.29, this equation can be transformed

into the following equation for the velocity Ú of the atom,

Ú = ´=Å µ Ú · ´ D =Å µ G´Øµ;

×c;ØÓØ (2.39)

dØ

G´Øµ hG´Øµi =¼ hG´ØµG´Ø µi =

where Å is the mass of the atom, and is deﬁned by and

¾g ´Ø Ø µ D

. The momentum diffusion coefﬁcient ×c;ØÓØ has already been discussed above. This stochastic differential equation is the so-called Langevin equation known

from diffusion theory [145]. A solution can be given in terms of the probability distri-

= Ô´Ú; Øµ Ú Ø

bution function Ô for the atom to have velocity at time .Forthecaseofa

¼ ¼

g ´Ø Ø µ Æ ´Ø Ø µ

Markov process , i.e. for vanishing correlation time c ,thisfunction

is deﬁned by the Fokker-Planck equation [145]

@ @

´Òµ

D Ô; Ô =

(2.40)

@Ø @Ú

Ò=½

´½µ ´¾µ ¾

D ´Ú µ = ´=Å µ Ú D = D =Å Æ

with and ×c;ØÓØ . For laser cooling the -correlation

is a reasonably good approximation when c is much smaller than the damping

×c

= Å= @Ô=@Ø ¼

time d , as is generally the case. For the stationary case , the Fokker-

Planck equation yields

¾ ¾

µ Ú =´¾

e Ô ´Ú µ = = D =´Å µ ;

Ú ×c;ØÓØ

Ú with (2.41)

¾ Ú which has the form of a 1D Maxwell-Boltzmann distribution for thermal equilibrium

with temperature Ì for which

= k Ì=Å B Ú (2.42)

This formalism for the description of the molasses is the same as for Brownian motion [145]. However the molasses is an open system far from thermal equilibrium (the

laser photons and vacuum ﬂuctuations cannot be considered as a thermal reservoir).

Ì Ô

The “temperature” is therefore simply deﬁned as a measure for the width of Ú .

D ×c;ØÓØ By equating Ú in eqs. 2.41 and 2.42 and plugging in the values for and

according to eqs. 2.30 and 2.34 one obtains

D ~ ½·´¾Æ= µ ~

Æ = =¾

×c;ØÓØ

k Ì = = ! k Ì

B D

B (2.43)

8 jÆ j= ¾ Ì

The minimum temperature D is called the Doppler temperature [143], and the corre-

Ú D sponding velocity width Ú the Doppler velocity.

Density distribution in a MOT. As described above, the force in the simple MOT model describes a strongly overdamped harmonic oscillation that would lead to a a localization of atoms at the trap center in the absence of ﬂuctuations. When the force ﬂuctuation term is included in eq. 2.35, it can be shown, again in analogy to Brownian

20 CHAPTER 2. BASIC ISSUES

= Ô´Þ; Øµ motion that the density distribution Ô for atoms in the overdamped limit can be described by a Fokker-Planck equation of the form of eq. 2.40 with the stationary solution of a Gaussian [145] 2 (the force ﬂuctuation term is the same as that for the molasses because to ﬁrst order, the total scattering rate is constant everywhere in the

trap):

¾ ¾

Þ =´¾ µ

Ô ´Þ µ = e ; = k Ì=

Þ B

Þ where (2.44)

Ô = Ô´Ü; Ý ; Þ ; Øµ The temperature Ì is the same as that of the molasses. In a 3D MOT is anisotropic because of the anisotropy of the magnetic ﬁeld gradient. The single-atom discussion can be extended to a cloud of atoms trapped in the MOT. If the atoms can be treated independently (which is the case for low densities),

the density in a MOT increases linearly with the atom number Æ . This is called the “temperature limited regime” as the volume of the trapped cloud is only determined

by the trap temperature. The cloud then has a Gaussian shape3 with center density

: Ò =

¼ (2.45)

´ ¾ µ

Ü Ý Þ

½¼ ¿

Ò > ½¼

However, for densities ¼ cm , collective optical effects (photon reabsorption and beam attenuation [150]) start to become important. In this “multiple scattering regime” [25] the independent-atom approach breaks down and the density stays

constant while the volume grows linearly with the atom number4.

´Ö;Øµ MOT loading and decay. The evolution of the local density Ò in the MOT is

described by [152]

= Ð «Ò ¬Ò

Ò (2.46) @Ø

Here, Ð accounts for the loading of atoms into the trap, e.g. from a slow atomic beam, ¬ and the second and third terms with constants « and describe one-body and two- body losses, respectively. The one-body losses in a MOT arise from collisions with hot

background-gas atoms that are in thermal equilibrium with the walls of the vacuum

8 ½

½¼ « ½ chamber (at pressures mbar, the rate s ).

2It is important to note that even though it looks as if eq. 2.44 couldalsobeobtainedfromeq.2.41 by

simply applying the equipartition theorem, this is not justiﬁed as the system is not in thermal equilibrium;

Ô ´Ú µ in fact the velocity distribution Ú and therefore the mean kinetic energy are the same everywhere in the trap. 3For imperfect beam alignments, shapes deviating from the Gaussian can be observed, such as clouds with interference fringes [146] (see also the discussion of the MOST) or clumps and rotating rings [147, 148, 149]. 4A third (yet transient) regime, is the “two component regime” that can be reached by compressing a MOT in the multiple scattering regime by rapidly increasing the magnetic ﬁeld gradient [151]. The cloud then spills out into the high magnetic ﬁeld region without polarization gradient cooling. 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 21

In the temperature limited regime, eq. 2.46 can be integrated spatially and then

Ò ´Øµ

solved for the center density ¼ (which is directly connected to the atom number

´Øµ Æ via eq. 2.45). The beginning of the loading process for an initially empty trap is

characterized by

Ò = Ä=Î ´Ø ! ¼µ;

¼ (2.47)

dØ

Ä Î ´ ¾ µ

Ý Þ where is the total loading rate and Ü . With increasing density, the

trap losses become larger, and ﬁnally the density reaches a steady state

¼ ¾ ¼

Ò = [«=´¾¬ µ] · Ä=´Î¬ µ «=´¾¬ µ; ;×Ø

¼ (2.48)

¼ ¼ ¼ ¾

= ¬=´¾ ¾µ Ä Ä=´¬ Î µ [«=´¾¬ µ]

with ¬ . For large with , this density scales with

Ä ¼

Ä. The trap decay, characterized by ,isgivenby

Ò ´¼µ

Ò ´Øµ= :

¼ (2.49)

«Ø ¼ ¼

e ´½ · Ò ´¼µ¬ =«µ Ò ´¼µ¬ =«

¼ ¼

«Ø ¼

Ò ´Øµ » e Ò ´¼µ¬ =« ½ ¼ The decay becomes exponential ¼ for long times or for .

Polarization gradient cooling. The Doppler temperature is the cooling limit for the two-level atom. For atoms whose ground state consists of two or more Zeeman substates, additional cooling mechanisms due to polarization gradients in the laser ﬁeld can come into play that lead to lower temperatures. Such mechanisms were ﬁrst observed in 1988 by Lett et al. [26] and described in 1989 by Dalibard and Cohen- Tannoudji in an intuitive model [18].

In the so-called “lin?lin” conﬁguration, the 1D molasses beams have orthogonal linear polarizations (cf. ﬁg. 2.4). The superposition is then a stationary gradient of

alternating linear and circular polarizations. The simplest model system to illustrate

= ½=¾ ° ¿=¾

this mechanism is an atom with a Â transition. At a position with

½ ½

; i

polarization the population for the atom at rest is optically pumped to the j

¾ ¾

½ ½

j i

substate. At the same time this state experiences a larger negative light shift than ;

¾ ¾ due to the difference in the Clebsch-Gordan coefﬁcients and is therefore the lowest

energetically.

× ×

For low saturation (cf. eq. 2.25), the rate for optical pumping is of order Ô

and therefore can be arbitrarily small. If the atom is allowed to move out of the region before getting pumped, the internal energy of the atom increases at the cost of its kinetic energy, and the light shift of the other sublevel ﬁnally exceeds the shift of the occupied one. If optical pumping then occurs at such a point, the emitted photon is bluer than the absorbed one, and therefore energy is dissipated. In the next cycle, theatomthenrunsupthepotentialhillagain,thistimeintheothersubstate,gets pumped, and so on. Because of the analogy to the Greek myth this scheme is also called Sisyphus cooling. The ultimate limit of this cooling scheme is given by the recoil

Ú = ~k =Å Ä velocity Ê arising from the emission of the last photon .

5The recoil limit can be overcome with the methods of velocity-selective coherent population trapping (VSCPT) [29] and Raman cooling [30].

22 CHAPTER 2. BASIC ISSUES

¿ ¿

;

j i

;

i i

;

¾ ¾

;

i j

;

¾ ¾

......

Energy

;

lin lin lin lin

¿=8

¿=4

=¾

5=8

= ½=¾ ° ¿=¾ Figure 2.4: Illustration of the Sisyphus cooling scheme for a Â transition (the

numbers in the level scheme give the squares of the Clebsch-Gordan coefﬁcients).

Æ ! Ê

For the limit of large detuning Ä and low intensity , it can be shown

~k ´Æ = µ

[18] that the damping coefﬁcient is Ä and that the diffusion coefﬁcient

¾ ¾

D ´~k µ ! = Ä

is dominated by the dipole force ﬂuctuations, diÔ such that

k Ì = D = B

diÔ (2.50)

C jÆ j

Ä =8

where C from a more exact calculation [18].

· A second 1D conﬁguration is the “ ” molasses formed by two circularly polarized (both right-handed or left-handed) counterpropagating laser beams. In that case, the polarization gradient consists of a spatially rotating linear polarization, and there are no light shifts, such that Sisyphus cooling does not occur. However as the atom

moves along the beam direction, it sees a temporally rotating polarization vector. For

Â ½

g this induces an alignment of the substates that changes the radiation-pressure

balance such as to slow down the motion of the atom [18]. Here the friction coefﬁ-

´ =Æ µ ~k

cient is given by Ä which is much weaker than for Sisyphus cooling, but Ä this is in turn compensated by a weaker diffusion coefﬁcient that is exclusively due to

ﬂuctuations in the photon emission and absorption rates. From this, an equilibrium of

½¼

the form of eq. 2.50 results, with C .

For 3D molasses and 3D MOTs with uncontrolled relative phases the light

· ﬁeld from the interference of the 6 laser beams contains mainly and regions and the stronger Sisyphus mechanism dominates [144]. Close to the recoil limit the 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 23 atoms start getting localized in the light shift potential wells. When the light shift potentials are reduced below a critical value the channeling of atoms in the potential leads to a breakdown of friction, which is connected to an abrupt increase of temperature [153, 154]. The achievable minimum kinetic energies turn out to be one order of magnitude above the recoil limit, in agreement with experimental observations [155,156,157]. Polarization gradient cooling is very sensitive to the ground-state sublevel Zeeman shifts [143] which must not exceed the light shifts. Nevertheless, in 3D MOTs temperatures close to those for a molasses can be reached [158,27].

Optical dipole traps. Laser-cooled atoms can be stored in optical dipole traps (ODTs) formed by local extrema of a laser field [5,34]. Depending on the sign of the detuning of the laser light from the atomic resonance, atoms can be confined in maxima (red detuning) or minima (blue detuning) of the field intensity. Such traps allow for coherent storage of atoms since for a given potential the spontaneous scattering rate can

suppressed by increasing both the detuning and the intensity of the laser. ODTs are typically up to a few ½¼¼ K deep and allow for storage of up to several minutes [159]. In macroscopic (weakly confining) ODTs, the potential varies on a length scale that is large compared to the atomic de Broglie wavelength, and the atomic motion in those traps is classical. The simplest (macroscopic) ODT can be realized in the focus of a single red-detuned Gaussian laser beam, as was first shown in 1986 [32]. Tight confinement is provided in optical lattices [5] which are produced through the interference between laser beams. The interference gives rise to a periodic sinusoidal intensity modulation typically on the length scale of an optical wavelength. The confinement in the resulting periodic array of microscopic potential wells generally is comparable to the de Broglie wavelength of the trapped atoms, and the atomic motion is strongly quantized, giving rise to a band structure. In our experiments, we have trapped atoms in the optical potential of a red-detuned standing light wave formed by the reflection of a Gaussian laser beam. This trap is characterized by tight confinement in one dimension and weak confinement in the other two, and thereby forms a planar waveguide for atoms. A more detailed discussion can be found in chapter 5.

2.1.3 Reﬂection of Atoms from an Evanescent Wave

Evanescent waves. The simplest evanescent-wave atom mirror [38, 39] is realized

by total internal reﬂection of a blue-detuned laser beam at an interface of a bare glass "

prism (dielectric number ½ ). The evanescent wave gives rise to a repulsive optical

potential at which incident atoms can be reﬂected.

¼Ü¼Þ k k

Let the laser beam be incident in the plane with wave vector Ä at an

= aÖc×iÒ "

c ½

angle i beyond the critical angle (cf. ﬁg. 2.5). By applying Snell’s law,

E´Ö;Øµ = E eÜÔ[ik ¡

the propagation of the ﬁeld on the vacuum side of the interface, ¼ 24 CHAPTER 2. BASIC ISSUES

atom

" =½

Á ´Þ µ

" = " > ½

Figure 2.5: Evanescent-wave mirror realized by total internal reﬂection in a glass prism

i! Ø]

Ö , is characterized by wave vector components

¾ ¾

k = " ×iÒ ; k =¼ ; k = i " ×iÒ ½ ;

½ i Ý Þ ½ i

Ü (2.51)

where is the vacuum wavelength. This is an evanescent wave characterized by an

exponential decay into the vacuum and a running component parallel to the surface.

Ej Þ

The decay length of j in the direction is given by

½ ½

= =

: (2.52)

¾ jk j 4

" ×iÒ ½

½ i

½=e Û For a Gaussian beam with power È ,a -radius (waist) and lateral intensity

proﬁle

h i

¾d ¾È

Á ´dµ=Á eÜÔ Á = ; ¼

¼ with (2.53)

¾ ¾

Û Û =¼ that is reﬂected at the interface symmetrically about Ö , the intensity of the evanes-

cent wave above the surface is given by

h i

¾ ¾

¾Ü ¾Ý

Þ=

Á ´Öµ=Á ´Ü; Ý µ e Á ´Ü; Ý µ=FÁ eÜÔ :

eÚ ;¼ eÚ ;¼ ¼

eÚ with (2.54)

¾ ¾

´Û= cÓ× µ Û i

The proﬁle parallel to the surface is a Gaussian spot with waists Û perpendicular and

Û= cÓ× > Û F

i parallel to the plane of incidence of the beam. The factor (“intensity enhancement factor”) connects the surface intensity of the evanescent wave in the center of the Gaussian spot to the peak intensity of the incident laser beam. The ana-

lytical expression (which can be obtained from Fresnel’s formulae [160]) describes an

enhancement of the ﬁeld intensity that depends on i as well as on the polarization of the wave. Typical maximum values reached with BK7 glass at the critical angle are well below 10. Large intensity enhancement factors for the realization of evanescent-wave

2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 25

½¼ atom mirrors can be achieved by resonant amplification. The highest factors F have been demonstrated with dielectric layer systems on the prism [161]. Another possibility is the use of thin metallic films coated on the surface. Such films are used for the resonant excitation of surface plasmons (see below).

Optical potential of the evanescent wave. The dipole potential for the atom mirror

can be obtained directly from the discussion of the dipole force. In the far blue-detuned

Æ ! Ê

limit, Ä , and for a two-level atom initially in the ground state which evolves into

½i

the dressed state j , the dipole potential is given by

Á ´Ü; Ý µ

eÚ ;¼

Þ=

Í =· e :

EÏ Å;diÔ (2.55)

8Æ Á

Ä Ë

¾i For the state j it has the opposite sign, i.e. it corresponds to an attractive force .

Atom-surface interaction. Near a surface, the modiﬁcation of the vacuum ﬁeld distribution changes the radiative properties of a nearby atom. The general solution for this quantum-electrodynamical problem in the case of a conducting surface is given

in [162], and the special case of a two-level atom (transition wavelength )isad-

dressed in [163], including a discussion of important limits. For small atom-surface

=´4 µ distances, Þ , the interaction is determined by the electrostatic interaction of the ﬂuctuating atomic dipole with its instantaneous mirror image, giving rise to the

attractive van der Waals interaction

½ ½

¾ ¾

jg i] jg i ·¾hg jd Í = [hg jd

ÚdÏ (2.56)

4¯ ½6Þ

d d Þ for the ground state, where and are the components of the dipole moment parallel

and perpendicular to the surface. It can be shown that an equal shift results for the

=´4 µ excited state. For large distances, Þ , the interaction is given by a position- dependent Stark shift produced by the modiﬁed vacuum ﬁeld mode density near the

surface. This gives rise to the attractive Casimir-Polder interaction7

½ ¿~c

Í = « ; CÈ

¼ (2.57)

4¯ 8Þ

« = ¾jhejdjg ij =´¿~! µ

for the ground state, where ¼ is the static polarizability of the

atom. The shift of the excited state in that case is dominated by an oscillatory contribu- !½ tion (around zero) that also depends on the dipole orientation and vanishes for Þ , similar to the energy of a classical dipole antenna in its own reﬂected radiation ﬁeld.

6 Ú

For an ground-state atom incident with velocity iÒc , the repulsive potential holds for the reﬂection as

½i

long as the atom evolves adiabatically in the state j . This requires (1) the scattering time to be long ¾½

compared to the time spent in the evanescent ﬁeld, and (2) the absence of motion-induced, nonadiabatic

Ú = Æ transitions between the dressed states ( iÒc which is typically fulﬁlled for laser-cooled atoms). 7Casimir and Polder [164] originally interpreted this interaction as a retarded van der Waals interaction. 26 CHAPTER 2. BASIC ISSUES

For intermediate distances the van der Waals ground-state shift agrees with the general

¼:½¾ solution [162,163] to within a factor of 2 for Þ< , while the Casimir-Polder shift is the better approximation beyond that point.

The case of multilevel atoms can be treated by including the contributions from !

the different optical transitions with frequencies eg [162]. The variance of the

È È

¿ ¾ ¾ ¿

=! hg jd jg i = jhg jdjeij = ¿¯ ~c eg

dipole is then ¼ , where the last equal-

e e

ity is the Weisskopf-Wigner theorem [140]. The static polarizability is then given by

« = ¾ jhejdjg ij =´¿~! µ eg

¼ . e

Total potential. The total potential of the evanescent-wave atom mirror is determined both by the optical potential and the attractive atom-surface interaction as dis-

cussed in the next paragraph. Close to the surface it can be written as

Í = Í · Í

EÏ Å ÚdÏ E Ï Å ;diÔ (2.58)

to a good approximation8. As illustrated in ﬁgure 2.7, the short-ranged atom-surface

Í ´¼µ

interaction leads to a reduction of the maximum potential value EÏ Å;diÔ (for the

Í Þ ÑaÜ optical potential only) to ÑaÜ at a position , which must be determined numerically. This value deﬁnes the maximum kinetic energy an incident atom can have classically in order to be reﬂected.

] Í 8 E Ï Å ;diÔ

[ Í 6 ÑaÜ

ÑaÜ

2 Í ÚdÏ

potential 0.2 0.4 0.6 0.8 1

-2

] distance from surface [

Figure 2.6: Illustration of the total reﬂection potential of the evanescent-wave mirror for

½× ° ¾Ô 9 metastable argon used in our experiments for the parameters of the 5 (812 nm) transition (the sublevel structure is neglected) as the sum of the optical potential and the van

der Waals interaction in the electrostatic approximation. The evanescent ﬁeld is characterized

= ¿¿¿ F = ½½4 by nm and , and the (local) intensity in the excitation laser beam is 100 mW/cm¾ .

2.1.4 Generating Evanescent Waves with Surface Plasmons

Surface plasmons [165] are coherent charge ﬂuctuations propagating along the surface

" = " " = " = ½ ¿ of a metal ﬁlm, i.e. of the metal( ¾ )-dielectric( ) interface. They are

8The simple algebraic summation requires the potentials to be independent which is the case if the

relative level shift between the ground and excited state due to the atom-surface interaction is small

Æ ¾ ¢ ½ compared to the detuning of the evanescent wave. For metastable argon and detunings Ä GHz, this condition breaks down for distances below 50 nm [43] (where the total force is already attractive). 2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 27

accompanied by evanescent ﬁelds on both sides j of the interface. For surface plasmons

Ü Þ =¼

propagating along ¼ in the plane, it can be shown [165] that the ﬁelds have the

E´Ö;Øµ=´E ; ¼;E µ eÜÔ[ik ¡ Ö i! Ø]

Þ;j j

form Ü;j with

¾ ¾ " "

¾ ¿

j ½

k ; k =¼; k =´ ½µ : k =

Ü Ý Þ;j

Ü;j (2.59)

" · " " · "

¾ ¿ ¾ ¿

" = <" · i =" !

¾ ¾ The metal’s dielectric number ¾ for a given optical frequency in general

<" " k

¿ Þ;j has a large negative real part ¾ . As a consequence, both components perpendicular to the surface have a large imaginary part which leads to evanescent

decay both into the vacuum and into the metal. The vacuum intensity decay length as

=½=´¾=k µ " =½

¿ ¿

deﬁned above is given by Þ; , which by using simpliﬁes to

= = " ·½:

¾ (2.60)

=" > ¼

Because of damping in the metal, ¾ , the intensity of the surface plasmons also

´¾=k µ

decays in the propagation direction with a 1/e damping length Ü which is con-

nected to the resistive heating inside the metal.

×Ô E

Figure 2.7: Evanescent-wave mirror realized by the resonant excitation of surface plasmons

via attenuated total internal reﬂection (ATR) of a Ô polarized laser beam, also known as the Kretschmann conﬁguration [167].

The setup for the resonant optical excitation of surface plasmons on the surface of

a metallic ﬁlm on a glass prism is shown in ﬁgure 2.7. In this so-called Kretschmann

conﬁguration [167], a Ô polarized beam of frequency is incident at an angle "

larger than the critical angle in the glass ( ½ ) and generates an evanescent ﬁeld with

k ´ µ=¾= " ×iÒ "

½ ¾

Ü that penetrates into the ﬁlm ( ), thereby coupling to the surface

! k

plasmons. For a resonant excitation at a given , the wave vector Ü can be matched to

k ¿

the required value of the surface plasmon by adjusting the angle of incidence (as Þ; is

k ¾= " " >"

¿ ½ ¿

imaginary, Ü must exceed which explains why a dielectric is needed

for this kind of optical excitation). For the surface-plasmon resonance angle ×Ô and perfect matching of the ﬁlm thickness, all power is absorbed and dissipated in the ﬁlm10, in the form of heat and straylight [165].

9 ¾

" ´! µ= ½ ´! =! µ È

In the Drude model for the free electron gas, ¾ [166], where the plasma frequency !

È lies in the UV for metals. 10The surface-plasmon evanescent wave that penetrates back into the ﬁlm transforms into a traveling 28 CHAPTER 2. BASIC ISSUES

Surface plasmons - intensity enhancement. The ﬁeld intensity enhancement fac-

F ´ µ

tor i for the Kretschmann conﬁguration can be calculated by propagating a wave through the interface system and applying Fresnel’s formulae at each inter-

face [160,168]:

i = ½ i = ¾ i = ¿

For the regions i between the interfaces ( : glass, : metal, :vac-

·; E

uum/air) one can decompose the p-polarized electric ﬁeld E into components

i propagating in upward ( · ) and downward ( ) directions (assume that the ﬁlm has horizontal orientation). The ﬁeld amplitudes immediately below and immediately above

the metal ﬁlm then are related by

· ·

E E

½ ¿

= Ì ¡ ;

(2.61)

E E

½ ¿

Ì = Ì ´ µ

where the matrix i describes the transmission of the ﬁelds through the inter-

face system. Ì can be written as

Ì = Ì ¡ ¨ ¡ Ì ;

;¾µ ´d µ ´¾;¿µ

´½ (2.62)

Ì ¨

i;i·½µ ´d µ

where the matrices ´ describe the ﬁeld behavior at the interfaces and de-

¾ d

scribes the ﬁeld transmission through the metallic ﬁlm (thickness ¾ ),

ik d

¾ ¾

e ¼ ·

i i i i

: ; ¨ = Ì =

´d µ ´i;i·½µ

ik d

¾ ¾

¼ e ·

i i i i

= " ="

i i·½

In these expressions, the i relate the dielectric numbers on either side of

= k =k

Þ;i Þ;i·½

thesingleinterfaces,andsodothe i for the wave vector components

k = " " ×iÒ

i ½ i ?

perpendicular to the surface. These are given by i; .Now,since

¼ E ½

there is no interface above the surface, E . Setting , one obtains

¿ ¿

¬ ¬ ¬ ¬ ¬ ¬ ¬ ¬

¾ ¾

¬ ¬ ¬ ¬ ¬ ¬ ¬ ¬

½ E ½ E Ì

½¿

¿ ½

¬ ¬ ¬ ¬ ¬ ¬ ¬ ¬

F = Ê = :

Ô and (2.63)

· ·

¬ ¬ ¬ ¬ ¬ ¬ ¬ ¬

" Ì Ì

" E E

½ ½½ ½½

½ ½

= ×´Êµ h×i = ¼ Surface plasmons - straylight. Due to surface corrugations Þ , ,the non-radiative surface plasmons can decay into straylight by scattering at surface impurities. Often (as in our experiments) this is an unwanted effect that needs to be

minimized. In the following we concentrate on the case of a small rms surface rough-

= h× i = !=´¾cµ ness as compared to the optical wavelength . This case has been discussed by Henkel et al. [169] for the case of a dielectric evanescent-wave

mirror, however this also applies to the case of surface plasmons11. The scattered ´½µ

ﬁeld amplitude E is linearly related to the Fourier spectrum of the surface proﬁle,

iÉ¡Ê

Ê ×´Êµe ´Éµ=

Ë d ,by[169]

´½µ

¼ ½ ¼ ¼

E ´Ã µ=´¾ µ Ë ´Ã Ãµ f ´Ã µE ;

¾ (2.64) ¾ wave at the interface with the glass. This wave interferes destructively with the totally reﬂected wave from the excitation laser beam. For the optimum ﬁlm thickness, the interference is completely destructive. 11A more general description for surface plasmons can be found in Ref. [165].

2.2. EXPERIMENTAL APPARATUS 29

¼ ¼ ½

¾ ¼

f ´Ã µ=¾ ´i ´e !=cµ jÃ j ·´¾ µ µ

where ¼ is an electromagnetic scattering factor,

E Ã Ã

¾ denotes the evanescent ﬁeld amplitude at the surface and is the in-plane

Ã ´k ; ¼µ

wave-vector transfer between the the incident wave Ü and the scattered wave

¼ ¼ ¼ ¼

Ã =´k ;k µ jÃ jk ¡k < ¼ Ü

. For cases where the ﬁnal wave vector ¾ ,wethenhave

Ü Ý (see the previous section) which means that the surface plasmon has lost its evanescent character and has decayed into a straylight photon. For a description of the straylight intensity proﬁle above the surface, one has to take the ﬁnite spot size of the excitation laser beam into account. It can be shown that the

straylight intensity, averaged over the surface roughness spectrum, is the incoherent

sum over Gaussian laser beams (t Û ) propagating into the vacuum above the

prism,

¾ ¼

d Ã

¾ ¼ ¼ ¾ ¾ ¼

Á ´Öµ= µ Ë ´Ã Ãµ jf ´Ã µj E G´Ã ; Öµ; ´¾ (2.65)

sc ¾

´¾ µ

jÃ jk

¾ ¾

G´Ã; Öµ = eÜÔ[ ¾´Ê Þ Ã=k µ =Û ]

where Þ is the proﬁle of a Gaussian beam centered

Ü; Ý µ = ¼ Ã

around ´ that is scattered in the direction of . Under the assumption of

¼ ¼ ¾

´Ã Ãµ jf ´Ã µj

isotropic scattering, Ë const, integration yields [137]

¾ ¾

¾ Þ =Û

Þ e ¾

eff ¾

´Þ =Û µ Á ´¼; ¼;Þµ=Á ½ ½

sc ¾ E (2.66)

¾ Û

Á = jE j = FÁ cÓ×

¾ ¼

for points on the axis above the spot center, where ¾ is the spot

¾ ¾ ½=¾

=[´k =4 µË jf j ]

center intensity at the surface, is an effective rms roughness, ¾

Ê eff

´Üµ= Øe =Ø

and E ½ d is an exponential integral [170]. Ü The straylight intensity therefore is proportional to the square of the surface roughness. It approaches a constant value at the surface and decays on a scale given by the

laser spot radius Û .

2.2 Experimental Apparatus

2.2.1 Argon 4¼

Our experiments were carried out with Ar (natural isotopic abundance: 99.6 ±), a ½8

bosonic atom without nuclear spin and electronic hyperﬁne structure. The electronic

¾ 6 ¾ 6 ground state has the closed-shell conﬁguration 1s¾ 2s 2p 3s 3p , and the lowest elec-

tronic excitation possible requires more than 11 eV for an electron to be transferred

¿Ô Ò Ð

from to higher shells e . Due to its large distance from the core, the excited elec-

tron couples with the core only weakly. The coupling is described in the jÐ (or Racah) Ë

approximation [171]: the angular momentum Ä and spin of the core couple to a Ð

momentum j which couples with the angular momentum of the excited electron to × a momentum Ã which, ﬁnally, couples with the excited electron’s spin to the total

angular momentum Â. A complete description of the singly excited state is then given

¾×·½

Ä Ò Ð [Ã ]

e Â by the Racah notation j . A simpliﬁed spectroscopic description is given

30 CHAPTER 2. BASIC ISSUES

ÆÐ ´Â µ Æ Ö

by the Paschen notation Ö ,where labels the shell conﬁguration, and counts

the states in the conﬁguration with decreasing energy.

× 4Ô The level scheme of argon with the lowest-lying excitations (to the 4 and shells) using Paschen notation is shown in ﬁgure 2.8. The scheme is divided into a left and j = 1/2 j = 3/2

{

{ J= 2p1 0

2 1 5 3 2 34pp 4 1 5 0 6 2 7 1 { 8 2 9 3

10 1

715 nm 795 nm 812 nm

J= 1s 1 5 2 34ps 3 0 { 4 1 105 nm 5 2 3p6

1s1 J=0

6 5 5 4¼

Ô ¿Ô 4× ¿Ô 4Ô

Figure 2.8: Ar energy levels in the ¿ (ground state), and conﬁgurations [171] ½8

with transitions relevant for our experiments (Paschen notation).

=½= ¿=¾

right side according to the core momenta j 2and , corresponding to the singlet

½×

:::;5

and triplet sides for LS coupling, such as e.g. in helium. There are four states ¾ in

× Â

the 4 conﬁguration (the momentum number is omitted for simplicity) and ten states

¾Ô 4Ô ½×

;:::;½¼ ½ ½ in the conﬁguration. As an exception to the rule, the term is attributed to the ground state. The transitions between these two conﬁgurations are in the near

infrared. Intercombination transitions between the two sides that change the state j of

4× ½× ½× 5

the core are weak. In the conﬁguration the states ¿ and are metastable. The

·8

½× ¿8 ½× ¿

lifetime of 5 has been measured to be s[172]. For the state a value of 45 s

has been predicted [173].

½× ° ¾Ô 9

In our experiments, the closed 5 transition at 812 nm was used for laser

½×

cooling and atom reﬂection in the MOST. The weak intercombination line from 5 to

¾Ô ½× ¿

4 at 715 nm was used for optical pumping to the state , with a pumping efﬁciency

56± 4¾± ¾Ô ½× ¾ of (with probability, the state 4 decays to the state , which subsequently

decays to the ground state under emission of a 105 nm UV photon with a lifetime of 2

¾Ô ½× ¾± ½× ° ¾Ô

5 ¿ 4 ns. The decay of 4 back to contributes with probability). The open

transition at 795 nm was used for far-off resonance optical trapping and manipulation

½×

of ¿ atoms in the waveguide. Properties of these transitions are listed in table 2.1.

2.2. EXPERIMENTAL APPARATUS 31

½× ´Â =¾µ° ¾Ô ´Â =¿µ

9 ¼

5 = 811.757 nm [174]

½ 6

´¦8±µ ¿¿:½ ¢ ½¼ (MOST) A = s [174]

= (closed transition)

Á ½:¾9

Ë = mW/cm

Ì ½¾7

D = K Ú

D =17cm/s Ì

Ê = 361 nK Ú

Ê =1.2cm/s

¾ 57

h½× jd j½× i ¾:¼ ¢ ½¼ 5

5 = (Cm) [174]

¿¼

« 4¯ ¢ ´44:7 ¦ ¼:9µ ¢ ½¼ ¼

¼ = m[175]

½× ´Â =¾µ° ¾Ô ´Â =½µ

4 ¼

5 = 714.903 nm [174]

6 ½

¼:6¾5 ¢ ½¼ ´¦8±µ

(optical pumping) A = s [174]

Á ¼:¼¿6

Ë = mW/cm

½× ´Â =½µ° ¾Ô ´Â =½µ

4 ¼

¾ = 852.381 nm [174]

6 ½

½¿:9 ¢ ½¼ ´¦8±µ

A = s [174]

½× ´Â =½µ° ¾Ô ´Â =½µ

4 ¼

4 = 747.322 nm [174]

½ 6

´¦8±µ ¼:¼¾¾ ¢ ½¼

A = s [174]

½× ´Â =¼µ° ¾Ô ´Â =½µ

4 ¼

¿ = 795.036 nm [174]

6 ½

A ½8:6 ¢ ½¼ ¦8±µ

(waveguide) = s ´ [174]

Á ¼:77

Ë = mW/cm

¿¼

« 4¯ ¢ ´49:5 ¦ ½:¼µ ¢ ½¼ ¼

¼ = m[175]

4¼

Table 2.1: Properties of optical transitions in Ar for experiments in laser cooling: ¼ =

½8

A Á

vacuum wavelength; =EinsteinAcoefﬁcient; = linewidth, Ë =(effective) saturation

Ì Ú Ì Ú

D Ê Ê

intensity; D = Doppler temperature; = Doppler velocity; = recoil temperature; = «

recoil velocity; ¼ = static polarizability.

½× ½× 5

In trapped atomic ensembles, the metastability of the ¿ and states gives rise

9 ¿

to strong collisional losses that limit achievable densities to around ½¼ cm . The

£ £ ·

· ! · e

losses are dominated by Penning processes Ar Ar Ar · Ar and associative

£ £

! · e

ionizations Ar · Ar Ar . With an argon MOT, one generally is well in the ¾

temperature-limited regime. For our standard MOT parameters12, the value for the

¬ ½× ° ¾Ô ¼

two-body loss constant for collisions between atoms trapped on the 5 tran-

8 ¿ ½

½ ¢ ½¼ ¬

sition is ¬ cm s . The values for in the case of collisions between atoms

½× ° ¾Ô 4 that are optically trapped on the ¿ transition appear to be of the same order of

magnitude [110]. The same holds for ”two-species” collisions between atoms trapped

½× ° ¾Ô ½× ° ¾Ô

9 ¿ 9 on the 5 and transitions (cf. chapter 5).

12The collisional loss rate generally depends on the laser beamparameters because of the inﬂuence of

¿ ½ 8

=´½:4 ¦ ¼:¾µ ¢ ½¼

light-induced molecular interaction potentials [6]. We determined ¬ cm s [177]in

Æ = 8

measurements on a 6-beam MOT with detuning Ä MHz, single-beam intensity = 22 mW cm and

½ =5 magnetic ﬁeld gradient b Gcm . This value agrees with results obtained in previous measurements [178].

32 CHAPTER 2. BASIC ISSUES

Ñ =

Ñ = Â -1 0 Â -1 0 1 1

J=1 J=1

¾ ½ 1 (795 nm) 1 ½ 1 (715 nm)

1 ¿

1 ¾

½ ¾

J=0 ¾ J=2

Ñ =

Ñ = Â -1 0 2

Â 0 -2 1 = Ñ 0 3 Â -3 -2 -1 1 2

J=3

¿ 8 ½

1 8 1 (812 nm)

5 ½5

¿ ½5

½ ½

5 5 ½5

½5 J=2 = Ñ 0

Â -2 -1 1 2

= ¼ ° Â = ½ Â = ¾ ° Â = ½ Â = ¾ °

Figure 2.9: Kastler diagram for the Â , and =¿ Â transitions used in the experiments, containing the the squares of the Clebsch-Gordan coefﬁcients [176].

2.2.2 Beam Machine and Laser System

Beam machine. The experiments were performed in the atomic beam machine ½

showninﬁgure2.10. A beam of metastable s 5 argon atoms is generated in a DC discharge source [179] cooled with liquid nitrogen. The beam is collimated in a 2D

optical molasses at 812 nm with multiple beam recycling [180] and is decelerated with

a counterpropagating laser beam at 812 nm in a Zeeman slower [181]. The

¢ ½¼

pressure difference between the source chamber (¾ mbar) and the main UHV

¢ ½¼

chamber (5 mbar) is maintained by differential pumping.

½4

¾ ¢ ½¼ ½

The atom source emits s 5 atoms/(s sr) corresponding to an excitation

efﬁciency of ½¼ . The velocity distribution of the cooled source is characterized by

Ú i =¿¼¼ hÚ i=¡Ú =¾:5

h m/s and . The Zeeman slower transforms this distribution into 7¼±

aslow1s5 beam in which of the atoms have a velocity below 30 m/s. The 2D transverse laser cooling stage is realized in a separate chamber behind the source [182,183]

and typically yields a 20-fold enhancement of the beam intensity, resulting in loading 7 rates in the main chamber of around ½¼ atoms/s for a standard [184] argon MOT. The atom beam can be shuttered electro-mechanically behind the collimation stage. The large main chamber (inner diameter 45 cm, height 28 cm) houses the experimental setup, several pressure gauges and a mass spectrometer. The atomic beam machine is described in detail in [178] where also a characterization of the Zeeman-slowed atomic beam can be found. 2.2. EXPERIMENTAL APPARATUS 33

atomic beam main chamber source beam atom detector collimation Zeeman slower

prism

turbomolecular pumps

LN¾ bafﬂe

oil diffusion pumps

0 0.5 m 1m

Figure 2.10: Schematic of the beam machine.

Laser system. The laser system used in our experiments is depicted in ﬁgure 2.12. Laser beams were needed for a variety of purposes including transverse atomic beam

collimation (ABC), atomic beam slowing (ABS), magneto-optical trapping (MOT), re- ¿ flection from the surface (EWM), internal transfer from 1s5 to 1s via optical pumping (OP), trapping in the waveguide (WG) and local detection (WGD). The laser setup is located on a laser table in a separate temperature-stabilized room, and single-mode fibers are used to guide the light to the beam machine. For the 812 nm transition we modified the setup used in previous experiments [184,182,185] by turning the ABC laser into a master laser for injection-locking [186] the three slave lasers ABS, MOT and EWM which are frequency detuned by means of acousto-optic modulators (AOMs)13. The ABC laser (output power: 13 mW, detun-

ing +9 MHz) is a commercial external-grating cavity diode laser (TUI DL-100 with a

° 9 Sharp LTO16MFO diode) that is stabilized to the 1s5 1p transition via Doppler-free saturation spectroscopy (cf. [187]) in a RF argon discharge cell. The injection-locked slave lasers are single-mode high-power laser diodes (SDL 5422-H1) operated at a power of about 100 mW each [184, 188]. The seeding of the ABS and MOT diodes is done with part of the ABC light at a detuning of -161 MHz. The beam emitted from the MOT diode, before entering the ﬁber, is shifted close to resonance with an AOM whose frequency and power can be controlled externally via PC [184]. We have set up an additional feedback-loop stabilization for the MOT beam power. This is achieved by

referencing the MOT beam to a photodiode behind the ﬁber and regulates to better that ½± within 10 s. The ABS beam enters the ﬁber without an additional frequency shift.

A part of this beam, after being shifted to +687 MHz in a quadruple pass through an 9¼± AOM (single-pass efﬁciency > ), is used as an injection beam for the EWM diode.

The OP laser for the 7½5 nm transition is a cryogenic external grating cavity diode

13Previously a separate master laser had been used, however its frequency stability was too poor for the stringent requirements in the experiments with the MOST. 34 CHAPTER 2. BASIC ISSUES

source beam Main chamber chamber collimation Zeeman slower

1m Optics setup

turbomolecular pumps LN2 baffle

oil diffusion pumps

Figure 2.11: View into the beam machine lab. laser [184,185] that is stabilized to the transition by means of optical double-resonance spectroscopy (cf. [187]), for which a part of the frequency-modulated spectroscopy beam from the ABC laser is used. The diode setup is located in a liquid nitrogen cryostat which is used to lower the emission wavelength of the laser diode (Sharp LTO30MDO) from 750 nm at room temperature down to 715 nm. This laser is operated at 1.5 mW. Due to the boiling of liquid nitrogen in the cryostat the laser has a mechanical frequency jitter of about 20 MHz [184]. The WG and WGD beams for the 795 nm transition are generated with a single- mode Ti:Sapphire ring laser (Coherent 899-21) that is pumped by an argon ion laser (Coherent Innova 400). The Ti:Sapphire laser is locked to an external cavity and has an experimentally measured drift around 20 MHz per minute. The WG and WGD beams behind the fiber are limited to about 300 mW each by stimulated Brillouin scattering [189] in the monomode fiber. This can be exploited for a passive stabilization of the beam power. The WGD beam is fed into the same fiber as the EWM beam with an orthogonal linear polarization, and behind the fiber the beams are separated again with a polarizing beam splitter cube. The available beam powers for the ABC, ABS, MOT and

OP beams after the ﬁber outputs are 3 mW,12 mW,8 mW and 100 W,respectively. The MOT laser beam power is switched by controlling the corresponding AOM power, and the other laser beams are switched with commercial electro-mechanical shutters behind

the ﬁber within 100s after a delay of about 2 ms. The experimental reproducibility is 2.2. EXPERIMENTAL APPARATUS 35

71 + mod.

-1

Faraday isolator

opt. diode /

Foto diode

current divider

spectrum analyzer

Fabry-Perot

ABC

diagnostic beam

main beam

seed beam / spectroscopy beam

AOM freq. (MHz)

diffraction order

spectroscopy cell

fiber coupler

RF dischar

MOT

Lambda meter

60...100

cryogenic

cavity diode laser

EGC diode laser

laser diode

external grating

ArI laser

796 nm (waveguide)

796 nm (WG deformation/detection)

715 nm (optical pumping)

WGD

EWM

quarter wave plate

pol. beam splitter cube

half wave plate

beam splitter

anamorphic prism pair

: evanescent-wave mirror)

: MOT beams)

Ti:Sapphire ring laser

ABS

812 nm (atomic beam collimation)

812 nm (MOST

812 nm (atomic beam slowing)

812 nm (MOST

212

-1

mirror

cyl. lens

flip mirror

mirror lift

spherical lens

ABC

MOT

EWM

ABS

Figure 2.12: The laser system for experiments with metastable argon. 36 CHAPTER 2. BASIC ISSUES

in the range of a few s.

Data acquisition. The experiments using the beam machine are typically performed by sequentially stepping the shutters for the atomic beam, the laser beams, the magnetic ﬁeld and the power and detuning values of the MOT beams, as well as setting triggers for data acquisition devices. Depending on the signal-to-noise ratio, individual sequence runs were typically repeated from 10 to up to 10000 times. For this purpose our sequence PC runs the control software ISAMES [184] that allows the user to de-

ﬁne sequences with minimum step durations of 35 s. To make the sequence control more ﬂexible, we use additional self-built digital delays in the output lines, e.g. for the compensation of individual differences between the shutter delays. The control PC is connected via trigger lines to two auxiliary PCs that control the CCD camera and the

atom detector. The CCD camera (Sony CV-M10BX with a Inspecta-2S frame grabber

¢ 58½ card from Microtron GmbH) has a 1/2“ chip with a spatial resolution of 7¿6 pixels and a dynamical resolution of 8 bit. The camera is asynchronously triggerable, and the control software [177] can be used to sum up images or to immediately save them to hard disk. The atom detector consists of an electron optics that allows to image atomic arrivals on the surface onto a multichannel plate detector. The setup and the properties of the atom detector are described in the next chapter.

2.2.3 The Surface An important part of the experimental apparatus is a gold-coated prism surface located in the main chamber. It was used as a mirror for the MOT beams of the magneto-optical surface trap (cf. chapter 4), as a negatively biased conversion electrode for the atom detector (as described below), and for the generation of the surface-plasmon enhanced evanescent ﬁelds for the MOST’s evanescent-wave atom mirror (EWM) and for optical pumping (OP) and local detection (WGD) in the waveguide experiments (cf. chapter 5).

2.0 cm

Figure 2.13: The gold-coated prism surface. The prism is mounted to the surface atom detector (cf. chapter 3)withaluminarods.

Preparation. The mirror surface was prepared by thermal evaporation of a gold ﬁlm

¢ ¾:8 onto the ¾ cm cm hypotenuse face of a clean, right-angle isosceles BK7 glass 2.2. EXPERIMENTAL APPARATUS 37 prism (Melles Griot 01PRB019). Gold as a coating material combines favorable optical properties in the IR with high thermal and chemical stability14, and smooth surfaces canbegrown.Toimprovetheadhesionofthegoldﬁlmontheprism,wecovered the prism face with a few monolayers of chromium before depositing the gold ﬁlm.

The depositions were performed at room temperature and a background pressure of

3 ¢10 mbar prior to deposition in a commercial vapor deposition machine (Univex- 450). The deposition rate for the gold ﬁlm was held at about 2 nm/s and and a ﬁlm with a thickness of around 45 nm (as measured with an oscillating crystal probe) was produced to optimize the surface-plasmon resonance at 812 nm for the evanescent-

waveatommirror.

´bµ ´aµ 7 R(t) 6

photo diode [a.u.] Í 5 Ê 4 3

´Í µ i

1 Í P-pol. 0

reﬂected intensity 41 41.5 42 42.5 43 43.5 44

[ ]

galvanometer angle of incidence i

Figure 2.14: Characterization of the surface plasmon resonance. (a) – Setup to measure the reﬂected intensity as a function of the angle of incidence. (b) – Experimental ATR curve for 812 nm, together with the curve ﬁt from the transfer matrix model.

Optical properties. The dielectric numbers of the gold ﬁlm and the properties of the evanescent ﬁelds above the surface were determined by recording surface plasmon

resonance curves. For this purpose we built a setup with which the reﬂected intensity

could be recorded as a function of the angle of incidence i of a collimated beam (cf. figure 2.14 (a) ). The measurement for an incident 812 nm beam in the BK7 glass prism is shown in figure 2.14 (b), together with a fit of eq. 2.63 to the data. The results for the dielectric numbers of the gold film and the parameters of the evanescent fields at 812 nm (EWM), 796 nm (WGD) and 715 nm (OP) are listed in table 2.2. The straylight intensity distribution above the gold film resulting from the radiative

decay of the surface plasmons was measured, for the excitation with a 812 nm laser

= ¼:67 beam of waist Û mm, by scanning a photodiode over the surface at different heights. Experimental results are shown in ﬁgure 2.2.3 together with theory curves

14In previous experiments we had also tried silver coatings which, despite their superior optical properties, were subject to rapid thermal degradation at high laser powers and yielded much rougher surfaces. For those coatings, the ratio of evanescent-ﬁeld to straylight intensities was more than an order of magnitude worse than for the present case.

38 CHAPTER 2. BASIC ISSUES

[ ] " [ ] [ ] F ¾ ¼ nm SP nm 812 -29.6 + i 0.99 42.4 333 114 796 -27.9 + i 0.90 42.6 316 111 715 -25.5 + i 2.96 42.7 277 32

Table 2.2: Dielectric numbers of the gold film and resonance angle SP,fieldintensitydecay F length , field intensity enhancement factor of the evanescent fields obtained from the fit of

the model eq. 2.63 to the measured ATR curves. The ﬁts consistently yield a ﬁlm thickness of

¦ ½ 4½ nm.

0.7 1 z= 7.0 mm 0.6 PD 0.5 0 1 0.4 z= 4.0 mm 0.3 w = 0.67 mm 0 0.2

(0, ) / [%] (1 ) [norm.] z= 1.0 mm

sc 0

IzI 0.1

I x,z 0 0 0123456 -10 -5 0 5 10 Heightz [mm] Lateral positionx [mm]

Figure 2.15: Characterization of the straylight distribution above the surface resulting from surface-plasmon decay. A photodiode was scanned over the surface in the lateral and normal directions. (a) – Straylight intensity above the spot center (relative to the intensity of the

incident beam) vs. distance from the surface. The data points correspond to a measurement

¢ ¾ ´ µ cÓ×´ µ with a photodiode with an area of ¾ mm and a directional characteristics .The

dotted line is a ﬁt of eq. 2.65 averaged numerically over the these quantities; the solid line gives

´¼;Þµ the corresponding on-axis intensity Ásc (eq. 2.66). (b) – Normalized results of lateral

scans (along the surface plasmon propagation direction) at different heights Þ ,togetherwith

´Ü; Þ µ normalized theory curves Ásc . The measurement shows that the scattering is isotropic. of the model, eq. 2.66. The lateral scans at different heights show that the straylight

distribution is indeed isotropic, which justiﬁes the assumption made in the theory. From

´¼µ =

a ﬁt of the theory to the data, we deduce a maximum straylight intensity Ásc

´7 ¦ ½µ ¢ ½¼ Á = ´6:¼ ¦

¼ , corresponding to an effective surface roughness of eff

:¿µ ¼ nm. For a comparison we characterized the surface with a scanning atomic force

microscope. From these measurements we deduce a rms roughness of about 1 nm

¢ ½6 on the sampling area of ½6 m , from which one would expect a much smaller straylight intensity. It therefore is likely that the main part of the scattering is due to the presence of gold clusters and/or dust on the surface that were not statistically accessible in the measurement. The reﬂectivity of the gold ﬁlm for laser beams at 812 nm and 795 nm was deter-

mined, by direct measurement, to be about 96±. Chapter 3

Surface-Assisted Detection of Ar £

We have studied an experimental scheme for the detection of argon atoms in the

½× ½× ¿ metastable 5 and states at a gold-coated surface. Based on this scheme we have demonstrated a method for 3D time-of-ﬂight spectroscopy of laser-cooled metastable atoms.

3.1 Introduction

For our experiments with metastable argon close to a prism surface, an efﬁcient detection scheme can be realized by letting the atoms collide with the gold-coated surface. Upon impact, the metastable states decay to the electronic ground state, and single electrons are ejected out of the metal which carry information about the time and lateral position of the single-atom impact events. These electrons are imaged onto a detection element with temporal and spatial resolution using an electrostatic lens system. Our detector was originally designed by M. Hartl [185] after that described in Ref. [190] and has already been used in earlier experiments [110,111]. For the present work, which placed greater demands on the detector, it was modiﬁed to improve its performance, and subsequently characterized and calibrated using atom-optical methods. These measurements are described in the following subsections, after a brief summary

of the principles and technical realization of the detector. As a physical “byproduct” we

½×

have also determined the hitherto unknown electron yield for the ¿ state of argon at a gold surface (cf. Ref. [191]).

3.2 Experimental Scheme

Overview. The surface atom detector is shown in ﬁg. 3.1. The electron optics of the detector consist of a column of hollow electrodes set to different voltages. The surface, a 40 nm thick gold ﬁlm deposited onto a glass prism, is held at negative voltage and acts as a conversion electrode from which the ejected electrons are accelerated upward to the grounded entrance electrode. The open aperture of the electrode forms a divergent

39 40 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £

(a) (b) PreA +3kV PosA RAE MCPs detection unit e-

HBM

4 D Trig

Ð tube lens

¿ Í

¾ tube lens Ä

¾ hole lens d

Ä Ar*

½ conversion Í ½ electrode

Figure 3.1: The surface atom detector. (a) – The electron optics. The cylindrical electrodes are made of polished stainless steel and are mounted to alumina rods. The unit also includes coils and mirrors used for the realization of the magneto-optical surface trap and the waveguide. (b)

– The components of the detector. The gold-coated prism surface acts as a conversion electrode

Í = 4:56

( ½ kV) for incident metastable argon atoms. The electrons are accelerated towards

d =¿ Ä = ½5:6

the hole lens in the grounded entrance electrode ( mm, ½ mm), and two tube

Í = ¾:76 Ð =¼:8 D =½¼ Ä =½5:8 Ä =¾¼:8

¾ ¿

lenses ( ¾ kV, mm, mm, mm, mm) are then used

Ä =¿½5 to image the electron emission pattern onto a detection unit ( 4 mm). This unit consists of a stack of two multichannel plates (MCPs) with a resistive area element (RAE). After pre- ampliﬁcation (PreA) the signal of the RAE is digitized in a position analyzer (PosA) and stored in a histogramming buffer memory (HBM). The data acquisition and readout of the HBM is controlled with a PC. 3.2. EXPERIMENTAL SCHEME 41

e- e- e- F F EF E+ E* metal metal metal

M* M* adsorbate M* (a) (b) (c)

Figure 3.2: Deexcitation mechanisms for metastable atoms M* at a metallic surface: (a) Reso- nance ionization followed by Auger neutralization, (b) Auger deexcitation, (c) Penning ionization of adsorbates. hole lens [192] behind which two convergent tube lenses [192] are used to image the electrons onto a multichannel plate (MCP). In our earlier experiments, one of the main shortcomings of the electron optics was severe image distortion due to inhomogeneities in the acceleration field (cf. Ref. [111]). In the present work, this effect was reduced substantially by using a prism with a linear surface extension much larger than the 3 mm aperture of the hole lens and by reducing the distance between the prism and the hole lens. The detection unit consists of a stack of two multichannel plates(MCPs) in a chevron configuration and a resistive area element (RAE). Each incident electron produces a localized charge avalanche which is deposited onto the RAE. This generates currents at the four contacted corners of the RAE, encoding the position of the electron. The processing of the signal is done with a commercial system (2502A Position Analyzer and 3300/2500 Series Imaging Detector System, Quantar Technology, Inc. (Santa Cruz, California)). The imaging detector system consists of a pre-amplifier (PreA), a position analyzer (PosA) where the analog signal is digitized, and a histogramming buffer memory (HBM) for data storage. The HBM is controlled and read out by PC, and the HBM data are subsequently processed with a self-written MATHEMATICA package that contains the results of the experimental calibration.

Atom-to-electron conversion. The most fundamental aspect of the detection scheme is the conversion of metastable atoms into electrons at the surface. In general, two main deexcitation mechanisms for metastable atoms at an atomically clean metallic surface

can be distinguished [193,191]. For large work functions ¨ the atom (internal energy £

E ) can undergo resonant ionization, followed by Auger neutralization if the recombi-

¾¨ nation energy E , as shown in ﬁgure 3.2 a. Without an empty resonant state in

the metal, e.g. when ¨ is too small, the excited electron can still be ejected by Auger deexcitation, cf. ﬁgure 3.2 b. For adsorbate-covered surfaces, Auger deexcitation with adsorbed molecules (i.e. Penning ionization of the adsorbate) can become dominant,

cf. ﬁgure 3.2 c. ± A crucial parameter is the electron yield ± of an atom at the surface, where is 42 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £ deﬁned as the average number of electrons emitted per metastable atom. A survey of

different metastables and metals is given in Ref. [191]. From our experiments with a

¨= 5:½ ± = ± > ¼:½4

gold ﬁlm ( eV), a stable and constant value ¼ for both metastable

£ £

½× E =½½:5 ½× E =½½:¾ ¿ 5 ( eV) and ( eV) states can be deduced, as will be explained

further below.. On the time scale accessible with the detection unit the electron emis-

½¿

sion process can be considered instantaneous (typical time scales are ½¼ s[194]).

=´E ¨µ 7 The maximum kinetic energy of the electrons is given by " eV.

Imaging with the electron optics. The components of the electron optics are dis- cussedindetailinRefs.[190,185]; therefore only some very relevant aspects are summarized here.

Electrons ejected at a point È on the surface at varying angles follow classical, parabolic trajectories in the homogeneous acceleration ﬁeld. In the plane of the hole

lens in the entrance electrode, the bundle of trajectories lies within a circle of diameter

Æ = 4Ä "=´eÍ µ ¾:4 ½

½ mm (using the parameters of ﬁg. 3.1). Due to the ﬁnite

= ¿ È

aperture d mm of the hole lens, trajectory bundles originating from points at

:6 more than ¼ mm distance from the optical axis get truncated, giving rise to a position

dependence of the local detection efﬁciency. A second consequence of the spreading is

¡Ü Ä "=´eÍ µ ¾4 ½

a blurring of points in the image plane of ½ m[195]. However, this blurring is a negligible contribution compared to the resolution of ½¼¼ m imposed by the detection unit.

The hole lens in the entrance electrode acts as a thin divergent lens with focal

f 4Ä

length ½ [192]. Together with the parabolic spreading of the trajectories it

È È Ä =¿

acts to displace the origin downward to a virtual origin at a distance ½ below

the surface. The tube lenses between the adjacent electrodes can be described by ABCD

= Ì´ µ ray transfer matrices Ì with focal lengths and principal plane positions that

depend on the ratio of the potentials of the adjacent electrodes between which the

tube lenses are realized (cf. Ref. [190]). Using standard light-ray ABCD matrices [196]

À È Ä Ä Ä Ä

½ ¾ ¿ 4 for the hole lens and i for free propagation (distances 4/3 , , , ), the

electron optics is described by

Å = È Ì´ µ È Ì´ µ È ÀÈ ;

¿ Ö ¾ ½

4 (3.1)

= Í =´Í Í µ Å Ö

½ ½ ¾ i

where Ö . The matrix relates input rays with axis distance and

¼ ¼ Ø ¼ Ø ¼

Ö Ö Ö ´Ö ;Ö µ = Å ´Ö ;Ö µ

Ó i

slope to output rays Ó , according to . Focusing is reached

Ó Ó

i i

Í Í Å = ¼

¾ ½¾

for a given voltage ½ by adjusting such that . The linear magniﬁcation

Å = Å Í = 4:56 ½

is then given by ½½ .For kV a numerical calculation using the

Ì Í = ¾:85

expressions of Ref. [190] for the matrix yields a focusing voltage of ¾ kV

=¿:4 and a magniﬁcation of Å . This is comparable to our experimentally determined values as described below.

Detection and data acquisition. Both the PosA and HBM units impose limitations which are important for the performance of the detector. In the setup, we used HOT1

1HOT = “high-output technology” 3.3. CHARACTERIZATION OF THE DETECTOR 43

MCPs (Burle Electro Optics, Inc.) with an active diameter of 25 mm. These MCPs

are characterized by a small recharging time [197] and allow for count rates around

6 ½

½¼ s on the area of a single electronic bin of the RAE. However, the maximum allowable overall count rate for error-free analog-to-digital conversion is one order of

2 ¢

magnitude lower due to the contribution of statistical coincidences .Atarateof½

5 ½ 6 ½

½¼ ½:5 ¢ ½¼ s for incident electrons, the counting error is less than 5±;yetat s the overall count rate is already suppressed by a factor of 2. In our experiments involving the magneto-optical surface trap, care had to be taken to keep the count rate low

enough to avoid such errors.

The spatial resolution of the MCP/RAE unit is speciﬁed to ¾5¼ m, which corre-

½¼¼ sponds to a resolution of m on the surface. The 20-bit HBM unit is conﬁgured as to store the incoming data in a temporal sequence of 64 images with 128 pixels x 128 pixels spatial resolution each. The time interval between the single images is freely deﬁnable, and the start of the entire sequence can be triggered. Splitting a single run into two 32-image sub-sequences for a main run and a reference run is possible, as

well as a summation over multiple experimental runs. The HBM’s temporal resolution is limited to a minimum exposure of ¾¼ s per recorded image.

3.3 Characterization of the Detector

For the characterization of the detector, we performed in-situ experiments with atoms from a magneto-optical trap realized above the surface, combined with an evanescent- wave atom mirror (A discussion of these components can be found in chapters 2 and 4).

3.3.1 Focusing, Length Calibration and Spatial Resolution In order to determine the focusing voltage and to characterize the spatial imaging properties of the electron optics, a test object (i.e. a well-deﬁned electron emission pattern) needed to be created. This experimentally challenging problem was solved

by using an evanescent-wave surface-plasmon atom mirror at 812 nm with spatially

½×

modulated reﬂectivity that was illuminated with 5 atoms released from a MOT. At the positions of high intensity, atoms did not collide with the surface and no electrons were ejected. In this way, the electron emission pattern could be obtained as the “negative” of the optical intensity distribution of the atom mirror. The structured mirror was realized by diffracting the EWM beam at an absorption grating and then imaging the diffraction pattern onto the gold ﬁlm using a cylindrical

lens, as shown in ﬁgure 3.3. Absorption gratings were realized with the help of a

=¼:6 ::: ¿:¼

laser printer on transparent foils, with periods Ô mm mm and slit widths

= Ô=¾

a . The corresponding imaged diffraction patterns then had fringe separations of

¾¼¼ 1.0 mm::: m. As a result of the ﬁnite diameter of the EWM beam, only a small

2Single charge pulses must be separated by at least 300 ns, otherwise one pulse or even both pulses (for separations below 100 ns) are discarded [198]. 44 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £

100. (a) (b) 1.5 MOT absorption 0.75 75. grating

D cyl. 750 mm 0 50.

E y -0.75 25.

EWM -1.5 0. -1.5 -0.75 0 0.75 1.5 w~1cm x @ mm D DCts. @ % D

Figure 3.3: (a) – Experimental setup for creating a test object for the atom detector. A blue- detuned laser beam (waist 1 cm) is diffracted from an absorption grating and used to form

an evanescent-wave atom mirror (EWM) with spatially modulated intensity. The diffraction = 75¼ pattern is imaged onto the prism with a cylindrical lens ( f mm) at the surface-plasmon resonance angle. When the surface is “illuminated” with atoms released from a MOT, the intensity fringes lead to a local reﬂection of atoms and thus to a suppression of the electron

emission. (b) – Measured distribution for a 1.5 mm-period grating, resulting in a stripe separation of 4¼¼ m (the length scale of the image has been calibrated accordingly). The counts in the displayed field of view represent the relative change in the distribution compared to the case for which the mirror beam is blocked. 3.3. CHARACTERIZATION OF THE DETECTOR 45 number of slits were illuminated, and typically only the 0th and 1st order fringes had enough intensity to reflect atoms (which was sufficient for our purpose, however). As

a criterion for focusing, the visibility of the stripe patterns was measured for different

Í Í Í = 4:56 Í =

¾ ½ ¾ voltages ½ and . The best values were obtained for kV and

¿± ¾:76 kV. The ratio of these values deviates by only from the calculation .An example for a measured pattern is shown in ﬁg. 3.3 (b).

From the test-object measurements, the length scale of the detector was determined

¦ ½µ to be ´½4 pixels/mm. Since in the image plane 128 pixels correspond to the 25

mm active diameter of the MCP, this yields a magniﬁcation of the electron optics of

=¾:7 ¦ ¼:¾

Å . If one calculates the magniﬁcation for the chosen set of voltages, one

=¿:¼ obtains a similar value of Å .

The smallest diffraction pattern that could be realized experimentally had a 200 m period, a value only slightly above the effective, full reﬂective width of the evanescent intensity fringes4. This pattern could still be resolved in the center of the ﬁeld of view;

however its visibility reduced by 5¼± when shifted to the outer regions, indicating inhomogeneous focusing. Another distortion is apparent in the slight curvature of the stripes, in contrast to the optical intensity distribution. Such effects, which were also observed in Ref. [190], are probably due to residual inhomogeneities in the electric

acceleration field or insufficiently compensated magnetic fields.

½× ½× ¿ 3.3.2 Detection Efﬁciencies for the 5 and States

Spatial profile. As discussed above, the local detection efficiency of the detector is expected to vary with the distance from the optical axis due to the truncation of the electron trajectory bundles. In addition, there can be a contribution from the MCP itself, e.g. due to contamination by dust particles. We determined the detection efficiency profile of the focused detector by comparing a known physical arrival distribution with the corresponding recorded electron emission pattern. For this purpose, a MOT located on the symmetry axis of the electron optics with a temperatures of about

200 K parallel to the surface was prepared, and the ballistically expanded Gaussian

arrival distribution was recorded 30 ms after release at which time the Gaussian was 4

5.5 mm. The efficiency profile was deduced from ½¼ experimental runs by comparing the calculated and measured arrival distributions and is shown in fig. 3.4. The profile deviates from cylindrical symmetry, probably as a result of residual inhomogeneities in the electric acceleration field or insufficiently compensated magnetic fields inside the main chamber. Also, variations in the electron yield of the MCP cannot be excluded (a similar profile behavior was observed in Ref. [190]). This profile was used as a

3In order to minimize the spreading of the trajectories between the surface and the hole lens, one

jÍ j jÍ j ¾

would like to choose ½ as large as possible, which also requires larger values for . However, for

jÍ j ¾:8 values of ¾ above kV,spark discharges would occasionally occur between the tube lens electrodes. 4The reﬂective width depends on the atomic velocity distribution arriving at the surface which is time dependent for a released MOT cloud. In the experiment, we averaged over the entire time-of-ﬂight spectrum. 46 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £

60 50 40 30

[pixel]

y 20 10 0 0 102030405060 x [pixel]

Figure 3.4: Contour plot of the experimentally determined detection efﬁciency proﬁle of the

atom detector (the contours are equally spaced, the black region corresponds to zero counts). 4¼ The visible diameter of the recorded distribution ( pixels) corresponds roughly to the diameter of the hole lens aperture. The “ﬁeld of view” of the detector is deﬁned operationally as the circle centered about pixel (32,32) with radius 23 pixels.

dynamical normalization for all subsequent experiments5.

½× ½× E = 5

Detection efﬁciency for 5 . The absolute detection efﬁciency for atoms (

:5 ½½ eV) was determined from the arrival distribution of a MOT with known position, temperature and atom number. The atom number was determined from ﬂuorescence

measurements and carries a ¿¼± uncertainty from the effective Clebsch-Gordan coupling coefﬁcient. By comparison of the calculated and measured arrival distributions

(cf. the section on the TOF method further below), the efﬁciency of the atom detector

:5 ¦ ½:6µ±

was found to be ´5 averaged over the ﬁeld of view with a local maximum

:4 ¦ 4µ±

of ´½4 . At the same time this maximum is the lower bound for the physical

±´½× µ

electron yield 5 .

´½× µ

The case of metastable argon 5 at a gold-coated substrate has previously been

studied in Refs. [199, 200]ina½¼ mbar environment. The measured values were

:7± 4:4± ¾6± found to be in a wide range between ¼ to (at 300 K) and (at 360 K),

which the authors ascribe to the presence of adsorbates, in particular water, that were

9 removed by heating. Given the low pressure of less than ½¼ mbar in our experiment

and considering the relatively high and stable value for ± measured, it can be concluded that the role of adsorbates in the deexcitation process in our case was small.

5An additional electronic artifact was compensated ﬁrst. The fast analog-to-digital converters (separate Ý for the Ü and directions) in the position analyzer exhibit nonlinearities that result in a variation of the

with of neighboring electronic bins of up to 5¼± and give rise to a pronounced small-period modulation pattern. This pattern was independently assessed by defocusing the detector completely, such that a physically smooth and slowly varying distribution was obtained over the whole active area of the MCP. The modulation was extracted from the data by applying high-frequency linear ﬁlters to the measured

data until it just disappeared. By comparing the smoothed distribution with the data, local compensation

c´Ü ;Ý µ= c´Ü µ ¢ c´Ý µ ´i; j µ

j i j factors i for the data bins were then calculated and subsequently used for a normalization of all measurements. 3.3. CHARACTERIZATION OF THE DETECTOR 47

MOT 500 µs CCD OP 1s3 1s5

EWM

½×

Figure 3.5: Scheme for the measurement of the electron yield for ¿ atoms. An optical pump-

ing pulse is applied to atoms trapped in a MOT above the surface, releasing a deﬁned fraction

½× ½× 5 of ¿ atoms. Residual atoms are shielded from the surface with an evanescent-wave atom

mirror.

½× ½× ¿ Detection efﬁciency for ¿ . The detection efﬁciency for atoms is important for

experiments that involve the storage of atoms in the optical potential of the atom

½×

waveguide. Compared to the case of 5 atoms, the efﬁciency can be expected to

be directly connected to the electron yield ± for the electron emission process. The

E =½½:¾ ½× ½× ´½½:5 5 internal energy of eV for ¿ is only slightly lower than for eV) such

that differences in the imaging of the ejected electrons can be neglected.

±´½× µ

In the literature the yield ¿ for argon has so far only been measured for a

±´½× µ

stainless steel surface, for which it was found to coincide with 5 to within an

6± ½×

experimental uncertainty of [201]. On the other hand, in a comparison of 5 to

¾Ô ´½¿:½

9 eV) at a chemically clean gold surface, differences in the electron yield of up to a factor of 4 were observed [200], which indicates the possibility of a strong energy

dependence, depending on the nature and state of the surface. Therefore it seemed

½×

useful to test the case of ¿ atoms at the gold ﬁlm experimentally.

±´½× µ ½× 5 To determine ¿ , the following scheme was used. First a MOT (containing

atoms) was prepared above the surface. A short optical pumping pulse at 715 nm

½× ½× ¿ was then applied, transferring a deﬁned fraction of the 5 atoms to the state. For these atoms the electron emission was then measured, and the detection efﬁciency was obtained by a comparison of the counts with the number of pumped atoms. The

practical realization of this scheme is shown in ﬁg. 3.5. The MOT was turned off immediately after applying the 5¼¼ s long pumping pulse (this was necessary since

the atom detector does not work when the magnetic ﬁeld of the trap is on). The

½× ½× ½×

5 ¿

mixture of ballistically expanding ¿ and atoms was then “ﬁltered” for atoms

½×

at the surface by using the 812 nm evanescent-wave atom mirror to repel the 5 atoms

½× ´¼:7 ¦ ¼:¾µ±

(the residual 5 transmission was .

To get the electron yield, we ﬁrst determined the relative decrease in the cloud

ﬂuorescence caused by the 715 nm pumping pulse of duration 5¼¼ s. The decrease

¡ = ´¾5¿ ¦ ¿µ ¢ ½¼ ×

was determined to be ½ in the experiment. The error bar is 5 48 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £

counts

0 1 2 3 4 time [ms] AB B-switch

Figure 3.6: Suppression of the detector overall count rate in the presence of the magnetic quadrupole ﬁeld of the MOT. The surface was illuminated by the atomic beam at grazing inci-

dence while the B ﬁeld was switched electronically. When the ﬁeld is on, the count rate drops

¢ ½¼ ¿¼¼ to ½ . The rise and fall times of about s agree with measurements using a test coil.

given by ﬂuctuations in the MOT light intensity. Using the branching ratio for optical

½× Õ = ¼:56½ ¦ ¼:¼5

pumping to ¿ , (which is obtained from the transition rates given

½× ¡ =¡ Õ =

½× ½×

in [174]), the fraction of ¿ atoms in the cloud is then deduced to be

¿ 5

:½4¾ ¦ ¼:¼½ ¼ . Next, we compared the arrival spectra for the case with and without

the pumping pulse (in the latter case the atom mirror was not turned on). While

½×

the ﬁrst measurement is sensitive to the fraction of pumped ¿ atoms, the second

½×

measurement yields the arrival distribution of 5 atoms from the MOT. By comparing

½× ¼:½44 ¦ ¼:¼½ ½× 5 the total number of counts, the ¿ signal was found to be of the signal. Here the uncertainty is determined by a slight difference in the shape of the arrival distributions (both temporally and spatially) due to the ﬁnite duration of the pumping pulse and the photon momentum kicks in the optical pumping process. By

comparing atom detector and CCD measurements, one therefore ﬁnds that

±´½× µ=±´½× µ=¼:98 ¦ ¼:½: ¿

5 (3.2)

½×

Therefore the detection efﬁciency of the atom detector for ¿ atoms is indeed the same

½×

as for 5 atoms.

3.3.3 Sensitivity to Magnetic Fields

When the quadrupole ﬁeld of the MOT is turned on (ﬁeld gradient 5 G/cm), the count

¢ ½¼ rate is suppressed almost completely (to a fraction of ½ ), as illustrated in ﬁg. 3.6. On the one hand, this forbids measurements on a MOT in the stationary state. On the other hand it can be employed for gating the detector during data acquisition, thereby only exposing part of the triggered sequence of HBM pages to the electron ﬂux. This proved to be a very useful feature for the measurement of the loading and decay curves of the atom waveguide. 3.4. APPLICATION: 3D TIME-OF-FLIGHT MEASUREMENTS 49

3.4 Application: 3D Time-of-Flight Measurements

A standard technique for measuring the temperatures of trapped atoms is the time- of-ﬂight (TOF) method [26]. A probe laser beam passing at some distance below a trapped atom cloud is usually employed to monitor the arrival signal for atoms after the trap is turned off. After release, the atom cloud expands ballistically according to its velocity distribution, and from the probe ﬂuorescence signal the temperature can be deduced. For metastable rare gas atoms, a MCP below the trap is usually employed instead of a probe laser beam. By using the surface atom detector it is now possible to implement TOF measurements with spatially resolved resolution. This allows to directly assess the 3D velocity distribution in the trap. On a practical side, it provides an excellent method to test the detector calibration.

Ballistic expansion and TOF signal. For an atomic cloud trapped in a MOT the Ü spatial and velocity distributions along any axis ¼ through the center of the trap are

given by

½ ½

¾ ¾ ¾ ¾

µ Ü =´¾ µ Ú =´¾

Ô Ô

Ô ´Üµ= ; e ; Ô ´Ú µ= e Ü

Ú (3.3)

¾ ¾

¼ Ú

= k Ì=Å Ì ¼Ü B

where Ú deﬁnes the temperature of the cloud along .Atagiventime

Ø Ü Ú

after release, atoms originating from a position ¼ with initial velocity have moved

Ü = Ü · ÚØ · gØ g

to the position ¼ ,where denotes the on-axis gravity component. ¾

Taking the initial distribution of velocities into account, the spatial distribution for the Ü

atoms released from ¼ is given by

dÚ ½

¾ ¾ ¾

gØ µ =´¾´ Øµ µ ´Ü Ü

Ô ´Ü; Øµ=Ô ´Ú µ = e Ú

Ü (3.4)

dÜ

´ Øµ ¾ Ú

The spatial distribution function after the time Ø for the entire cloud is obtained from Ü

the contribution from all positions ¼ in the initial spatial distribution, i.e. by the

convolution

¾ ¾ ¾

´Ü gØ µ =´¾ ´Øµµ

e Ô ´Ü; Øµ= dÜ Ô ´Ü µÔ ´Ü; Øµ= ;

¼ Ü ¼ Ü

Ü (3.5)

´Øµ ¾

½ Ü

where

´Øµ= ·´ Øµ : Ú

Ü (3.6) ¼

During the ballistic expansion the Gaussian shape of the cloud is maintained, however

the variance Ü increases with time, depending on the temperature .

To get an expression for the TOF signal produced at the prism surface, Cartesian

f¼Ü g = f¼Ü; ¼Ý; ¼Þ g ¼Þ

coordinates i , are introduced with pointing downward to the surface along the optical axis of the detector. First of all, the ballistically expanded

50 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £

Ø Ô ´Ö;Øµ = Ô ´Ü ;Øµ Ô

Ü i Ü

spatial distribution at time is given as the product Ö ,where

i i

Ô Ô Þ

and Ý are deﬁned as in eq. 3.4 . To calculate the distribution perpendicular to

Þ ½ Þ c the surface, the upper integration limit must be chosen as c instead of ,where

is the height of the Gaussian density maximum above the surface, as there cannot be

Þ ´¼µ Þ

any atoms below the surface. This is irrelevant as long as c , yet it becomes

Þ ´¼µ Þ important for low clouds c for which the Gaussian proﬁle is “truncated” by the surface. The TOF signal, up to a constant amplitude factor, is then simply given by

the evolution of the spatial distribution at the plane of the surface,

´Ü; Ý ; Øµ = Ô ´Ö;Øµj

Þ =Þ

TOF Ö

h i

¾ ¾

´Þ gØ µ

Ý Ü ½

eÜÔ =

¾ ¾ ¾

¿=¾

¾ ´Øµ ¾ ´Øµ ¾ ´Øµ

´¾ µ ´Øµ ´Øµ ´Øµ

Ü Ý Þ

h i

¾ ¾

½ ´g ´¼µ ·¾Þ µØ

Þ c

¢ ;

½·erf (3.7)

¾ ´¼µ ´Øµ

Ú Þ Þ

¼Þ g =

where the quantity Ú;Þ is the variance of the velocity distribution along ,

9:8½ =

Ý Þ

m s ,and Ü , and are deﬁned along the coordinate axes analogously as

Ì ;Ì Ì

Ý Þ in eq. 3.6. From this spectrum, the temperatures Ü and of the cloud can be

deduced.

Þ =´665¦ ¿¼µ ´¼µ = ´½7¼ ¦ Þ

Experiment. For the experiment, a MOT with c mand ¾µ m (as determined from a Gaussian ﬁt to the cloud ﬂuorescence measured with the CCD camera) was prepared above the surface. The data acquisition of the detector was triggered upon release of the cloud when the MOT light and the magnetic quadrupole

ﬁeld were turned off.

´Ü ;Ý ;Ø µ

e i j

For the analysis of the experimental data TOF k , the marginal distributions

È È

´Ü ;Ø µ = ; ´Ý; Øµ = ´Øµ = ´ µ

Ü i e Ý e Þ Ü ;Ý e

TOF k TOF TOF TOF and TOF max TOF are

i j

Ý Ü

i i

Ì Ü;Ý

considered. To determine the temperatures , the distributions TOF Ü;Ý are ﬁrst ﬁtted

´Øµ

with 1D Gaussians (in accordance with eq. 3.7), yielding variances Ü;Ý .Aﬁtof

Ì Ì Þ

eq. 3.6 to these variances then yields Ü;Ý . To determine the temperature ,the

Ì Þ distribution TOF is ﬁtted with TOF(0,0,t) as given in eq. 3.7,with Þ as a free ﬁt

parameter. The measured sequence of detector images is shown in ﬁg. 3.7 (a). The

Ý Þ

deduced distributions TOF Ü ,TOF and TOF are shown in ﬁg. 3.7 (b), (c) and (d),

Ì =´49¦ ½µ Ì = Ý

respectively. The weighted least-square ﬁts yield temperatures Ü K,

·6

´4½ ¦ ½µ Ì =¿6

K parallel to and Þ K perpendicular to the surface. The ﬁt curves

4 are shown as solid lines7.

For a consistency check, temperatures were determined alternatively from strobo-

´Øµ

scopic ﬂuorescence measurements of the variance using the CCD camera (as de-

Þ 45 ¼Ü ¼Ý scribed in ch. 4), along the axis ¼ and along an axis at between and along the

6An alternative derivation of this formula is given in Ref. [202] on the basis of a Green’s function.

´ ½¼¼ Å

Due to the ﬁnite detector resolution D m), the measured variances exceed the physical

¾ ¾

= · Å

values È according to . However, this does not affect the temperatures when ﬁtting eq.

È D 3.6. 3.4. APPLICATION: 3D TIME-OF-FLIGHT MEASUREMENTS 51

(a) 0 counts

t=0.5 ms 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 ms

(b) (c) (d)

x 0.7 0.7 y

TOF 0.65 TOF 0.6 -1.5 x [mm] 1.5 -1.5 y [mm] 1.5 0.6

[mm] 0.5 [mm] 0.55 Ü Ý 0.5

0.4 local peak value 0.45 0

0123456 0123456 0123456

Ø Ø

Ø [ms] [ms] [ms]

Þ = ´665 ¦

Figure 3.7: Ballistic TOF data of an atom cloud released from a MOT at a height c ¿¼µ m above the surface, obtained from a summation over 800 measurement runs. (a) –

Excerpt of the sequence of 64 detector images, showing every ﬁfth image. (b) and (c) – Fitted

Ü Ý Ý variances Ü and of the Gaussian marginal distributions along the and directions. The

insets show typical TOFÜ;Ý distributions obtained by summing over centered windows of 40

Ü Ý

pixels ¢ 14 pixels, with the long side along and ,resp.Thesolidcurvesareweightedmodel

Ì =´49¦ ½µ Ì = ´4½ ¦ ½µ Ý ﬁts that yield temperatures Ü Kand K. (d) – Local peak values of

the TOF data obtained from a summation over the four brightest pixels. The ﬁt of the model,

·6

Ì =¿6

shown as a solid curve, yields a temperature Þ K perpendicular to the surface.

52 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR £

Ì = ´¾8 ¦ ¾µ Ì =´¿8¦ 5µ Û;C aÑ viewing direction. This leads to values Þ;CaÑ K, and K, which are comparable results.

3.5 Conclusion

We have studied a detection scheme for metastable atoms at a surface with atom- optical methods. This scheme is based on the imaging of secondary electrons released

from the surface upon impact of single atoms. We have separately determined the de-

½× ½× ¿

tection efﬁciencies for the metastable 5 and states of argon. This has allowed us

½×

to access the hitherto unknown electron yield for the ¿ state at gold surfaces, which

½× ½4±

was found to coincide with that for the 5 state at a value . We have demonstrated a method for time-of-ﬂight spectroscopy of ultracold atoms in three dimensions. The properties of the detector can be summarized as follows. The detector has a

circular ﬁeld of view of 3 mm diameter, a spatial resolution of about 100 mandan

electronically limited temporal resolution of 20 s. The single-atom detection efﬁciency

near the center of the ﬁeld of view is ½4±. The maximum allowable overall atom ﬂux

½ ¢ ½¼ without signiﬁcant counting errors is atoms/s. Chapter 4

Magneto-Optical Surface Trap

We have realized and studied a novel magneto-optical surface trap (MOST) for metastable argon atoms. This hybrid trap combines a magneto-optical trap with an optical evanescent-wave atom mirror. It allows us to laser-cool and trap atoms in contact with the evanescent ﬁeld that separates the atomic cloud from the surface

by only a fraction of an optical wavelength. In the experiment, we were able to

:¿ ¦ ¼:4µ ¢ ½¼ ´¿9¼ ¦ ¿¼µ trap ( ½ atoms in the MOST with a lifetime of ms, which was limited by collisions with the surface.

4.1 Introduction

In laser cooling and trapping [203], one of the most common configurations is the magneto-optical trap (MOT), first demonstrated in 1987 by Raab et al. [24]. The MOT has been intensely studied and improved in the last decade [25] and today is a standard initial step for experiments that involve trapping and cooling of neutral atoms. The usual design consists of three mutually orthogonal pairs of counterpropagating laser beams that intersect at the zero of a quadrupole magnetic field (cf. chapter 2). Variants have been described that match special design needs of experiments [204, 205, 206, 207] and more recently, MOT geometries have been realized to prepare atom clouds close to surfaces [129, 126], following work by Lee et al. [131] and ourselves [111]. The loss of atoms from a MOT close to a surface was examined in Ref. [208]. The reflection of atoms from a blue-detuned optical evanescent wave, suggested in 1982 by Cook and Hill [38], was first demonstrated in 1987 by Balykin et al. [39]with atoms from a grazing-incidence thermal beam, to be followed by experiments with cold atoms from a MOT [40, 41, 44]. In these experiments, the evanescent field that builds up when a laser is totally internally reflected at a glass-vacuum interface was used. In other experiments, surface plasmons [42, 43] (cf. chapter 2) and dielectric layer systems [161] were employed to resonantly enhance the evanescent field. A combination of the two techniques, i. e. a MOT in contact with an evanescent field that separates the atomic cloud from the surface by only a fraction of an optical wavelength, is useful for the realization of a reservoir of cold atoms close to a surface.

53 54 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

It allows for the implementation of a continuous loading scheme for the planar surface matter waveguide demonstrated by us in an earlier work [110]. In the following

description this conﬁguration is called a magneto-optical surface trap (MOST). Prelim-

½× ° ¾Ô 9 inary results on the MOST, which is realized with metastable argon on the 5 transition at 812 nm, can be found in Refs. [188,111]. This chapter is organized as follows. The next section introduces the basic concepts and the conﬁguration of the MOST, and the third section discusses a simple model for its physical properties. The fourth section is devoted to the experiments, in which the properties of the trap and its components are studied.

4.2 Conﬁguration of the MOST

The magneto-optical surface trap (MOST) discussed in the following is a hybrid trap that combines a magneto-optical trap (MOT) with an evanescent-wave surface- plasmon atom mirror (these components are discussed in chapter 2). In order to bring a magneto-optically trapped cloud close to a mirror surface, one first needs to find a suitable beam configuration. For geometrical reasons it is clear that the standard 6- beam MOT configuration (cf. fig. 2.3) is not suited for such a purpose since inevitably one or more beams would get chopped by the mirror surface 1. The basic idea for getting around this problem is to use the surface itself to generate MOT beams by reflection.

2D representation. The principle can best be illustrated by starting in 2D with the standard 6-beam configuration as depicted in fig. 4.1 (a) in a radial-axial plane of the quadrupole field. In agreement with fig. 2.3 the axial beams are left-handed circularly (lhc) polarized and the radial beams are right-handed circularly (rhc) polarized. The counterpropagating beams are usually generated by retroreflection at a mirror, combined with a double pass through a quarter-wave plate in order to reverse the ensuing

helicity flip. Yet for our purpose this flip can be actively used to realize the MOT at Æ the mirror surface, as shown in fig. 4.1 (b). The beams are incident at 45 such that the mirror reflects the axial beams into the radial direction, and vice versa2.Onecan easily see that the light field above the surface is the same as for the standard MOT with respect to its polarization, and atoms therefore can be trapped right down to the surface. The combination with the atom mirror is then simply realized by adding the laser beam for the excitation of the surface plasmons (EWM), fig. 4.1 (c).

3D conﬁguration. An extension to 3D is not immediately evident, however. For example, if a 2D cut in a radial-radial plane were considered instead of the above radial- axial plane, the beams would all be right-handed circular, and therefore the mirror

1A6-beamMOTclosetoatransparent glass slide was demonstrated by the authors of Ref. [208]who shifted a glass-cell MOT into the vicinity of one of the walls. 2The one-beam MOT in a hollow mirror [131] makes use of the same principle. 4.3. SIMPLE MODEL FOR PROPERTIES OF THE MOST 55

rhc rhc

lhc lhc B

coil

=4 4 { = { EWM (a) (b) ()c

Figure 4.1: Principle for the realization of the MOST in a 2D representation. (a) - standard MOT, (b) - MOT near the mirror surface, (b+c) - magneto-optical surface trap (MOST) reflection scheme would not work. Still, it is possible to find a 3D beam configuration that is entirely based on mirror reflection and also satisfactorily fulfills the requirements for the operation of a MOT. This configuration is illustrated in figure 4.2: Four of altogether eight MOT beams propagate essentially in radial directions, being rhc polarized as required (those to the right-hand side in the figure). They are connected via reflection to the other four beams which are lhc polarized and propagate in semi- axial directions. The axial components of these beams fulfil the requirement for the generation of a restoring MOT force; the radial components cannot be expected to provide confinement from simple 1D MOT theory but still contribute to molasses friction. The magnetic coil configuration allows to shift the magnetic field zero normal to the surface. This configuration provides for both to trapping and the investigation of the properties of the trapped cloud at different heights.

4.3 Simple Model for Properties of the MOST

In this section, a simple model of the MOST is developed, focusing on two aspects. First, the influence of losses to the surface at the trapping behavior is discussed, and expressions are given for the density distribution and the one-body loss rate of the trapped cloud, which depend on the position of the magnetic field zero. A second important point concerns the physics at the evanescent-wave mirror in the presence of MOT light. Both laser fields couple to the same transition, and during the reflection process the atoms interact with a bichromatic light field. A simplified picture is developed for how this changes the behavior of the atom mirror and influences the lifetime of the MOST. On the basis of this model, the main experimental results will be explained.

Density distribution and temperature: model ansatz As discussed in chapter 2,the atom cloud in a well-aligned MOT in the temperature-limited regime has a Gaussian

density proﬁle. Under the assumption of a homogeneous light ﬁeld in the overlap Þ region of the MOT beams, the cloud can be shifted freely along ¼ by adjusting the

56 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP Æ

Figure 4.2: Configuration of the MOST in 3D. Eight MOT beams at 45 to the surface provide for confinement and cooling above the prism surface, and the EWM beam is used to generate a surface-plasmon enhanced evanescent field for the reflection of atoms. The axis of the coil pair for generating the magnetic quadrupole field (“MOT coils”) is tilted by 45 Æ with respect to the surface and lies symmetrically between the MOT beam pairs. An additional coil pair (”offset field coils”) is used to generate a homogeneous magnetic field to control the height of the magnetic field zero above the surface (and therefore the center of the trapped atom cloud). The trap is loaded from a slow atomic beam. The laser beam used for atomic beam slowing

(not shown in the ﬁgure) passes the surface at grazing incidence. Þ

height ¼ of the magnetic ﬁeld zero. The trapping potential perpendicular to the surface

Í = Þ =¼ [Ö ´¼; ¼;Þ µ] ÅÇÌ

is then described by ¼ with an absorbing boundary at .

Þ = ¼ Þ ½= e

When the cloud is near the surface ( ), i.e. when ¼ is comparable to the

radius Þ of the cloud, this boundary condition requires, in a rigorous treatment, to

´Ö;Øµ find the new density distribution Ò on the basis of a Fokker-Planck or Langevin equation, e.g. with a numerical molecular dynamics method [145]. This will not be attempted here; instead a phenomenological, quasi-stationary 1D ansatz is made that is in good qualitative agreement with our fluorescence measurements of the cloud density profile (cf. the experimental section below): Parallel to the surface, the density distribution remains unaffected as the harmonic

oscillator potential and diffusive motion separate spatially. After integrating parallel to

Ò Ò ´Þ; Øµ=Ò ´Þ µÒ ´Øµ

Þ ½ ¼

the surface, the remaining 1D density proﬁle Þ canbewrittenas ,

Ò ´Þ µ Þ ¼

taking the form of a truncated Gaussian proﬁle ½ centered about with decaying

Ò ´Øµ

“amplitude” ¼ ,

h i

¾ ¾

´Þ Þ µ =´¾ µ

Ò ´Þ; Ø : Þ µ=Ò ´Øµ e Ù´Þ µ

¼ ¼ Þ (4.1)

4.3. SIMPLE MODEL FOR PROPERTIES OF THE MOST 57

´Þ µ

The function Ù describes the local density variation at the surface (on a length scale

Í ÅÇÌ

(a) ÅÇÌ (b)

Þ Þ

Figure 4.3: Model for a MOT near a surface: (a) For large distances ¼ , the conﬁning

Í Ò´Þ; Øµ potential ÅÇÌ leads to a Gaussian density . (b) For small distances the surface acts as an absorbing boundary that truncates the Gaussian density proﬁle; surface losses combined with

the diffusive motion in the volume above the surface lead to the global decay of the density.

that is small compared to Þ ); in the following it is approximated by a unit step func-

= k Ì= Þ

B ¼ tion. The width Þ is not expected to change with since the temperature

Ì is homogeneous over the volume of the trap according to the simple 1D MOT model. Þ

Dependence of the one-body loss rate on ¼ . For a cloud trapped in the 8-beam

Þ Þ MOT conﬁguration well above the surface ( ¼ ), the probability for trapped atoms

to reach the surface is small, and therefore the same one-body loss rate as for a standard

Þ Þ MOT can be expected. However when ¼ becomes comparable to , collisions of trapped atoms with the surface (which is at room temperature) start to play a role. These lead to a one-body loss of atoms from the cloud with high probability, similar

to collisions with thermal background gas3. The dynamics of the trapped cloud near

Ò´Öµ = Ð «Ò´Öµ ¬Ò ´Öµ the surface can still be described locally by the expansion _ ,

just as in the standard MOT, but one must now be careful with the deﬁnition of «.In

the presence of surface losses, « necessarily becomes position-dependent, remaining constant in the cloud volume while taking a large value at the surface. On the other hand, as a result of the diffusive random walk of the trapped atoms, the surface losses

end up affecting the entire cloud. In the following we therefore introduce an overall

«´Þ µ Æ

loss rate ¼ that describes the decay of the total atom number in the trap. This Þ

rate will increase smoothly with decreasing ¼ as the available volume for diffusion above the surface becomes smaller and smaller.

3One would expect losses from adsorption and/or heating to thermal energies. However, for metastable argon, a major additional mechanism is the decay to the electronic ground state. In previous experiments with metastable argon, we determined (from measurements of the reﬂectivity of the bare mirror surface) the overall survival probability for an Ar £ atom colliding with the gold-coated surface

to be below 0.1 ± [182].

58 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

«´Þ µ Ò ´Øµ ¼

The decay rate ¼ for the evolution of canbewrittenasthesumofthe «

background-gas collisional value ¼ and the loss rate due to the presence of the surface,

« ´Þ µ ¼

× ,

«´Þ µ=« · « ´Þ µ:

¼ × ¼

¼ (4.2)

« Ò Þ To ﬁnd an expression for × one can exploit that, since the distribution above the surface remains Gaussian, according to the ansatz, the diffusive motion in that part of the potential must be the same as it would be in a large-distance case, i. e. it is not inﬂuenced by the presence of the surface. Therefore, by direct correspondence, the collision probability at any point in time equals the relative statistical weight of the

extrapolated fraction of the density distribution behind the surface (shown as a dashed

Ò =Ò ½ ¼ ¼ line in ﬁg. 4.3) which is given by the integral over Þ from to . This directly

leads to the loss rate

¾ ¾

µ ´Þ Þ µ =´¾

« ´Þ µ = Ê dÞ

× ¼

Ê Þ

= :

½ erf (4.3)

¾ Þ

The proportionality constant Ê can be interpreted as a uniform trial rate for an atom in the trap to collide with the surface.

Reduction of the one-body loss rate with the atom-mirror potential. The velocity distribution of atoms at the surface is given by the 1D Maxwell-Boltzmann distribution, eq. 2.41, for which at any point in time half of the atoms are incident on the surface. When the evanescent-wave mirror is turned on, the repulsive optical potential reﬂects

those incident atoms with absolute velocities smaller than the critical velocity

Ú = ¾Í =Å; ÑaÜ

ÑaÜ (4.4)

Í ´Ü; Ý µ

deﬁned by the height of the potential hill ÑaÜ (cf. ﬁg. 2.6). Here and in the

¾ =e following it is assumed (in accordance with the experimental situation) that the ½

radii of the evanescent-ﬁeld spot, eq. 2.54, are much larger than the transverse width Í

of the atom cloud. In that case the value for ÑaÜ is the same for all incident atoms. At any instant, the fraction of incident atoms with energies above the barrier is then

simply given by

ÑaÜ

= dÚ ¾Ô ´Ú µ Ì

Ú (4.5)

! ;

eqs.2.41 Ö Í

2.42 ÑaÜ

½ ;

= erf (4.6)

k Ì B where the factor 2 accounts for the fact that, at any point in time, only half of the laser-cooled thermal distribution eq. 2.41 is incident on the surface. In the following,

4.3. SIMPLE MODEL FOR PROPERTIES OF THE MOST 59

we call Ì the “translucence” of the mirror for the thermal velocity distribution. With Í

an increasing potential maximum ÑaÜ (this point will be discussed further in the next

paragraph), Ì gets smaller and and reaches zero asymptotically. The loss rate at the

surface decreases accordingly,

« ´Þ µ= « ´Þ µ:

¼ Ì × ¼

×;eÚ (4.7)

Í !½

In the limit ÑaÜ all atoms are reﬂected from the evanescent ﬁeld and the lifetime

=´« · « µ ×;eÚ of the atom cloud, ¼ , is again only determined by collisions with the background gas.

Atom-mirror potential in the presence of MOT light. In the absence of MOT light, the properties of the evanescent-field mirror (EWM) for incident atoms are those described in the second section of this chapter. However, when the resonant MOT light (which couples to the same transition!) is present, the situation changes drastically. Due to the circular polarization of the MOT beams, the electric field takes a finite value at the mirror surface (the field for a single beam pair at a given instant in time is illustrated in fig. 4.4), and the atoms are reflected in a bichromatic light field. The

lhc

Æ 45

4 rhc Þ Òc

i ¾

Á=Á

¼ ¼ distance from surface

Figure 4.4: Light field distribution for the reflection of a MOT beam at the mirror surface. While the field components parallel to the surface vanish at the surface (dashed curve), the

components normal to the surface take a maximum (dot-dashed curve). The solid line shows Á

the total ﬁeld intensity in units of the intensity iÒc of the incident beam.

question is, how does the MOT light affect the potential of the evanescent-wave mirror? A simple treatment of this problem in the dressed two-level atom model discussed in chapter 2 is not possible in general as the usual rotating-wave approximation runs into problems when more than one laser frequency is present, preventing stationary eigenstates to be constructed. In the case that the MOT light is much weaker than the evanescent ﬁeld, it is however possible to maintain the rotating frame deﬁned by 60 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

the evanescent-ﬁeld frequency while treating the inﬂuence of the MOT light as a weak

time-dependent perturbation. In that case it can be shown for a two-level atom (see

×Ø

j¾i

appendix A) that the MOT light increases the population of the attracted state , ¾¾

thereby reduces the absolute value of the dipole force according to (compare eq. 2.21)

~@ !

×Ø

´½ ¾ F i = µ:

h (4.8)

¾¾

Æ Ä For general parameters, the complications of the bichromatic problem stand in the way of a rigorous yet simple description. However at this point a very crude picture can

be developed. Suppose that the detuning of the evanescent ﬁeld is sufﬁciently large to

½´Æ µi jg; Æ ·½i

prevent the bare states from being signiﬁcantly mixed such that j

¾´Æ µi je; Æ i

and j . When the MOT light is added, it drives transitions between the

×Ø

g i jei

atom’s internal states j and , leading to a steady-state population of the ee;Å Ç Ì

excited state (as deﬁned in eq. 2.25) entirely determined by the MOT light . This value ×Ø

coincides with because of the large EWM detuning, and therefore the MOT light ¾¾ ﬁeld also leads to a cycling between the dressed states (owing to the large detuning of

the EWM beam, the dressed states readjust quickly after an internal state change). In ×Ø

the limit of large MOT saturations, takes a value close to 1/2 with little spatial ee;Å Ç Ì variation over the entire range of the evanescent ﬁeld. One then obtains for the optical

potential, using eq. 2.55, the simple steady-state average

×Ø

µ; Í Í ´½ ¾ ÓÔØ

E Ï Å ;diÔ (4.9)

ee;Å Ç Ì Í

a value that is much smaller than the “monochromatic” value EÏ Å ,eq.2.55. There-

fore the translucence Ì forthebichromaticcasewillbemuchhigherthaninthe monochromatic case. This picture requires that a steady-state can be reached for the moving atom, which might be problematic as the mean free path between photon scattering events for an atom at Doppler velocity is only one order of magnitude below the decay length of the evanescent ﬁeld. Further aspects not taken into account here include the optical potential of the MOT light itself and the possibility of MOT-induced

ﬂuctuations of the dipole force. Í

To ﬁnally calculate the value ÑaÜ , one has to include the atom surface interaction. In principle, the model requires the temporal averaging over the interactions for the ground and excited state, for the same reasons as for the optical potential. However, if one takes the van-der Waals interaction there is no difference between the two for the two-level atom. One can then simply add the van-der Waals term, eq. 2.56,tothe optical potential, eq. 4.9 and numerically solve for its maximum value.

4.4 Experiment

½× ° ¾Ô 9

The experiments were performed with metastable argon atoms on the 5 tran-

Á =½:¾9 =¾ ¢ 5:¾7

sition at 812 nm ( Ë mW/cm , MHz), using the beam machine described in chapter 2. This section first describes the experimental setup for the realization of the 3D MOST configuration. A second part deals with the experimental 4.4. EXPERIMENT 61 results. In our experimental study, we first examined the behavior of a trapped atom cloud as far away from the surface as technically possible, and then studied the change in the parameters of the trap for decreasing heights of the magnetic field zero. Before studying the MOST itself, we characterized the atom mirror in the bichromatic light field, which exhibits a dramatic attenuation of its reflective behavior compared to the monochromatic case without MOT light.

4.4.1 Experimental Setup

The experimental setup is located in the main chamber of the beam machine as shown

in ﬁgure 4.5. The MOT beams are generated from a common Gaussian beam and have

=e ´½:4¼ ¦ ¼:¼5µ

a ½ diameter of 5.9 mm and a maximum power of of mW each. The

¾ =e EWM beam has a ½ diameter of 2.8 mm. In the experiments on the MOST we used the Ti:Sapphire laser for the generation of the EWM light, allowing for powers after the ﬁber of up to 80 mW. The gold-coated prism surface is located on the axis of the atomic beam with horizontal orientation. It is mounted to the electron lens column of the atom detector. All MOT beams incident on the surface are perfectly circularly polarized; the admixture of the “wrong-handed” polarization in the reﬂected beams is

below ¿± of the total beam intensity, as determined in an ellipsometric measurement. Because of limited optical access, a mirror inside the chamber is used to deﬂect the EWM beam onto the back side of the gold ﬁlm at the surface plasmon resonance angle.

A combination of a quarter- and a half-wave plate is used to generate a linear Ô polarization of the incident EWM beam as required for the excitation of surface plasmons. The magnetic quadrupole coils (”MOT coils”) consist of 1750 turns of coated copper wire (wire diameter 0.3 mm, resistance 27 Ohms) on a water-cooled, sliced copper mount and are located inside re-entrant tubes of diameter 3 cm [209]. The spacing be-

tween the coils is 9 cm. At the standard operation current of 700 mA, a ﬁeld gradient

=4:6

of b Gcm is produced along the axial direction that is approximately constant ½ in a range of ¦ cm from the center. The offset field coils are located inside the vacuum on the atom detector setup above and below the surface. Their diameter is 3 cm and they consist of 50 turns of KaptonTM wire (diameter 0.5 mm) each. At the standard quadrupole field gradient, currents of up to 120 mA are needed to produce a field for shifting the cloud in the range of about 1 mm. By measuring the wire resistance under UHV conditions and on the typical experimental time scales, we found no noticeable

temperature increase, so that cooling was not required. Both the quadrupole coils and

offset field coils are connected to homemade constant-current supplies (accuracy ½¼ ) and can be switched off electronically within ¾5¼ s. Finally, the field compensation of the earth’s magnetic field is done with three orthogonal pairs of homogeneous-field coils that are wound onto the main chamber from the outside. The atom clouds can be investigated via their fluorescence with the triggerable 8-bit CCD camera (Sony CV-M10BX) mounted to a 75mm TV objective (Cosmicar). The objective is located at a distance of 30 cm from the center of the chamber in the plane of the prism surface. A photomultiplier connected to an 8-bit storage oscilloscope 62 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

EWM

MOT P P Zeeman slower M

M CCD CCD1 PM 2 (a) ABS (b)

Figure 4.5: (a) – Experimental setup for the magneto-optical surface trap (top view). The trapping beams (MOT) enter the chamber through windows on the top side of the chamber after traversing a periscope. The atomic-beam slowing laser beam (ABS) passes the prism at grazing incidence. The evanescent-wave mirror beam (EWM) is deﬂected at a mirror M inside the chamber to the back side of the gold ﬁlm at the surface plasmon resonance angle. A

triggerable CCD camera (CCD ½ ) and a photomultiplier (PM) are used for measurements of the cloud ﬂuorescence. The surface atom detector (not shown) above the prism (P) can be used to

measure losses to the surface in situations with no applied magnetic ﬁelds. The CCD ¾ camera is used for additional monitoring of the cloud (the symbols for the optical components are

explained in ﬁg 2.12). (b) – View along the viewing direction of CCD½ into the main chamber. The large tube at the left is the rear end of the Zeeman slower; the two reentrant tubes at 45 degrees contain the quadrupole coils for the MOST. The prism is located in the center of the chamber. It is mounted to the lens column of the atom detector, which also carries the offset coils.

(Nicolet-450) is used to measure loading and decay curves from the fluorescence. Fi- nally, in order to determine the reflectivity of the atom mirror, the surface atom detector is used for an investigation of the atomic arrival distribution on the surface for optical molasses when the magnetic fields are turned off.

4.4.2 Properties of the Atom Cloud far from the Surface

Þ ½:½

For a study of the 8-beam MOT we started with a cloud centered at ¼ mm above the surface, which was the largest possible height at which a stable cloud could be produced, due to the ﬁnite size of the overlap region of the MOT beams. For this height, the lifetime of the cloud for proper beam alignment was roughly 3 s (see below), as expected from collisions with the background gas, and the loss of atoms to the surface did not play a signiﬁcant role. 4.4. EXPERIMENT 63

Density proﬁle. The cloud ﬂuorescence exhibited a characteristic stationary fringe

Þ ¿¼± pattern in the ¼ direction with a visibility around , as shown in ﬁgure 4.6.By changing the relative angle of incidence of the MOT beams, the separation of the fringes could be varied widely, while their orientation always remained parallel to the surface. In the most extreme cases, the cloud could be contained in a single fringe or, alternatively, the fringe separation could be made smaller than the camera resolution of

30 m. In the latter case the cloud fluorescence intensity profile then looked perfectly Gaussian in all three spatial dimensions, and we also observed that the cloud was much brighter and more stable against perturbations (e.g. fluctuations of the MOT laser frequency). In contrast, for large fringe separations the cloud would typically have fluffy and undefined shapes and sometimes even limply jump between distinct positions.

1D dens.

1.5

Position [mm]

0.5

Figure 4.6: CCD camera ﬂuorescence image of a trapped cloud exhibiting characteristic fringes parallel to the surface.

Similar observations of fringes were reported for a 6-beam MOT by Bigelow and Prentiss [146], who showed directly that the fringes not only affect the fluorescence but are in fact cloud density modulations. They interpreted their findings as the channeling and loss of atoms out of the optical potential of the light field formed by the interference pattern4. However, the authors of a later paper [144] argued that the effect might in fact rather be due to a difference in the diffusion and friction coefficients in regions of varying polarization, which make the trap “stickier” where Sisyphus cooling predominates. The orientation of the fringe pattern in our case can be deduced starting with the light field distribution of a single beam pair above the surface (fig. 4.4): The incident and reflected beams form a standing light wave above the surface that contains both intensity and polarization gradients with planar symmetry. Altogether four beam pairs

½ In the mentioned paper, a density modulation of up to ½¼¼± (with larger fringe separation mm) was observed. 64 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP with uncontrolled and ﬂuctuating relative phases are present in the setup and the time- averaged light ﬁeld intensity is the sum of the intensities of the single pairs. In the case of a deviation between the angles of incidence this results in a 1D intensity beat

pattern along Þ , containing positions where the single-beam field modulations interfere constructively and others where they average out. We verified the connection to the observed fluorescence intensity modulation, similarly as in Ref. [146], by changing the angle of incidence of a single beam and comparing the changes in the Fourier spectra of the observed distribution and the calculated light field [209]. Moreover we found the fringes of lower density to coincide with the antinodes of the beat pattern (this follows directly from an extrapolation of the observed fringe pattern down to the position of surface where the light field has the full single-beam intensity modulation depth, i.e. where there is such an antinode). For all further experiments and characterizations, we always prepared bright and stable Gaussian-shaped clouds with densely-spaced fringes on the order of the camera resolution5.

Atom number and peak density. For a determination of the atom number via the ﬂuorescence of the cloud, the average coupling of the atoms to the light ﬁeld (averaging

over the population of the magnetic substates and the local light polarization) was

= ¼:7 ¦ ¼:¾ included through an effective Clebsch-Gordan coefﬁcient [25]of Ceff,MOT

(see Ref. [177]). An intensity of 8 times the peak intensity of a single beam was

=4:6

assumed. For an axial magnetic ﬁeld gradient b G/cm and MOT beam parameters

Á = 6:8 Á Á = ½:¾9

Ë Ë

ÅÇÌ (single-beam peak intensity; saturation intensity mW/cm )

= ½:5 =¾ ¢ 5:¾7

and Æ (linewidth MHz), the typical steady-state atom number

= ´4 ¦ ½µ ¢ ½¼

using the cooled atom source was Æ , corresponding to a Penning

¿ 9

Ò =´¿¦ ½µ ¢ ½¼ ½= e

collision-limited peak density of ¼ cm . The radius of the cloud

¼Þ =¼:¾¿

in the direction was Þ mm.

Temperatures. The 1D velocity distributions of the cloud normal and parallel to the surface were measured by the free ballistic expansion of the cloud after release. For that

purpose the triggerable CCD camera was used. After a free expansion of duration Ø,the initial Gaussian cloud (eq. 2.44) with its homogeneous thermal velocity distribution

(eq. 2.41), expands into a Gaussian cloud with

¾ ¾

´Øµ= ´¼µ · ´ Øµ ;

Ú (4.10)

Ô 6

´¼µ = k Ì=Å Ì B

where and Ú are the initial parameters . The temperature can

´Øµ

therefore be deduced from a ﬁt to the experimentally determined function .We

´Øµ determined in the directions parallel and perpendicular to the surface in the following way. First the MOT was loaded. In the decay phase, i.e. after turning off

5This might sound like a piece of cake. In fact it took us almost the entire, nerve-wrecking year 1999 to ﬁnd out how to reliably and reproducibly get to this point with our shaky and extremely drift-friendly beam machine! 6A derivation can be found in appendix A of Ref. [202]. 4.4. EXPERIMENT 65

the atomic and slowing laser beams, the magnetic ﬁeld and MOT beams were rapidly

Ø Ø

switched off (within ¾5¼ s). After a dark phase of variable duration ( was succes-

¾5¼ sively increased from ¾5 s in steps of s), the MOT beams were then ﬂashed back on for 1 ms, and the ﬂuorescence was recorded with the camera. The 1D distributions were obtained by summing up the transverse direction in the 2D images, and then

ﬁtting the sums with Gaussians.

Á =Æ ÅÇÌ

The results for different light-shift parameters ÅÇÌ are shown in ﬁg. 4.7.

¿¼ The measured temperatures ranged from ¾5¼ K to about K for small light-shift

250

200

150

TD 100 0.5

temperature T [µK] 0.4

50 0.3 [mm] s t [ms] 0.2 0 1 2 3 4 0 0246

-IMOT/[I/]dGMOT S

¢µ ´£µ

Figure 4.7: Temperatures of the cloud in the directions parallel ´ and perpendicular

Á =Æ ÅÇÌ

to the surface for different light-shift parameters ÅÇÌ . The data points right of the

Á =6:8 Á Ë

vertical line were taken at a constant intensity ÅÇÌ for variable detuning. The data

Æ = 5:7

points left of the vertical line were taken at a constant detuning ÅÇÌ for variable

´Øµ Ì

intensity. The inset shows a typical result of a measurement of ,fromwhich is extracted

´Øµ as a ﬁt parameter. The single points for were obtained from a Gaussian ﬁt to single camera

images. Each of the temperature data points is an average over 10 experimental run series to

´Øµ measure .

parameters. The observed linear functional dependence of the temperature below

Ì = ½¾7

the Doppler temperature ( D K) is in agreement with polarization-gradient cooling theory. In particular, we were also able to observe the abrupt increase

in temperature connected to the breakdown of polarization gradient cooling below

Á =jÆ j ¼:¾Á =

ÅÇÌ Ë ÅÇÌ , in agreement with theoretical predictions [154]. A surpris-

ing result is the systematic anisotropy. The temperatures perpendicular to the surface

¼:¾Á =

are consistently lower for light-shift parameters above Ë ; the difference reduces

¼:¾Á =

for decreasing parameters and ﬁnally even seems to revert below Ë .Adeﬁnite

explanation for this behavior cannot be given at this point, most likely however, the Þ stronger polarization gradients in ¼ direction give rise to larger friction coefﬁcients 66 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

for Sisyphus cooling of the motion perpendicular to the surface. When the cooling mechanism breaks down the difference in the temperatures consequently vanishes.

4.4.3 Behavior of the Trap for Varying Magnetic-Field Zero Position In order to characterize the inﬂuence of surface losses, we measured the change of the

trap parameters with decreasing height of the cloud above the surface for ﬁxed MOT

Á =6:8 Á Æ = ½:5

Ë ÅÇÌ beam parameters ÅÇÌ and (the atom mirror was not used). For this purpose, a careful MOT beam alignment was required in order to generate a sufﬁciently homogeneous light ﬁeld over the entire range of heights.

Experimental method. For a translation of the cloud normal to the surface we var-

Á Á ¿ ied the current ½ in the upper quadrupole ﬁeld coil and the current in the off-

set field coils according to the method illustrated in fig. 4.8. Current configurations

´bµ

´aµ

´cµ

Á Á

¾ ½

Á ¿

Figure 4.8: Method used to shift the position of the magnetic ﬁeld zero towards the surface by changing the currents in the coils of the MOST setup. In (a) the ﬁeld zero (full circle) is

located symmetrically between the quadrupole ﬁeld coils (at 45Æ ) on the symmetry axis, which

Á Á ¾ have equal but opposite currents. By increasing the current of the upper coil from ½ to , the additional ﬁeld displaces the ﬁeld zero on the axis towards the lower coil (b). On the

axis of the offset ﬁeld coils there exists one point where the ﬁeld vector is parallel to that axis Á

(hollow circle). With the offset field coils (current ¿ ),thetotalfieldcanthenbezeroedatthat point (c). Small displacements are linear in the coil currents as the additional fields are nearly

homogeneous.

fÁ ;Á = 7¼¼ ;Á g Þ

½ ¿ ¼ ¾ mA were calculated for different desired heights of the ﬁeld zero by applying Biot-Savart’s law to the coil conﬁguration modeled by current loops [209].

Steady-state ﬂuorescence images of the trapped cloud are shown in ﬁgure for a series Þ

of linearly decreasing heights ¼ . For the highest position shown, the coil currents were

fÁ = 7¼8;Á = 7¼¼;Á =6g

¾ ¿

½ mA, and for the lowest position shown at the far right,

8½¼; 7¼¼; 8¾g f mA (for still higher currents in the upper MOT coil, the ﬂuorescence became too weak for the detection by the CCD camera7.). When the column sums of

7 Þ

It should be added here that the waveguide was ﬁnally loaded from a MOST with ¼ =-0.5mm 4.4. EXPERIMENT 67

the images are ﬁtted with truncated Gaussians, the positions of the maxima of these ﬁts Þ

agree with the calculated ¼ values for the magnetic ﬁeld zero to within a small error

5¼ =¾¿¼

of m. The widths perpendicular to the surface agree with the value Þ m

¿¼ to within an error bar of ¦ m. As expected from the simple model, the steady-state atom number in the cloud reduces with distance as a result of losses to the surface. A second reason for this reduction is the decreasing loading rate; this is discussed further below.

1mm Surface

Figure 4.9: Series of measured cloud ﬂuorescence images for an incremental linear downward

Þ = ½:½ Þ = ¼:½ ¼ shift of the ﬁeld zero from ¼ mm to mm. The position of the surface is

marked by a horizontal line; below this line the mirror image of the cloud can be seen. The cloud follows the calculated magnetic ﬁeld zero to within an error of 5¼ m. The atom number decreases with the downward shift due to the loss of atoms to the surface (the atom mirror was off).

Lifetime. After shuttering the atomic beam and the slowing laser, the trap decay was measured with the photomultiplier. The experimental decay curves were then ﬁtted

¼ 8

Ò ¬ « «´Þ µ ¼

with eq. 2.49 with ¼ , and as free ﬁt parameters . The results are shown

´Þ µ=«´Þ µ ¼

in ﬁg. 4.10 (a) for the inverse decay rate, i.e. the lifetime of the cloud, ¼ . Þ

The lifetime exhibits a strong dependency on ¼ , dropping by two orders of magnitude

¿:½ Þ = ¼:96 5¼ Þ = ¼ ¼ from sfor ¼ mm to ms for mm. The experimental data agree

very well with the model, eq. 4.3, which is shown as a solid line in the ﬁgure. Taking

=¿ =¾¿¼

s as the background-gas collisional value and setting Þ m (as obtained

from the CCD camera measurements), the data can be ﬁtted with the trial rate Ê as

=´4¼¦ 5µ the single ﬁt parameter, yielding Ê s .

Temperatures. It is an implicit assumption of the model for the behavior of the life-

Ì Þ Ì

¼ Þ time that the temperature Þ does not change as is varied ( should be homoge-

neous over the volume of the cloud, cf. the discussion in the second section of this

= k Ì= B chapter). An indirect indication for this is the approximate constancy of Þ already observed for the shift of the cloud. With the method described in the last section, we checked the constancy of the temperature in a direct ballistic measurement.

8Eq. 2.49 was derived for the peak density (or equivalently the atom number) of a Gaussian density ¼ distribution, but it can be shown that it is also valid for other cases if the quantity ¬ is accordingly modiﬁed by a geometrical factor. 68 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

The results are shown in ﬁg. 4.10(b). The measured temperatures parallel and per- Þ

pendicular to the surface indeed stay approximately constant when ¼ is varied. The ﬂuctuations are most likely due to local inhomogeneities in the light ﬁeld.

Loading rate. The trap loading depends on both the properties of the trap and of the

atomic beam and therefore cannot be considered an immediate trap property. Never- Þ

theless, under the assumption that the beam is homogeneous in the ¼ direction, the

Ð ´Þ Þ µ ¼

loading rate distribution Þ should have the symmetry of the cloud, extend- Ö

ing radially to a ﬁnite capture radius c (see the discussion of the MOT in chapter

Ä´Þ µ = Ð dÞ Þ 2). Therefore, one expects the overall loading rate ¼ to scale linearly with the remaining capture volume above the surface. The overall loading rates were extracted from the linear increase of the atom number during the ﬁrst 30 ms of load-

ing. The results are shown in ﬁg. 4.10(c). The measured data can be ﬁt with the

Ð ´Þ Þ µ

integral over a Gaussian-shaped distribution ¼ characterized by the variance

= ´¿¼¼ ¦ ¿¼µ

Þ;Ä m, which can also be interpreted as an effective capture radius. The maximum loading rate for the large-distance case using an optimized atomic beam (i.e.

by cooling the atom source and optimizing the transverse beam collimation) was de-

½ 6

Ä =´¾:¼ ¦ ¼:6µ ¢ ½¼ 5¼± Þ =¼

termined to be s . As expected, the rate drops by for ¼ when the cloud is cut in half.

4.4.4 Evanescent-Wave Bichromatic Atom Mirror As discussed in the MOST model, the performance of the evanescent-wave mirror is expected to depend on the presence of MOT light. In the bichromatic light ﬁeld, the MOT drives transitions between the evanescent-ﬁeld dressed states and attenuates the effective mirror potential. We therefore found it important to study the performance of the mirror separately before measuring its effect on the lifetime of the MOST. Such a direct investigation is possible on the basis of our surface atom detection scheme. By counting the secondary electrons from the deexcitation of metastable atoms at the surface, one has a direct measure of the losses of atoms to the surface.

Experimental characterization method. The interesting quantity is the translucence

Ì Ì of the atom mirror, eq. 4.5. For a measurement of for different parameters of

the bichromatic ﬁeld we proceeded in the following way. First an atomic cloud was

Þ = ¼:¾ Þ

prepared in a MOT near the surface ( ¼ mm ) for standard parameters

Á = 6:8Á ; Æ = ½:45

Ë ÅÇÌ ÅÇÌ . In the trap decay phase, the magnetic ﬁeld was switched off in order to enable the surface detection scheme and simultaneously the light ﬁeld parameters of the MOT were switched to the desired values. (For the connection with the MOST measurements described below, we measured the temperature

of the optical molasses, which directly inﬂuences the translucence, with a ballistic ex-

Æ = ½:45 ½7¼

pansion measurement. At ÅÇÌ , the temperature was K as for the MOT.) While the signal from the decay to the surface was recorded, the EWM beam

was switched on. For the short time scale required for switching (60 s) the decay 4.4. EXPERIMENT 69

(a) (b) 250

1 200

[s] 0.5 fluorescence [a.u.] 0.5 time [ms] 1 150

100 parallel 0.1 Lifetime 50 perpendicular

0.05 Temperature T [uK] 0

1 0.8 0.6 0.4 0.2 0 -0.2 1 0.8 0.6 0.4 0.2 0

Þ ¼ Height of ﬁeld zero [mm] Height of ﬁeld zero ¼ [mm]

0.8

[a.u.]

Ä 0.6

0.4

0.2

fluorescence [a.u.] Loading rate 0 time [ms] 0.5 0

1 0.8 0.6 0.4 0.2 0 -0.2 Þ

Height of ﬁeld zero ¼ [mm]

Á =6:8 Á Æ = ½:5

Ë ÅÇÌ

Figure 4.10: Properties of the trapped cloud ( ÅÇÌ , ) for different Þ

heights ¼ of the magnetic ﬁeld zero. (a) – Lifetime of the cloud. The insets shows a photo-

multiplier decay curve obtained by summing over 10 individual runs from which the lifetime

½ =4¼ was extracted as a fit parameter. The dotted curve shows the model calculation for Ê s . (b) – Temperatures of the cloud as determined from a ballistic expansion measurement with the CCD camera. The increase of the fit errors close to the surface is due to the decrease in atom number. (c) – Relative loading rate from the atomic beam into the trap. The rates are extracted from the linear increase of the atom number during the first 30 ms of loading. The

dashed curve is a Gaussian error function ﬁtted to the data.

= Æ =Æ

½ ¼

signal is approximately constant, and so the translucence is obtained as Ì

Æ Æ ½ where ¼ is the count rate immediately before the switching, and immediately after. The experimental scheme is illustrated in ﬁg. 4.11 (a) together with measured signals. Before these signals are discussed, it should be explained that the single data points 70 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

that give a measure for the instantaneous count rate are obtained by summing up over single, spatially resolved detector pages that are separated by ½¼¼ s. We subdivided the available set of 64 pages into two 32-page subsets, one for the time window in which the EWM beam was turned on and one for the time window in which it was again turned off.

Qualitative signal characteristics. Fig. 4.11 (a) gives typical experimental signals

Á =

for the case that the MOT light was operated at the standard parameters ( ÅÇÌ

6:8Á ;Æ = ½:45 µ ÅÇÌ

Ë and for the maximum available power of the EWM beam that

jÆ j =¾ ¢ 5¼¼

had a detuning EÏ Å MHz. For blue EWM detuning the signal drops as expected when the beam is turned on (black curve). However, as the beam is turned off again, the signal shows an almost instantaneous increase resulting in a rapidly decaying peak. This peak probably arises from the accumulation of atoms in a thin layer adjoining the evanescent potential. If one assumes that the temperature of the atoms in that layer is the same as everywhere in the molasses, one can estimate from the duration of the peak that the layer must

have a thickness of order 10 m. Its emergence is connected to the diffusive atomic motion in the presence of the reflecting boundary. We did not observe any peak when the MOT light was off. For red EWM detuning the dressed states are interchanged and the effective reflection potential should change from repulsive to attractive; reflection should not occur. The gray curve shows an example that proves this point. When the EWM beam is turned on, a transient increase of the signal can be seen instead of a drop as in the blue case. This can be attributed to atoms that are in the range of an attractive evanescent potential and are then “sucked” to the surface, emptying the volume in the range of the potential on a fast time scale. The opposite effect, i.e. a small dip, results when the beam is turned off again (this is not very well resolved). Apart from these transient effects, we found the signal to coincide with a reference spectrum, for the case without any reflection field at all, to within the counting error. This means that the reflection by

radiation pressure from the straylight of the surface plasmon can be ruled out for the

jÆ j =¾ ¢ 5¼¼

large chosen value EÏ Å MHz. The difference in the signal behavior for red and blue detunings is a direct proof that the reﬂection process is due to the optical

potential of the evanescent wave.

Monochromatic mirror. For a quantitative study of Ì for different parameters of the bichromatic light ﬁeld, we ﬁrst checked the performance of the monochromatic

atom mirror, i.e. for the case of vanishing MOT light intensity. The result is shown

in ﬁg. 4.11 (b). As expected, Ì drops rapidly with increasing EWM beam intensity

as most atoms in the thermal velocity distribution have small kinetic energies9,and

½×

the evanescent potential always wins over the attractive 5 van-der-Waals potential at

9The initial potential energy of the atoms can be neglected in comparison to the thermal energy of the cloud. 4.4. EXPERIMENT 71

large enough distances. The data can be ﬁt very well with the model, eq. 4.5,which

is shown as a dashed line (the accumulation layer is ignored in the model, as it is a

´Þ µ

feature of the “truncation function” Ù ). For the calculation of the optical potential,

=¼:48

an effective Clebsch-Gordan coefﬁcient Ceff,EWM was used (as in previous work,

= ¾ ° ¿ by assuming an unpolarized atomic sample on the Â transition [182, 185]).

The ﬁt requires an additional ¾5± reduction of the ensuing potential. This could be due to a polarization of the atomic sample, to the transverse dislocation of the arrival

distribution with respect to the surface-plasmon spot center10 (though not accounting F

for more than 10 ±), or to a deviation in the ﬁeld intensity enhancement factor .For

¾±

large EWM intensities, Ì remains at a finite value around (still for intensities that are six times higher than the highest one shown in the figure). This is most likely due to a deexcitation of atoms at spots on the surface where dust particles pierce the evanescent field.

Varying EWM beam intensity; constant MOT intensity. The resulting behavior of

Ì with increasing EWM intensity in the presence of MOT light is shown in ﬁg. 4.11

(c). For a comparison, the corresponding monochromatic data are displayed as well

( ). The behavior is similar in the sense that with increasing EWM beam intensity, Ì

reduces and finally reaches a value of ¿± (the data point for the highest EWM intensity is obtained from the data shown in (a)). This is a crucial result for the operation of the MOST as it shows that for the bichromatic light field the mirror can become almost perfectly reflective as well. There are however two important differences compared to the monochromatic case.

First, EWM beam intensities that are two orders of magnitude above those for the

monochromatic case are needed to obtain comparable values for Ì . Comparing corre-

sponding Ì values, one concludes that the height of the potential is effectively reduced

97± Á EÏ Å by about .Second, Ì obviously possesses a threshold at small values of . This does not follow immediately from the model, since the total potential formed by the exponential optical potential and the atom-surface interaction does not itself pos-

sess a threshold for reﬂection (cf. the monochromatic case). However the behavior Í becomes understandable if one admits the negative, Þ -dependent light shift offs of the red-detuned saturated MOT standing light wave as illustrated in ﬁg. 4.4,whichisex- pected from eq. 2.22 when only the MOT light is considered. In the bichromatic case it should locally counteract the repulsive EWM potential in the antinodes of the MOT

light field. Taking the sum of the two potentials, Íoffs has to be overcome first before atoms can get reflected.

The dashed line in the ﬁgure is the ﬁtted model calculation based on eq. 4.9 and

½×

the 5 van der Waals potential, with the following parameters: For the intensity of the evanescent ﬁeld, the value previously obtained for the monochromatic case is used.

10The position of the EWM spot was measured by reducing the EWM beam diameter, and then releasing a cloud from 1 mm height. In that case, the arrival distribution for late times covered the entire ﬁeld of view of the detector. The position of the EWM beam could be localized by the dark spot burnt into that distribution and was shifted to the center of the ﬁeld of view by a parallel translation of the beam. 72 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

(a) (b)

Á =¼

ÅÇÌ

Æ =¾ ¢ 687 ½ 1 EÏ Å MHz Æ = e- ¼ 0.8 Æ =

Ì 0.6

EWM Æ

¼ 0.4 Æ ½ 0.2 0

Detector counts [a.u.] EWM on Translucence 0

0 4 8 12 0 0.05 0.1 0.15 ¾

Time [ms] Á

EWM beam intensity EÏ Å [W/cm ] ¾

Á =8:8 Á =¼:½7 ÅÇÌ mW/cm EÏ Å W/cm ½

Æ =¾ ¢ 5¼¼

Æ =¾ ¢ ¿¼¼ EÏ Å MHz EÏ Å MHz Æ Æ = = 0.8 ¼

0.8 ¼ Æ Æ = 0.6 = 0.6 Ì Ì

0.4 0.4

0.2 0.2

Á =¼ ÅÇÌ

Translucence

Translucence 0 0

0 0.5 1 1.5 2 2.5 02 4 6 8

Á EÏ Å

EWM beam intensity [W/cm ] MOT beam intensity ÅÇÌ [mW/cm ]

Figure 4.11: Characterization of the evanescent-wave mirror for a bichromatic light ﬁeld with different parameters. (a) – Illustration of the experimental measurement method based on the detection of secondary electrons with the surface atom detector. We measured the change of the

count rate when the EWM beam was turned on and off again. Black curve: blue EWM beam

detuning, gray curve: red EWM beam detuning. (b),(c),(d) – Measured translucences Ì

Æ =Æ ¼

½ of the atom mirror for blue EWM detuning and different parameters of the bichromatic

Æ = ½:45

light ﬁeld. The detuning of the MOT was ÅÇÌ for all measurements. The dashed curves are model calculations as described in the text.

The ﬁt requires the 30-fold single-beam intensity for the total MOT intensity (which is

consistent with a partial coherence between the four MOT beam pairs), and an offset

= ¼:¾6 ~ term Íoffs for the effective MOT potential (this value is one order of magnitude smaller than the values one would calculate from eq. 2.22 for the monochromatic case). With the offset term included, the ﬁt reproduces the data very well. 4.4. EXPERIMENT 73

Varying MOT intensity; constant EWM intensity. The transition from the

monochromatic to the strongly bichromatic case is shown in ﬁg. 4.11 (d). For in-

Æ = ½:45 Ì creasing MOT light intensity at ÅÇÌ , increases almost linearly. The dashed curve is the model calculation based on the parameter set obtained from the ﬁt

for ﬁg. 4.11 (c), i.e. it contains no free ﬁt parameters. The offset potential is modeled

¾ ¾ ¾

Í = a ¢ [½ · ! =´Æ · =4µ] !

as ln ,where Ê;Å Ç Ì is the Rabi frequency ÅÇÌ offs Ê;Å Ç Ì

resulting from the 30-fold single-beam intensity, and a is a proportionality constant

¼:¾6 ~ that ﬁxes Íoffs to for the parameters of ﬁg 4.11 (c). Of course the model only

applies to the Doppler cooling regime where the temperature Ì of the cloud does not depend on intensity, cf. eq. 2.43.

4.4.5 Combined MOT–Atom Mirror

At this point of the discussion, the basic properties of the “ingredients” of the magneto-

optical surface trap have been characterized. The lifetime of the trapped cloud reduces Þ

when the magnetic field zero ¼ is brought close to the surface as a result of losses at the surface, while the temperature of the cloud remains unaffected. By adding the light field of the evanescent-wave atom mirror, atoms are still reflected in the presence of MOT light, despite severe bichromatic attenuation effects. We have shown that the reflection is due to the optical potential of the evanescent wave. The last point to demonstrate now is that by adding the magnetic field, atoms can actually be trapped in this configuration.

Lifetime. The most direct property to look at as a signature for trapping is the lifetime

Þ « = « ´Þ µ

× × ¼ of the atom cloud. At a given height ¼ the surface loss rate takes a value

according to eq. 4.3, and when the mirror is turned on, it should decrease to a value

« = «

Ì × Ì

×;eÚ with the translucence of the atom mirror. The expected lifetime of the

½ ½

= ´« · « µ « = ´¿ µ

×;eÚ ¼ cloud is then given by ¼ ,where s is the background-gas

value.

Þ =¼:¼

For the experiment, we prepared a trap with ¼ mm and standard MOT pa-

½ ½

Ê=¾µ «

rameters. In that case the surface-collision limited lifetime was ( ´¼µ= ×

50 ms, as in the above lifetime-versus-distance measurements. We measured the life-

Æ =¾ ¢ 5¼¼

time as a function of the EWM beam intensity for EÏ Å MHz, i.e. for the

same parameters as in the measurement of Ì ,ﬁg. 4.11 (c). The result is shown in ﬁg. 4.12. At the highest achievable EWM beam intensity, the lifetime rises to a value of around 400 ms. Being an order of magnitude above the value for vanishing inten-

sity, this clearly demonstrates the functionality of the MOST. For the model calculation

(dotted curve) the parameters are those of the Ì measurement except for the offset

= ¼:57 ~ potential which was chosen as a free fit parameter, yielding Íoffs . The inset in the figure shows the expected saturation of the lifetime on a semi-logarithmic plot. To verify the evanescent nature of the reflection process, we measured the lifetime

of the trap at 5¼¼ MHz red detuning of the EWM beam at maximum power. Within the ﬁt error of 5 ms, the lifetime remained at its zero-intensity value of 50 ms, in agreement 74 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

0.4 1 0.5 0.3 0.1 0.05 0.2 0 2 4 6 8 10

Lifetime t [s] 0.1

0 0.5 1 1.5 2 2.5

¾ Á

EWM beam intensity EÏ Å [W/cm ]

Þ =¼:¼

Figure 4.12: Lifetime of the MOST ( ¼ mm) as a function of the EWM beam intensity.

Á =6:8Á ; Æ = ½:45 Æ =¾ ¢ 5¼¼

Ë ÅÇÌ EÏ Å The light ﬁeld parameters are ÅÇÌ and MHz. The inset (with the same units as the main plot) shows the extrapolation of the lifetime for

higher powers of the EWM beam.

with the measurement of Ì .

Other properties. The cloud temperature for the operating MOST could not be directly measured with the CCD camera due to technical problems associated with the intense straylight of the EWM surface plasmons. It is very unlikely, however, that the

temperature of the cloud is affected by, e.g., diffusive heating in the evanescent ﬁeld:

5 ½ ½¼ The damping rate in the MOT s is orders of magnitude larger than the trial rate

Ê with which trapped atoms probe the evanescent ﬁeld, such that atoms rethermalize quickly. Also the scattering rate from the straylight of the evanescent ﬁeld is orders of

magnitude smaller than the scattering rate of the saturated MOT. Therefore, it should be relatively safe to assume an averaged temperature around ¾¼¼ K. We also measured the loading rate in the presence of the reﬂection ﬁeld and found

no difference to the case without the field, to within an error of 5±. This was as expected since the evanescent field is not strong enough to reflect atoms that are much faster than those in the trap, and also since the atoms from the beam were incident parallel to the surface. The equilibrium between loading and decay determines the steady-state atom number in the trap. At the highest possible EWM beam intensity, we measured an atom

number of

=´½:¿ ¦ ¼:4µ ¢ ½¼ Æ (4.11)

with the calibrated photomultiplier. For this number, the peak atom density is on the

¿ 9

order of ½¼ cm . The exact value depends on the trapping volume above the surface 4.5. CONCLUSIONS 75 which could not be determined directly with the CCD camera as a result of the intense straylight from the surface plasmons. Such a density is already in the regime where Penning collisions become important; therefore the achievable steady-state atom number cannot be expected to be much higher, even for perfect reﬂectivity of the atom mirror.

4.5 Conclusions

We have demonstrated and characterized the magneto-optical surface trap (MOST), which is a combination of an 8-beam MOT with an optical evanescent-wave (surface- plasmon) atom mirror. In this trap, the atoms are in contact with an evanescent ﬁeld

that separates the atomic cloud from the mirror surface by a fraction of an optical

:¿ ¦ ¼:4µ ¢ ½¼

wavelength. In the experiment, we were able to trap ´½ atoms with a

´¿9¼ ¦ ¿¼µ Þ

lifetime of ms in the situation where the zero ¼ of the magnetic quadrupole ﬁeld was located at the surface. We have investigated the behavior of the trapped cloud for varying distances from

the surface (in the absence of the evanescent ﬁeld) and found a dramatic decrease of Þ

the lifetime by two orders of magnitude to about 50 ms when ¼ was reduced from 1 mm above the surface down to zero. For large distances, the behavior of the trap resembles that of a standard MOT. However a characteristic modulation of the cloud

density normal to the surface can be observed, and the velocity distribution of the cloud

Þ =¼

is clearly anisotropic. For a cloud with ¼ with a lifetime of 50 ms we have shown that the evanescent field of the atom mirror can increase the lifetime by one order of magnitude, which can be expected to be limited by the available power for the atom mirror. We have investigated the atom mirror in the presence of the MOT light and found a drastic reduction of its reflectivity compared to the case without MOT light, due to a bichromatic effect. We have characterized this effect for different parameters of the bichromatic light field. A simple model of the MOST has been developed which is consistent with the experimental observations. 76 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP Chapter 5

Continuous Loading and Manipulation of Atoms in a Surface Waveguide

We have demonstrated the continuous loading of a planar waveguide for atoms

in sub-m distance from a metallic surface. The loading of the waveguide, which is formed by the optical potential of a red-detuned standing light wave above a mirror surface, is achieved via evanescent-ﬁeld optical pumping from a magneto- optical surface trap (MOST). We have demonstrated light-induced elements for the manipulation of atoms in the waveguide geometry, including a continuous atom source, a switchable channel guide, an atom detector and an optical surface lattice. We have combined the source, the channel and the detector to form a simple atom- optical integrated circuit.

5.1 Introduction

In the well-established field of integrated optics, optical circuits have been built that combine a number of miniaturized, interconnected optical components on a common substrate such as light sources, optical waveguides, modulators and detectors [134]. These devices find widespread use in telecommunication and instrumentation techniques. The atom-optical analogue to integrated optics, i.e. the realization of atom- optical setups in a miniaturized, substrate-based geometry, offers intriguing prospects for atom interferometry [8] and quantum computing [135,136] and also is of interest for the study of atomic gases in low-D [72,71] and close to surfaces [44,109]. Over the last years, techniques to guide laser-cooled atoms over macroscopic distances have been developed, based on optical potentials in hollow-core optical fibers and laser beams [116, 117, 118, 119] and magnetic potentials along current-carrying wires [120, 121, 122]. This has recently been extended to the use of microfabri- cated wires on substrates for which isolated components such as weakly confining

77 78 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS... linear [124, 125, 126] and (switchable) Y-branch atom guides [127, 128], magnetic traps [129] and a conveyor belt [130] above a substrate have been demonstrated. On the other hand several schemes have been proposed for the realization of surface traps with tightly conﬁning 1D optical and magnetic potentials [105,106,107,108,112]that can be interpreted as planar waveguides for atoms. One of these schemes, in which laser-cooled atoms are transferred into a single potential layer of a standing light wave

(SLW) in sub-m distance from a reﬂecting surface via evanescent-wave optical pumping [107] has been demonstrated by us in earlier work on metastable argon [110,111]. The present work addresses the manipulation of atoms in our planar waveguide. This opens a novel route to integrated atom optics. The waveguide provides a planar geometry above a substrate surface into which atom-optical components are subsequently integrated, and transverse guiding inside the waveguide is achieved by laterally structuring the waveguide potential. This all-optical approach is in close analogy to the realization of integrated optics [134]. One of the central issues of the present work is the continuous loading of the waveguide, which allows for the realization of a CW atom source in the planar waveguide geometry. Such a continuous loading scheme also is of interest for scenarios to reach quantum degeneracy in low-dimensional, open systems [92,100,112]. This chapter is divided into two main parts. The ﬁrst part discusses some basic concepts of continuous loading and the implementation of atom-optical components, and the second part describes our experimental work and results.

5.2 Basic Concepts

5.2.1 Overview

Our experimental schematic is shown in ﬁg. 5.1, together with the relevant levels

and transitions in argon. As in our earlier work, Ref. [110], the waveguide potential

½×

for ¿ atoms is generated by a 1D standing light wave (SLW) that is red detuned with

½× ° ¾Ô 4 respect to the ¿ transition. The SLW itself is generated by reﬂecting a Gaussian

laser beam at the gold-coated prism surface. Parallel to the surface, the atoms in the 4

SLW are weakly conﬁned and behave classically (on the order of ½¼ bound states are populated), while perpendicular to it there exist only a few bound states. The SLW waveguide is an atom-optical analogue to planar optical waveguides known from integrated optics1 [134].

The scheme for the continuous loading of the waveguide combines the magneto-

½×

optical surface trap (MOST) with an evanescent ﬁeld for optical pumping to ¿ (OP).

½×

The MOST serves a reservoir of 5 atoms in contact with an evanescent-wave mirror (EWM) in which the trapped atoms approach the surface to within a fraction of the

1The analogy is based on the formal equivalence of Helmholtz’s equation to the (time-independent)

! Ò

Schrödinger equation [4]: For an electromagnetic wave E (of freq. ) in a medium with index one

¾ ¾ ¾ ¾

Ö · k µE = ¼ k = !=´c=Òµ ´Ö · k µ = ¼

has ´ ,where .Forthewavefunction one has ,where

= ´¾Å ´E Í µ =~; E Í k in which istheenergyoftheatomand the optical potential. 5.2. BASIC CONCEPTS 79

(a)1.5 mm (b) WG

2p4 2p9

Detection MOST - OP 1s 1s e MOT 5 3 WGD 820 nm WG 715 nm Ar* (1s3) 812 nm 795 nm EWM

EWM OP WGD * 1s3 * 1s5

Figure 5.1: (a) Scheme for experiments on “integrated atom optics” and (b) relevant levels

½× and transitions in argon. An array of tightly conﬁning planar waveguide layers for ¿ atoms is formed by the optical potential of a red detuned standing light wave (WG). Atoms are loaded

into the lowest waveguide layer 820 nm from the surface via evanescent-ﬁeld optical pumping

½×

(OP) from the steady-state MOST for 5 atoms, which is realized by combining a modiﬁed

MOT at the surface with an evanescent-wave atom mirror (EWM). The MOST is loaded from

½× a slow atomic beam. This CW loading scheme realizes a source of ¿ atoms inside the waveguide. Atoms propagate in the waveguide until they reach the detection area (WGD) where they hit the surface and are detected via secondary electrons. The detection scheme is based

on the deformation of the conﬁning potential with an attractive evanescent ﬁeld.

½×

optical wavelength by diffusive motion. The OP ﬁeld is used to transfer 5 atoms to

½× ½× ¿ the state ¿ in a short range above the surface. The optically pumped atoms scatter

locally into the few waveguide potential layers that are in the range of this ﬁeld2.

½× ° ¾Ô ½× ° ¾Ô

9 ¿ 4 Owing to the large difference in the wavelengths of the 5 and transitions of 17 nm, the atoms in the waveguide are completely decoupled from the

MOST light, and vice versa.

½×

For detection, we let the metastable ¿ atoms collide with the gold-coated surface and detect the secondary electrons ejected upon impact with the atom detector described in chapter 2.1.3. Making use of this method, we have implemented a scheme for an integrated atom detector. It is based on the deformation of the lowest waveguide layer with an attractive evanescent ﬁeld in a small spot (WGD) that results in the release of atoms towards the surface. The implementation of the source and the detector at separate positions in the waveguide layer allows for the realization of an elementary atomic beam experiment in the quasi-2D geometry of the lowest waveguide layer as shown in ﬁg. 5.1.

2The CW loading mechanism allows to couple atoms into the waveguide, directly from an atomic

beam. One might therefore be led to interpreting it instead as the realization of an input coupler for

½× atoms. However, the waveguide ﬁeld only interacts with atoms in the ¿ state, which are produced by optical pumping in the evanescent ﬁeld. Therefore the term source is appropriate for those atoms. 80 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

5.2.2 The Waveguide

Optical potential. In the far-detuned limit, the conﬁning optical potential generated

´Öµ

by the intensity distribution Á of the SLW is given by

~A Á ´Öµ

795

Í ´Öµ= ;

ÏG;diÔ (5.1)

8Á Æ

×;795 ÏG

6 ½ ¾

A = ½8:6 ¢ ½¼ × Á = ¼:77

×;795

where 795 is the Einstein coefﬁcient, mW/cm is the Æ

effective saturation intensity, and ÏG the detuning of the beam with respect to the

½× ° ¾Ô Æ < ¼

4 ÏG ¿ transition. Because of the red detuning , the minima of the optical potential coincide with the antinodes of the SLW.For the s-polarization of the WG beam

the intensity distribution of the SLW is given by

Á ´Öµ = Á ´Ü; Ý µ ×iÒ ´k Þ µ ¼ ¼ (5.2)

with

h i

¾ ¾

¾Ü ¾Ý ¾ cÓ×

Á ´Ü; Ý µ = 4Á eÜÔ k = ;

ÏG ¼

¼ and (5.3)

´Û = cÓ× µ

ÏG i ÏG

ÏG

Á =796 Æ = ¾ ¢

ÏG ÏG

where ÏG is the center intensity, nm the wavelength (for

6¼¼ ¡ = ½:¾5 Û ÏG

GHz red detuning, for which the increase in wavelength ÏG nm),

=45

the waist and i the angle of incidence of the waveguide beam. Close to the surface the attractive atom-surface interaction becomes important. The

total potential of the waveguide in a good approximation is given by

Í = Í · Í ;

ÏG CÈ

Ï G;diÔ (5.4)

Í ´Þ µ

where CÈ is the Casimir-Polder term, eq. 2.57, in which the static polarizability

¿¼

½× « =4¯ ¢ ´49:5 ¦ ½µ ¢ ½¼

¼;½× ¼

for the state ¿ is given by m[175]. The resulting ¿

total potential is illustrated in ﬁg. 5.2 for typical experimental parameters. As a result =¼ of the atom-surface interaction, the WG layer closest to the surface (i ) is strongly

deformed and does not provide conﬁnement while the interaction does not affect the

= ½ conﬁnement in higher layers. The distance of the potential minimum in layer i fromthesurfaceis820nm3, and the layers are separated by 560 nm.

Guided modes. In the optical potential, the motion of atoms perpendicular to the

surface is described by the 1D Schrödinger equation

h i

@ · Í ´Þ µ = E

ÏG;diÔ (5.5)

¾Å

= ¾7:9·i¼:9¼

The gold ﬁlm on the prism surface for 796 nm has a measured dielectric number "

:¼8 (cf. chapter 2). As a result, in-plane vector of the reﬂected beam is phase shifted by ½ (instead of for a perfect metal). This results in a 23 nm shift of the SLW towards the surface, compared to the ideal case. 5.2. BASIC CONCEPTS 81

Distance from surfacez [µm] WG s-pol. 0 0.5 1 1.5 2 2.5 0 2p (i=0) 4 -20 795nm -40 i=1 i=2 i=3 i=4 -60 1s3

WG potential [µK]

Á =44

Figure 5.2: Waveguide potential for a WG beam with intensity ÏG W/cm and 1.25 nm red detuning. While the motion of atoms is quasi-free parallel to the surface, it is quantized in the normal direction (shown are levels in the harmonic approximation), conﬁning the atoms

in planar waveguide layers i. Close to the surface, the optical potential is deformed by the

atom-surface interaction.

Í ´Þ µ

for the atomic wavefunction . Because of the periodic sinusoidal form of Ï G;diÔ ,

this equation is equivalent to Mathieu’s differential equation [170] whose eigenvalues

×iÒ ´k Þ µ ´k Þ µ ¼ form an energy band structure. In the harmonic approximation ¼ ,

which is a crude but sufﬁcient approximation for our purposes4, one obtains from eq.

5.5 harmonic-oscillator states j with eigenvalues

E = · ~ª ª = k ¾Í =Å;

Ó×c;Þ Ó×c;Þ ¼ ¼

with (5.6)

¾ Í

where ¼ is the potential (as deﬁned in eq. 5.1) that corresponds to the maximum

Á ª =¾ ¢ 8¼ = k =´¾~µ ¢

Ó×c;Þ B

intensity ¼ . For typical experimental WG parameters, kHz

:8 7 K, which corresponds to a number of ﬁve bound harmonic-oscillator states (i.e. guided modes) perpendicular to the surface.

Losses. Another important aspect of the waveguide is the loss of guided atoms from

the WG potential.

½× ° ¾Ô 4 Photon scattering on the ¿ transition is connected to heating of atoms out

of the WG potential as well as to optical pumping to untrapped internal atomic states

¾Ô

(with a branching ratio of 0.44 in the state 4 ). The rate for photon scattering is given

hÁ i

¾Ô

795

= ;

×c; (5.7)

8Á

×;795

ÏG

hÁ i = h jÁ j i j i

where the mean intensity is determined by the overlap of the state

Æ < ¼

of the atom with the WG light ﬁeld. For red detuning ÏG , the scattering rate

4Band structures have been studied previously in a 3D blue optical lattice experiment [210]thatwas realized with our beam machine in 1996 and is described in detail in Ref. [184]. Cf. also Ref. [185]fora discussion of the case of the 1D waveguide potential.

82 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

is highest for the ground state and decreases with the excitation .Since ×c;

Á =Æ Í » Á =Æ

ÏG ÏG ÏG

and Ï G;diÔ , it is possible to suppress the scattering rate while ÏG maintaining the WG potential by increasing both the intensity and the detuning of the

WG beam. For our experimental parameters, the photon scattering losses are on the

½ order of ½¼ s . Collisional losses arise from inelastic collisions (1) between WG atoms and ambient background gas atoms, (2) between WG atoms and impurities on the surface, or (3)

between WG atoms themselves. This is expressed by the loss rate

= « · ¬ Ò ;

¼ ¿¿ ÏG

cÓÐ Ð (5.8)

« ¬ ¿¿

where ¼ includes the ﬁrst two contributions, is a rate constant for two-body col-

½× Ò ÏG

lisions between ¿ atoms and is the density of atoms in the WG potential. In

½×

the presence of the MOST for CW loading, the background-gas density of 5 atoms «

reached a level for which the collisional loss rate ¼ became comparable to the rate for photon scattering.

Tunneling effects may crudely be estimated in the WKB approximation as

h i

½=¾

dÞ ¾Å ´E Í µ ; ª eÜÔ

ÏG Ó×c;Þ

ØÙÒÒ (5.9)

E <Í

ÏG for the higher modes. For the lower modes, band-structure calculations based on Math- ieu’s equation and a numerical treatment of the time-dependent Schrödinger equation of the system [185] show that the tunneling rates are negligible compared to photon scattering, which is consistent with our experimental observations. Thermal contact with the surface. A recent paper discusses the thermal contact of particles in surface traps with room-temperature surfaces [109]. The coupling depends on the mode density of thermal electromagnetic ﬁeld ﬂuctuations at the trap frequen-

cies, the type of interaction and the distance from the surface. Spinless neutral atoms

½×

such as argon in the ¿ state are only affected by time-dependent distortions of the

van-der-Waals potential due to thermal surface oscillations. At distances above ½¼¼ nm,

6 ½ the corresponding heating rates are below ½¼ s [109] i.e. negligible.

5.2.3 Continuous Loading

½×

In earlier work we have demonstrated a pulsed loading scheme in which 5 atoms were collected and then dropped from a standard 6-beam MOT half a centimeter above thesurface[110], from which they expanded ballistically. Atoms incident on the surface were decelerated in the EWM potential and optically pumped by the OP, ideally at their classical turning point in the EWM. This has been modeled in Ref. [107]onthe basis of a Quantum Monte Carlo simulation that tracked the motion of the atoms in the conservative potential until optical pumping occurred. For the present loading scheme (cf. ﬁg. 5.3 (a)), the situation is qualitatively different. Since the waveguide is loaded from the steady-state MOST, atoms that enter the range of the OP ﬁeld do not have a nearly uniform velocity but are subject to

5.2. BASIC CONCEPTS 83

½× ¾Ô 9 diffusive motion while cycling between 5 and in the bichromatic EWM light ﬁeld. Here, a comparable simulation of the atomic motion would not only be much more demanding numerically but would also require an exact theoretical understanding of the simultaneous interaction with the (spatially modulated) bichromatic light ﬁeld, which goes far beyond the simple model presented in chapter 4. Based on the MOST

model, a crude description can however be given. × ½ n MOST

WG 5

7½5

OP0 intensity

¾Ô

MOT 4

795

½×

¿ Ë } MOST

OP =½

EWM

=¼ WG pot. (a) (b)

Figure 5.3: Scheme for continuous loading (a) and simple model of the loading process (b).

½×

5 Atoms from a slow atomic beam are collected and cooled in the magneto-optical surface trap (MOST). In this trap, which is the combination of a surface-MOT and an evanescent-wave

atom mirror (EWM), atoms approach the surface to within a fraction of an optical wavelength

½× by diffusion. In the short range of the OP ﬁeld for optical pumping to ¿ , atoms are locally transferred from the MOST into the potential of the waveguide via optical pumping (see text).

The MOST density Ò is modeled as spatially uniform over the length scale of the evanescent fields5. As illustrated in fig. 5.3 (b), this spatially flat reservoir of atoms is

”tapped” at the surface by the evanescent OP ﬁeld,

Þ=

7½5

Á ´Öµ F Á e ;

7½5 ÇÈ

ÓÔ (5.10)

F 7½5

where 7½5 and is the decay length and ﬁeld intensity enhancement of the sur- Á

face plasmons and ÇÈ the power in the OP beam. The coupling to the light ﬁeld on

resonance is expressed by the Rabi frequency

! A Á ´Öµ=´¾Á µ;

7½5 ÓÔ ×;7½5

Ê;Ç È (5.11)

5 ½

A = 6:¾5 ¢ ½¼ Á = ¼:¼¿6

×;7½5

where 7½5 s and mW/cm . This coupling leads to a

¾Ô ½×

4 ¿ population 44 of the state , from which the atoms then decay to . For weak

coupling, this rate is given by

¾ ¾ ¾

·4Æ µ = A ; ! =´

795 44 44

ÇÈ and (5.12)

ef f Ê;Ç È ¾Ô 4

Very close to the surface this is certainly a very crude approximation since Ò should vanish near the EWM potential maximum.

84 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

6 ½

= ¿¿ ¢ ½¼ ¾Ô

Ô 4

The linewidth ¾ s is the full with of the state , and the effective 4

6 Æ

detuning ef f that accounts for the coupling to the other light ﬁelds . By being op-

½× j i

tically pumped, ¿ atoms can scatter into a bound (harmonic) state of the locally

Ôi

overlayed WG layer. For an atom in momentum state j this probability is given by

Ë = jhÔj ij

the Franck-Condon factor Ô . For the thermal momentum distribution of the MOST reservoir, a thermally averaged FCF [92] can be calculated, which can be

written as

¾cÓ× £ ¾ ¾

¾ a =´¾ µ

Ë = h Ë i = daÀ ´aµ e ; Ô

(5.13)

¾ !

ÏG

£ = h= ¾Å k Ì ¾¼ Ì =

B Þ Þ

where dB nm is the thermal de Broglie wavelength (for

½=¾

À = [¾ · ~ª =´~k Ì µ] ¾¼¼

Ó×c;Þ B Þ

K), the are Hermite polynomials and . For the

k Ì ~ª

Þ Ó×c;Þ

standard MOST and WG parameters, with B , the Franck-Condon factors ¾

Ë ½¼

all have comparable values . Provided that the MOST reservoir can be

regarded inﬁnite (such that Ò is not reduced much by loss from optical pumping), the

i Þ

loading rate into a waveguide layer centered about i can be written as

Ð Ò´Þ µ ´Þ µ Ë

i ÇÈ i

Ï G;i (5.14)

¾Ô

For weak coupling to the other ﬁelds ( ef f ) the loading rate therefore should 4 drop exponentially from one layer to the next, and it should be proportional to the OP beam intensity and the lifetime of the MOST.

5.2.4 Surface-Sensitive Detection. The scheme for an integrated atom detector is illustrated in fig. 5.4 (a). A beam that is split from the WG beam is incident from below the surface at the surface-plasmon resonance angle. It is used to generate an additional attractive evanescent potential (“waveguide deformation”, WGD) which simply adds to the WG potential, provided that the polarization of the evanescent light field is orthogonal to that of the WG. The effect of the evanescent field is illustrated in fig. 5.4 b: when the WGD beam is on, the attractive potential bends down the WG potential such that atoms are released towards the surface8. The number of layers that lose their confinement depends on the

power available in the WGD beam (the evanescent ﬁeld intensity has a decay length

= ¿½6 ÒÑ i i ·½

796 , and so going from layer to requires a power increase by a factor

½×

The effective detuning can be expected to arise from light shifts of the state 5 due to the EWM

¾Ô

andtheMOTaswellasofthestate 4 due to the WG [107]. Yet another additional contribution can

½× ° ¾Ô 9

be expected from the cycling transitions 5 that destroy the coherent internal evolution of the

½× ¾Ô ¾Ô ½× ½×

4 4 ¿ 5

Rabi oscillation between 5 and , similar as the decay from to itself: The state acquires

=¾ ½× ¾Ô

¾Ô ¿ 4

a“width” ×c that adds to the linewidth , thereby slowing the decay to via further (this is 4 similar to the Quantum Zeno effect [211]).

7 Ì

For much lower reservoir temperatures Þ the lower states are more likely to be populated. 8This scheme was devised by the author already for earlier work [111], where it was used to characterize the spatial selectivity of the pulsed loading scheme. 5.3. EXPERIMENT 85

of six). In the experiments we probed the population of the “surface waveguide layer” =½ i , as illustrated in the ﬁgure.

(a) (b) Distance from surfacez [µm] WG s-pol. 0 0.5 1 1.5 2 2.5 0 i=1 i=2 i=3

-20 WG -40

p-pol. -60 WGD

WG potential [µK] WG+WGD

Figure 5.4: Surface-sensitive detection. The attractive optical potential of the WGD beam

=¿½6

(exponential decay length 796 nm) deforms the WG potential, such that guided atoms are released towards the surface.

5.3 Experiment

5.3.1 Experimental Setup The setup for our experiments is depicted in ﬁgs. 5.5 and 5.6. It is a straightforward extension of that described in chapter 4, additionally including beams for the waveguide (WG) and detection (WGD) at 796 nm and optical pumping (OP) at 715 nm.

The WGD and OP beams were incident on the gold-coated surface at their surface-

=¾77

plasmon resonance angles, at which the evanescent-ﬁeld parameters are 7½5 nm,

= ¿½6 F =¿¾ F =½½½

7½5 796 796 nm, and , cf. chapter 2.

5.3.2 Continuous Loading The ﬁrst step towards integrated atom optics in our system was the realization of a CW loading scheme for the waveguide, which in a more general context is also the ﬁrst-time demonstration of CW loading of an optical trap.

For the demonstration and a study of the loading mechanism we chose the waist

Û = ¼:4¿

of the WG beam at the surface as ÏG mm, which was comparable to the transverse waist of the atom cloud in the MOST. For the initial alignment of the setup,

the position of the MOST cloud was taken as a ﬁxed parameter9. To align the OP beam

Û = ¼:7¾ Á = 6:½ ½×

ÇÈ 5

( ÇÈ mm, mW/cm ) we then released a cloud of atoms from

Þ = ½

aMOTwith ¼ mm, which gave rise to a broad arrival distribution that covered the entire ﬁeld of view of the surface atom detector. The OP spot could be localized

9As remarked earlier, the MOST proved to be an extremely fragile object that needed a lot of time- consuming beam alignment to be sufﬁciently stable. 86 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

Figure 5.5: Experimental configuration for the experiments on trapping and manipulation of atoms in the waveguide. The configuration is an extension of that of the MOST depicted in fig. 4.2, including additional beams for the waveguide (WG), optical pumping (OP) and surface-sensitive detection (WGD). The EWM, OP and WGD beams are incident at the respec-

tive surface-plasmon resonance angles.

½× ½× ¿ by turning on the EWM, suppressing the 5 atoms but transmitting all pumped atoms. After aligning the OP, we optimized the relative alignment of the OP, EWM and WG spots by using the pulsed loading mechanism demonstrated in earlier work, cf. Ref. [110], and maximizing the number of atoms in the WG potential.

The TOF signal. In the aligned setup, we switched to the conﬁguration for continu-

Þ = ¼:5 Á =½:¼ EÏ Å

ous loading by starting with a steady-state MOST ( ¼ mm, W/cm ,

Æ =¾ ¢ 687 ¡ =½:¾5 ÏG

EÏ Å MHz) to which we added the OP and WG beams ( nm,

Á =6¼

ÏG mW/cm ). After about 90 ms, the OP beam was turned off to stop loading,

followed by the MOST about 10 ms later. When the WG was subsequently switched

off, we observed a rapidly decaying TOF peak with a width of about ¿¼¼ s, as shown

½×

in ﬁg. 5.7 (the EWM was left on as a shield for residual 5 atoms during the detection phase). The appearance of this signal clearly shows that the CW loading mechanism works10. 10In some initial experimental runs we observed overlayed spectra that varied slowly on the time scale of the WG signal peak [212]. These could be minimized by lowering the MOST cloud, while the WG peak itself remained nearly unaffected, or by realigning the beams. Probably they were due to intense 5.3. EXPERIMENT 87

EWM WGD M3

MOT P M P 1 M M3 2 Zeeman slower

M4 M2 OP

M1 WG

(a) ABS (b)

Figure 5.6: (a) – Experimental setup for the experiments with the waveguide (top view). The atomic-beam slowing laser beam (ABS) passes the prism (P) at grazing incidence. The MOT

beams enter the chamber through windows on the top side of the chamber. The EWM, OP and

Å Å ¾ WGD beams are deflected at mirrors ½ and inside the chamber to the back side of the gold film. The EWM and WGD are separated with a polarizing beam splitter cube behind the fiber.

The waveguide (WG) beam is incident on the surface at 45 Æ . For this purpose, two deﬂection

Å Å 4 mirrors ¿ and above the prism are used which are mounted to the atom detector setup. The elements in the dashed rectangle in the bottom (cyl. lens and thin wire/ razor blade) are used for the realization of a channel waveguide and a switch, and the retroreﬂecting mirror in the other dashed rectangle for is used for the realization of a surface lattice. The symbols for the optical components are explained in ﬁg 2.12. (b) – View into the main chamber. The large tube at the left is the rear end of the Zeeman slower; the two reentrant tubes at 45 degrees contain the MOT coils.

Loading rate. For a characterization of the loading process, we measured the loading curve of the waveguide. For that purpose, the loading time was increased successively

in steps of 5 ms and the TOF signal was recorded each time. The measurement se-

Á =44

quence is illustrated in ﬁg. 5.8, and the measured loading curve (for ÏG W/cm ,

¾ ¾

Á = 6 Á = ½ EÏ Å

ÇÈ mW/cm and W/cm )isshowninﬁg.5.8. The increase of the Æ

atom number ÏG in the loading phase can be ﬁt by

ÏG

« Ø

ÏG

Æ ´Øµ= ½ e :

ÏG (5.15)

ÏG

Ä ½× ¿

The quantity ÏG is the overall loading rate for atoms in the WG potential, and «

ÏG is the overall one-body loss rate from the waveguide. The ﬁt of eq. 5.15 to the

¿ ½

Ä =´½:6 ¦ ¼:5µ ¢ ½¼

data yields a loading rate of ÏG s into the waveguide potential,

i = ½ of which a fraction of ¾5± is loaded into the lowest populated layer for the

OP straylight near local surface scatterers that lead to signiﬁcant optical pumping of atoms in the MOST

½ outside the range of the evanescent ﬁeld, i.e. into the “bulk” layers i . Apart from these initial runs, optical pumping by surface-plasmon straylight was however not an issue. 88 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

cts. cts. 1.5

0.75 0

y-0.75 [mm] WG -1.5 -1.5 -0.75 0 0.75 1.5 x [mm] MOT Integrated counts

0 012 3456 OP EWM time [ms] CW MOST EWM OP WG

Figure 5.7: Experimental TOF signal of the CW loaded atom waveguide. The spatially resolved Ý

image gives the lateral distribution in the waveguide. The projections on the Ü and axes can

Û =¼:¿¼ Û =¼:¿¿ Ý be ﬁt with Gaussians, yielding waists Ü mm and mm. chosen loading parameters (see below). In other experimental runs, we were able to

optimize the loading further by realigning the various beams, and we achieved steady-

Æ ½¿¼

state atom numbers up to ÏG . Assuming the same loss rate, this corresponds

½ ¿

Ä 4:8 ¢ ½¼

to an increase of the loading rate to ÏG s .

Æ =

Loss rate. In the loading curve, the atom number reaches a steady state value ÏG

Ä =« Æ = ¿6 « = ´45 ¦ ¿µ

ÏG ÏG ÏG

ÏG .With , one obtains a loss rate s ,which

½× ° ¾Ô =¿¾

4 ×c exceeds the photon-scattering rate on the open ¿ transition, s .To investigate this further, we measured the decay of the WG population after the loading phase. In this measurement, the loading time was held ﬁxed at 200 ms while the

decay time in the measurement sequence was sequentially increased. We measured an

« =´¿½¦ ¾µ

exponential decay with rate ÏG;dec s , consistent with the rate for photon

scattering11. This measurement shows that the additional losses during the loading

¡« =´½4¦ 4µ

phase, ÏG s , are due to collisions between atoms in the WG and atoms in the MOST, which act as a background gas12.

½×

Non-exponential decay due to collisions between ¿ atoms in the WG potential was observed for WG

9 ¿ 8 ¿ ½¼ densities ½¼ cm [110], whereas in our case the densities were of order cm (the 3D density is

calculated by approximating the distribution in the direction perpendicular to the surface as a Gaussian

´¾ ¾µ with waist 796 nm= ).

« ¡« ÏG

The collisional contribution c can be used to deduce a lower limit for the rate constant

½ 9 ¿

¬ = Ò ¡« Ò ½¼ c

¿5 . With the MOST density being of order cm (cf. chapter 4), one obtains

8 ¿ ½

¬ ½¼

¿5 cm s . (Qualitatively similar collisional losses were also observed by J. Stuhler et al. [103] 5.3. EXPERIMENT 89

Phase MOST/OP loading decay det.

Duration [ms] 70 DtL 5 2.5 30 AB/ABS

EWM { MOT

MOST B gate open OP

125µs 125µs WG det. trig.

detector signal pages

1 { 64

Æ ÏG

Figure 5.8: Single sequence step for measuring the WG loading curve. The loading is

started after an initial MOST/OP phase by switching on the WG beam. After a variable time

¡ Ø =¼:::¾¼¼ ½× ¿ Ä ms, the OP and MOT beams are switched off to stop loading, and the atom

distribution in the WG potential is subsequently detected. During detection, the EWM beam

½× is on in order to suppress counts from residual 5 MOST atoms. The detector is gated for a

2.5 ms time window by turning off the magnetic ﬁeld. This gating was used to store data for

¡ Ø different values of Ä inthesameimagesequence.

G 30 Ï Æ

Atom number

0 50 100 150 200

¡Ø

loading time Ä [ms]

Figure 5.9: WG loading curve determined from the summation over 200 sequential runs. Error

bars are due to the signal background (MOST atoms and atom beam). The dashed line is an

« = ´45 ¦ ¿µ exponential ﬁt with time constant Ä s .

for the case of a MOT overlapped with a magnetic trap.) 90 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

Parameter dependence and spatial selectivity. To characterize the steady state fur-

ther, we measured the dependence of the total atom number and of the population of =½ the lowest layer i on the intensities of the EWM and OP ﬁelds. For that purpose, the surface-sensitive detection scheme was used.

The waveguide ﬁrst was loaded from the MOST for 200 ms, with given intensities

Á Á Û = ¼:55

EÏ Å ÏGD

ÇÈ and . After loading, the WGD beam ( mm) was ﬂashed on

for 5¼¼ s before switching off the WG itself (this time was long enough for all atoms

= ½ in layer i to be released yet short compared to the decay time of the WG). To

check the detection method experimentally, we recorded the WGD signal for different Á

intensities ÏGD after the WG was loaded with a ﬁxed set of loading parameters. For

low intensities the signal ﬁrst increased and then saturated for intensities above 8¼±

Á = ¿¿

oftheﬁnalvalue ÏGD W/cm . This shows that the deformation of the higher =½ layers remained small enough to prevent noticeable loss, while layer i was emptied completely. Fig. 5.10 (a) shows a set of data, containing (1) the peak resulting from the release of atoms from the single layer when the WGD beam is turned on, followed by (2) the

peak of remaining atoms in higher layers when subsequently the WG is turned off. Peak

È i =½

(3) is from a reference run without WGD. The relative population ½ of layer can Æ

be determined by comparing the number of counts in the “depleted” peak ¾ (i.e. after

i =½ Æ

the loss of the atoms from layer ) to the number of counts in the reference peak ¿

È =½ Æ =Æ È

¾ ¿ ½

that contains all atoms, as ½ . The results for the relative population

È ¾¼±

are shown in ﬁg. 5.10 (b) and (c). In both cases, ½ remains above and typically

¿¼± Æ Á EÏ Å is around . The dependence of the total atom number ¿ on the intensities

13 Á

and ÇÈ is also shown in ﬁgs. 5.10 (b) and (c) . The atom number increases about linearly with the OP and EWM intensity, which is in rough qualitative agreement with

the simple model discussed above. The coupling to the evanescent OP ﬁeld is weak,

È Á Á

ÇÈ EÏ Å which can be seen from the constancy of ½ when is increased. Increasing increases the MOST density, and with it the local pumping rate (note that the WG signal does not vanish completely at zero EWM intensity, as well as the density in the

MOST). The experimentally observed spatial selectivity is considerably smaller than

È 85± ;Øh

expected value ( ½ ). This might be due to a reduction of the MOST density Æ

(or alternatively an increase of ef f , as explained in footnote 6) in the range of the evanescent ﬁelds.

Comparison with pulsed loading and possible improvements. It is interesting to compare the performance of CW loading to that of the pulsed scheme realized previ-

ously [110]. One benchmark is the loading ﬂux F , i.e. the loading rate per area, for

13For these measurements, an equivalent measurement sequence was used in which the reference peak itself was referenced to the atom number in the MOST. This was done in order to minimize effects of temporal drifts in the performance of the atom source. — For a direct comparison of the WGD and WG peaks it is important to note that, while for the WGD case all atoms are released towards the surface, in the WG case one half of the atomic distribution ballistically escapes upward without being detected in the observation time window, such that for a determination of the atom number corresponding to the WG peak, the signal has to be multiplied by a factor of two [182]. 5.3. EXPERIMENT 91

(a) 1 ¾

Á =6:½ =½:½

mW/cm Á W/cm ÇÈ (3) EÏÅ µ

¿ (b) (c ) (1)

tmnumber Atom (2) Æ 0.8 = ¾ Æ

TOF counts 0.6 0 01230123 time [ms] time [ms] =´½ 0.4 ½ È Æ ¿ £ 0.2 WG

WGD Rel. pop. 0 0

0 0.5 1 036

¾ ¾

] Á [ Á [ ] ÇÈ

EÏ Å W/cm mW/cm È

Figure 5.10: Dependence of the total atom number and the relative population ½ of layer

i =½ Á =

on the EWM and OP intensities. (a) – TOF data obtained for loading parameters EÏ Å

¾ ¾

½ Á =¿

W/cm and ÇÈ mW/cm . Turning on the WGD beam gives rise to a peak (1) from atoms

= ½ released from layer i . When the WG beam is subsequently turned off, the atoms stored

in the higher layers are released (2). This signal (2) is compared to a reference measurement £

without WGD beam (3). (b) and (c) – Dependence of the total atom number Æ (ﬁlled boxes,

È =

determined from a separate set of experimental runs, see text) and relative population ½

´½ Æ =Æ µ i = ½ Á Á Æ Æ

¿ EÏ Å ÇÈ ¾ ¿ ¾ of layer (open boxes) on and . and are determined as the sum of counts between 1.9 ms and 2.5 ms, minus the average of counts between 2.6 and

3.2 ms which is taken as a physical offset level after the decay of the peak.

i =½ A = Û Û Ý layer . For that purpose one can relate the loading rate to the area Ü of

the atomic distribution in the waveguide (cf. ﬁg. 5.7). For the pulsed loading scheme,

¾ ¿ ¾

½¼ ½× A =½:5 ¢ ½¼ Ô

up to ¿ atoms were tapped in the WG layer on an area cm after

6 ¾ ½

F ½¼

a 20 ms loading pulse, which leads to a loading ﬂux Ô cm s for the short

¿ ¾

A =¿¢ ½¼

duration of the pulse. For the present scheme, the area of the WG is c cm ,

¾ ½ 5 6

F Ä =A ´½¼ :::½¼ µ

ÏG c such that c cm s , this time in for CW operation. The

situation looks even more favorable for the new scheme when the loading efﬁciency

Ä =Ä Ä ÏG ÏG is compared, deﬁned as the ratio of the loading rate of the WG to

the loading rate Ä of the atom reservoir. For the CW loading parameters, the loading

5 ½

Ä Þ = ¼:5 Á = 6:8Á ½¼

ÅÇÌ ×

rate of the MOST ( ¼ mm, ) is on the order of s (cf.

= Ä =Ä ½¼ ÏG

chapter 4). This yields a loading efﬁciency c . On the other hand,

7 ½

for the pulsed scheme, the loading rate into the MOT was around ½¼ s , which yields

½¼

a corresponding efﬁciency Ô , which is one order of magnitude smaller (in that case, the lower efﬁciency is due to losses from the transverse ballistic expansion of the atom cloud [111]).

Our CW loading scheme has been discussed in connection with the realization of a

¾ ½ 9 ½¼ CW atom laser for argon [92,100,111]. This presumes a loading flux of > cm s [111], which is still far out of reach for the present, proof-of-principle realization. Sig- nificantly higher loading rates might however be reached with optimized parameters, 92 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS... as suggested by the data in fig. 5.10. In the present realization, we were severely limited by the maximum powers of the OP, EWM and MOT laser beams. Without these restrictions, it should be possible to better match the temperature of the MOST to the

depth of the WG potential and to increase the optical pumping rate in the evanescent

! ½ field. This way it should be possible to reach higher loading efficiencies .Forhigh OP intensities, optical pumping by straylight outside the range of the evanescent field may eventually become significant as a shielding effect; however this can be suppressed by further improving the quality of the surface. It should also be possible to increase the loading rate into the MOST by at least one order of magnitude by improving the flux of the Zeeman-slowed atomic beam with an another transverse cooling stage. Al- together, a WG loading flux of the required order might therefore be reachable with improved experimental apparatus.

5.3.3 Integrated Atom Source and Switchable Channel Guide The CW loading scheme can readily be used as an atom source for integrated atom optics. In this context it is sufficient to realize that, while the CW loading is limited to the overlap area of the MOST and the OP field (“source region”), the WG profile can

be much larger (“beam region”). By using an elliptically deformed Gaussian beam spot

½=½¼ (waist ratio , long axis waist 2 mm), we have realized a planar channel atom guide into which source was placed about 1.5 mm off center along the long axis.

MOST/OP

(a) 1mm

1mm

1mm1mm

MOST/OP Shadow WG

(b)

source beam

Figure 5.11: Guided atomic motion in a channel guide as observed with the surface atom detector using the TOF technique. The planar channel is formed by an elliptically shaped WG spot in which the atom source is put off center. (a) Measured lateral distribution for CW operation of the source (the image was taken after 100 ms). (b) Measured lateral distribution for CW operation obtained with a beam blocker (formed by the imaged shadow of a thin wire) behind the source region. The source and beam regions can be clearly identiﬁed.

The distribution of atoms in the channel is shown in ﬁg. 5.11 (a) for CW operation 5.3. EXPERIMENT 93

load (t<0) remove (t=0) MOST/OP

Shadow WG

0ms

5ms

10 ms

15 ms

20 ms

25 ms

Figure 5.12: Sequence of TOF images showing the propagation of atoms in the channel. The CW source is ﬁrst turned off, and then an “opto-atomic” switch behind the source region is quickly activated (by pulling a razor blade out of the WG beam proﬁle), allowing the atoms into the channel. The dynamic range of the single images is normalized to the brightest pixel.

of the source. The image, which was obtained with the TOF technique after turning off the WG beam, shows a distribution of atoms stretching along the entire field of view of the detector. In order to locate the source and beam regions physically and to demonstrate the flow of atoms, we first created a beam blocker behind the source. This was done by imaging the shadow of a thin wire onto the surface that was placed into

the WG beam along the short axis of the ellipse. The shadow, which had a transverse extension of less than 5¼¼ m, gave rise to a potential barrier that the atoms in the WG could not penetrate. We first placed this beam blocker into the source region and then displaced it downstream until the atom density in the remaining channel vanished, as showninfig.5.11 (b). This is a clear proof that the atoms in the right half of the field of view of fig. 5.11 (a) must have originated from a spatially separated source. 94 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

In order to observe the motion of atoms in the channel directly, we extended the beam blocker concept to allow for switching. In principle this could have been done by quickly removing the wire from the WG beam in a controlled way. We decided however for a simpler technique that was physically equivalent for our purpose by using a razor blade mounted to an electro-mechanical relay that was placed in the WG beam (replacing the wire). In analogy to integrated optics, this might be called an “opto-atomic” switch 14. In the “open” status, only the source region was exposed to WG light, whereas in the “closed” status, no part of the beam proﬁle was chopped, enabling the ﬂow of atoms out of the source region. The switching time, i.e. the time required to remove the blade from the beam, was approximately 2 ms.

In the experiment we ﬁrst operated the source CW with open switch in order to

½×

accumulate ¿ atoms in the source region. After turning off the source, the switch was closed. This resulted in atoms propagating downstream the channel whose motion could be tracked using the TOF technique. Results are shown in ﬁg. 5.12. The motion is an accelerated ballistic expansion (there is a potential gradient towards the center of the WG beam spot) with velocities on the order of a few centimeters per second.

5.3.4 Integrated Atom Detector and Simple Integrated Circuit In the above experiments on the channel, atoms were detected by turning off the WG beam and recording spatially resolved TOF images. This detection method, which relies on the spatial resolution of the surface atom detector’s MCP, necessarily releases atoms everywhere in the waveguide potential. An alternative scheme can be implemented using the surface-sensitive potential deformation (WGD) method. As illustrated in fig. 5.1 the position and size of the detection are are determined by the parameters of the WGD beam and therefore can be easily adjusted. The scheme is intrinsically local and does not require, as such, the spatial resolution of the MCP. At the same time it also allows to probe atoms in the operating waveguide. It is therefore an atom-optical analogue to an integrated optical detector15. In the experimental demonstration of this integrated atom detector, the WGD spot (WGD beam waist 0.32 mm) was located in the channel at a lateral distance of 1.5 mm from the atom source as illustrated in fig. 5.1, and the results are shown in fig. 5.13 (b). The upper image of the figure displays the recorded background distribution for

the operating WG. As shown in the lower image of the ﬁgure, an additional ﬂashing of the WGD beam (for 5¼¼ s) resulted in electrons being locally ejected from the surface,

as expected. =½ We also used the detector to determine the fraction of atoms in WG layer i ,as done already for the characterization of CW loading. For this purpose, the image for

14Integrated electro-optic switches [213] locally change the transmission of a waveguide via its index

of refraction, using the Pockels and Kerr effects. In our case the shadow changes the index of refraction

= ½ Í=E Í E for atoms, Ò [4], where is the optical potential and is the kinetic energy of the atom incident on the barrier. 15Integrated optical detectors commonly are realized by semiconductor photodiodes that are incorporated into or grown on top of the integrated waveguide [214, 215]. 5.3. EXPERIMENT 95

local detection was compared to a reference image as in ﬁg. 5.11 (a). Evaluated in the

È =¾7±

area of the detector, the data yield a relative population ½ .

MOST/OP WGD

WG on

WG on, flash WGD

Figure 5.13: Demonstration of an integrated atom detector. The images show the recorded

lateral distributions for the operating WG immediately before (top) and while (bottom) the WGD beam is ﬂashed on for 5¼¼ s. The detector (WGD) is located at a distance of about 1.5 mm from the source. The combination of source, guide and detector realizes an elementary integrated circuit.

The setup shown in ﬁg. 5.13 used to demonstrate the atom detector incorporates, in the planar geometry of the waveguide, the source and detector as interconnected functional elements. In analogy to integrated optics, this setup can thus be viewed as a simple atom-optical integrated circuit. Our circuit realizes an elementary atomic beam experiment in the lowest WG layer at a distance of 820 nm from the surface, as is also sketched in ﬁg. 5.1 (a).

5.3.5 Optical Surface Lattice

One of the advantages of our optical system over the realization of atom optics in magnetic potentials is the large ﬂexibility to modulate and reshape the conﬁning potential. This was already exploited for the integrated atom detection. Another example is the realizability of an optical “surface lattice”.

Principle. As illustrated in ﬁg. 5.14, the optical surface lattice is realized by retrore-

ﬂecting the (elliptical) WG beam. This gives rise to a WG intensity modulation along Ý the long axis (¼ ) which, together with the modulation perpendicular to the surface, produces a periodic array of quasi-1D channel waveguides16. The modulation of the

optical potential along the surface is given by

i h

Í = Í ± cÓ× ´k Ý µ ; ½·± ¾

¼ ¼Ý ÇÄ;diÔ (5.16)

16The term channel waveguide is appropriate here, since the atomic motion is quantized in the radial direction, with only a small number of bound states. 96 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

Attenuator WG P2

Mirror P1

MOT

Ar* (1s3)

EWM OP

Figure 5.14: Experimental scheme for an optical surface lattice. A periodic array of quasi- È

1D channels is produced by retroreﬂecting a fraction (power ¾ )ofthes-polarizedWGbeam È

(power ½ ). The modulation depth can be adjusted with an attenuator in front of the retrore-

ﬂection mirror. The lattice is loaded via evanescent-ﬁeld optical pumping (OP) from the MOST.

Í ± = È =È

¾ ½

where ¼ is the depth of the single-beam waveguide potential, is the ratio È

between the powers (intensities) of the reﬂected beam ( ¾ ) and the original WG beam

È k = ¾ ×iÒ = ¼Ý

¼Ý i ÏG

( ½ ), and is the wave vector along . For the incidence angle

=45 k ¼Þ

¼Ý i , coincides with the wave vector for the modulation along , which leads to equal oscillation frequencies in the channel waveguides parallel and perpendicular

to the surface. Depending on the ratio ± (which can be adjusted with an attenuator),

¼ 4 Í

the depth of the modulation can be varied from to ¼ .

Experiment and interpretation of results. In a simple experiment we operated the

± = È =È ½ lattice and atom source CW for 200 ms for different ratios ¾ ,whichwere

chosen between 0 and 1, covering a range of four orders of magnitude, and then took

½×

TOF data for the distribution of ¿ atoms in the lattice potential. A set of experimental

TOF images is shown in ﬁg. 5.15 (a). With increasing depth of the intensity modula-

½×

tion, ¿ atoms increasingly accumulate in the source area while the number of those in the “beam area” reduces. For full modulation, the atoms are completely conﬁned in the source area. Even though the modulation period (560 nm) is much too small to observe the channel structure directly, this transverse conﬁnement is clear evidence for the atom localization in the array of channel waveguides at the surface. To interpret the data further one can exploit that, in the absence of a heating mech-

anism in the optical potential, atoms in the beam area must be those atoms from the

½×

thermal distribution in the source area (after optical pumping to ¿ ) whose kinetic energy exceeds the modulation depth of the lattice 17. The fact that these atoms spill

17A second possibility for an escape from the source area (neglecting tunneling as a third possibility) is diffusion due to a Langevin force, cf. eq. 2.39, which arises from photon scattering: by absorbing

lattice photons, atoms can accumulate enough energy to hop to adjoining lattice sites [216, 217]. In our

½× ° ¾Ô ¾Ô

4 ½ case, however, photon scattering on the open ¿ transition leads to a loss to the ground state 5.3. EXPERIMENT 97

MOST/OP (a) l/ 2 WG

(b) PP21/ =0

µ 1 B

· 0.8 A ´ 2x10-3 = A 0.6

0.4 x

-2 1x10 S 0.2 x A 0 B

Localized fraction 0 0.01 0.02 0.05 0.1 0.2 0.5 1 -1

1x10 Ô

È =È ½ Relative modulation depth ¾

Figure 5.15: Localization of atoms in the optical surface lattice. (a) Atom distribution for CW

È =È ½ source operation for different ratios ¾ of the beam powers (and intensities) measured 200

ms after the WG beam is turned on (the dynamic range of the single images is normalized to the

½×

brightest pixel). With increasing depth of the intensity modulation, an increasing fraction of ¿

atoms accumulate in the source area, which is indirect evidence for the transverse localization

= A=´A · B µ

of these atoms in the array of channels. (b) Fraction f of localized atoms in

± = È =È f ½ the source area versus relative modulation depth ¾ .Thefraction is obtained as

illustrated in the inset (see text). The solid curve is the model with maximum modulation depth

Í =6:5 k Ì

B Ý Ç Ä;ÑaÜ .

out ballistically into the neighboring beam area is, of course, a trivial statement in the

=¼ ± 6=¼ limiting case ± , but it also holds for the other cases in which a variable frac-

tion of the thermal distribution in the beam area does remain localized in the lattice.

Í ±Í

½ Ç Ä;ÑaÜ

Foragivenmodulationdepth ÇÄ; , this fraction is given by

ÇÄ;½ =

f erf (5.17)

k Ì

B Ý Ì

where Ý is the transverse temperature, in direct analogy to the treatment of the translucence of the atom mirror’s potential barrier for a thermal distribution, eq. 4.6.

already after two scattering events. An inﬂuence of diffusion on the (conservative) atom dynamics in the waveguide due to photon scattering can therefore be neglected. 98 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

The fraction f can be extracted from the experimental TOF data in the following Æ

way. The total atom number Ë in the source area is the sum of a localized atom B number A and a ballistic background , which is the same as in a neighboring beam area of equal size (the average of the regions left and right of the source is taken).

Then f is given by

Æ B A

: f =

= (5.18)

Æ A · B

=¾¢ ½¼ An example (for ± ) is illustrated in the inset of ﬁg. 5.15 (b). Fig. 5.15 (b) also summarizes the results of our measurements. The experimental

values for f agree very well with the model, eq. 5.17, which is shown as a solid curve.

± = ½ Í

In the model, the absolute value of the full ( ) modulation depth, Ç Ä;ÑaÜ ,is

Í =´6:5 ¦ ¼:5µ k Ì

B Ý

taken as a single ﬁt parameter, resulting in Ç Ä;ÑaÜ (unfortunately

Ì Í Ç Ä;ÑaÜ neither Ý nor are not known well enough to allow for a direct comparison).

Further experiments. The surface lattice can readily be transformed into a conveyor belt for atoms. Such a device could e.g. be used to deliver atoms to other functional elements for atom manipulation with high accuracy18. The easiest realization is to move the retroreﬂection mirror along the beam axis: this shifts the array of channels along the prism surface19. Still another possibility would be to frequency-shift the retroreﬂected beam to obtain a moving standing-wave surface lattice. Other possible applications include studies of single-atom dynamics in (temporally modulated) optical lattices, complementary to work on single ions [217].

5.4 Conclusions

In our experiments with metastable argon, we have demonstrated the continuous load-

½×

ing of atoms into a surface atom waveguide. The optical waveguide potential for ¿ metastable argon atoms is formed by a red-detuned standing light wave (SLW) above a gold-coated prism surface. In this planar system the atomic motion is quasi free parallel to the surface while normal to it only a few bound states exist. The CW loading mech-

anism is based on the combination of the magneto-optical surface trap (MOST) with

½× ½× ¿ an evanescent ﬁeld that pumps the atoms from 5 to the other metastable state

in its short range above the surface. Experimentally, we have achieved a loading rate

¿ 5 ¾ ½¼ on the order of ½¼ atoms/s, which corresponds to a ﬂux of atoms/(s cm ). This is

18An optical conveyor belt has been realized recently for free space [218]. 19We have indeed tried to demonstrate the conveyor belt experimentally. For that purpose we mounted a 1-inch retroreﬂecting diameter mirror to a large loudspeaker coil at 1 m from the surface that was

driven by a sawtooth function generator. In order to maintain the overlap of the WG spots on the sur-

face over the whole translation length of 3 mm, a stability of order ½¼ intheanglewouldhavebeen

¿ required. Experimentally, however, we managed to achieve only down to ½¼ with the help of a mechanical stabilization mechanism. Despite some indications of operation, we have not anymore been able to convincingly demonstrate the conveyor belt in time. 5.4. CONCLUSIONS 99 roughly comparable to the peak loading ﬂux of our previously realized pulsed loading

scheme. The evanescent loading mechanism led to a relative population of around ¿¼± for the lowest confining waveguide layer centered at 820 nm from the surface, orders of magnitude closer than achieved in the work on atoms trapped in magnetic potentials at surfaces. Based on the continuous loading scheme for the waveguide, we have implemented a local atom source in its planar geometry. We have realized a switchable channel guide connected to the source and have directly observed the propagation of atoms in this guide. We have realized an atom detector in the channel guide via a local deformation of the confining waveguide potential with another evanescent light field. The combination of the source, the guide and the detector forms a simple atom-optical integrated circuit that realizes an atomic beam experiment in the waveguide geometry. Finally, we have demonstrated and studied the localization of atoms in an optical surface lattice. Our scheme for integrated atom optics is extremely flexible since the confining optical potential of the waveguide can be modulated easily both in space and time. In future applications, one might envision using addressable liquid crystal pixel arrays as transmission masks in the waveguide beam that are combined with a high-resolution imaging system. In this way, miniaturized and time-dependent atom-optical setups could be realized, paving the way to novel integrated elements and complex integrated circuits. In addition, the extreme closeness to the surface makes our system interesting for the probing of atom-surface interactions. 100 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS... Appendix A

Dressed Atom in a Bichromatic

Light Field

Ä =´! · ¼

The optical potential acting on a two-level atom in a bichromatic light ﬁeld ½

Æ ;! µ Ä =´! · Æ ;! µ

½ Ê;½ ¾ ¼ Ä;¾ Ê;¾ Ä; and is of immediate interest for the magneto-optical

surface trap. The dressed-atom model can give an intuitive insight into the underlying

! !

½ Ê;¾ physical processes as long as Ê; . It is then possible to construct dressed states from the coupling to the strong ﬁeld, and the weak ﬁeld then merely acts a time- dependent perturbation that induces transitions between those states. The treatment presented here (for details, see Ref. [212]) is based on a suggestion in Ref. [219]; a similar approach can be found in Refs. [220,221]. The evolution of the system, including spontaneous emission, is again given by the

master equation 2.15, where the Hamiltonian of the total system is now

À = À · Î : AÄ

AÄ (A.1)

¾ ½

À Ä ¾

Here AÄ describes the coupling of the atom to the mode as discussed in chapter

Î ¼ ½ Ä ½

2,and AÄ ( ) describes the additional perturbation due to ,

h i

Ê;½

i´! ·Æ µØ i´! ·Æ µØ

¼ ½ ¼ ½

e Ä · e Ä : Î =

AÄ (A.2)

½ ¾

The density of the system can be expanded into a perturbation series

´¼µ ´½µ ¾ ´¾µ

= · · · ::: (A.3)

that is expressed in the unperturbed dressed-state basis by the density matrix elements

X X

´Òµ

´Òµ ´Òµ ´Òµ

hi ´Æ ¦ ½µj jj ´Æ µi ´i 6= j µ: hi ´Æ µj ji ´Æ µi; ´¦µ = =

ij (A.4)

Æ Æ

´¦µ ij Steady-state solutions for ii and to the different orders in canthenbefound in a straightforward way starting from the zeroth-order solution discussed in chapter

101

102 APPENDIX A. DRESSED ATOM IN A BICHROMATIC LIGHT FIELD

×Ø

=½ ¡ ´ µ ½½ 2. Setting , the result for the steady-state population difference ¾¾

cÓ× ×iÒ

¾ ¾

×Ø;´¼µ =

¡ (A.5)

cÓ× ·×iÒ

¾ ¾

×Ø;´½µ

= ¼

¡ (A.6)

cÓ×

×Ø;´¾µ ×Ø;´¼µ ¾

= ¡ ! ·

¡ (A.7)

Ê;½

·´ª · Æ Æ µ

¾ Ä;¾ Ä;½

cÓh;¾

×iÒ

cÓh;¾ ¾

; (A.8)

¾ 4

·´ª · Æ Æ µ

×iÒ ·cÓ×

¾ Ä;½ Ä;¾

¾ ¾

cÓh;¾

¾ ¾ ¾

where cÓh; and are given by the coupling to the mode and are deﬁned as Ä

in section 2.1.1. This means that the coupling to the weak mode ½ acts as reduce

×Ø;´¾µ

the population difference in second order by ¡ , proportional to its intensity. The Ä

physical interpretation of this is therefore that the mode ½ drives additional transitions

between the dressed states. These then lead to an attenuation of the optical dipole force

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Diese Dissertation beschreibt Experimente zur Speicherung und Manipulation lasergekühlter metastabiler Argon-Atome an einer Oberﬂäche. Die einzelnen Punkte der Arbeit lassen sich wie folgt zusammenfassen:

Magneto-optische Oberflächenfalle. Eine neuartige magneto-optische Oberflächen- falle (MOST) wurde realisiert und charakterisiert. Bei der MOST handelt es sich um die Kombination einer oberflächennahen magneto-optischen Falle (MOT) mit einem optisch-evaneszenten Atomspiegel. Die in der MOT gespeicherte Atomwolke wird durch das evaneszente Lichtfeld, dessen Reichweite ein Bruchteil einer optischen

Wellenlänge beträgt, von der metallischen Oberﬂäche des Spiegels ferngehalten. Im

:¿ ¦ ¼:4µ ¢ ½¼ ´¿9¼ ¦ ¿¼µ Experiment konnten so ´½ Atome bei einer Lebensdauer von ms gespeichert werden. Die Eigenschaften der gespeicherten atomaren Wolke wurden, zunächst ohne das evaneszente Feld, für verschiedene Abstände der Wolke zur Oberﬂäche un-

tersucht. Insbesondere wurde, bei einer Abstandsverringerung des Quadrupol- Þ

Magnetfeldnullpunks ¼ der MOT von 1 mm über der Oberﬂäche auf Null, eine dramatische Abnahme der Lebensdauer um zwei Größenordnungen auf etwa 50 ms beobachtet. Die Eigenschaften des Atomspiegels in der Gegenwart des MOT-Lichts wurden untersucht; hierbei wurde eine starke Reduktion der Reﬂektivität im Vergleich

zum Fall ohne MOT-Licht festgestellt. Dieser bichromatische Effekt wurde für ver-

Þ = ¼

schiedene Parameter der Lichtfelder charakterisiert. Für eine Falle mit ¼ konnte schließlich nachgewiesen werden, daß die Lebensdauer der gefangenen Wolke mithilfe des evaneszenten Felds des Atomspiegels um mindestens eine Größenordnung ver- längert werden kann. Die Eigenschaften der MOST werden anhand eines einfachen Modells erklärt.

Kontinuierliches Laden eines planaren Wellenleiters für Atome. Durch Verwen- dung der MOST als Atomreservoir an der Oberfläche konnte ein kontinuierlicher Lade- mechanismus für einen planaren Atomwellenleiter demonstriert werden. Der Wellen- leiter wird durch das periodische optische Potential einer stehenden Lichtwelle über der Oberfläche gebildet, die gegen einen optischen Übergang rotverstimmt ist. Dieses System ist durch quasi-freie atomare Bewegung parallel zur Oberfläche charakterisiert, während senkrecht dazu nur wenige gebundene Zustände existieren. Ein kontinuier-

119 120 ZUSAMMENFASSUNG licher, oberﬂächensensitiver Lademechanismus für den Wellenleiter konnte experi- mentell demonstriert werden. Der Mechanismus basiert auf der MOST als Reservoir lasergekühlter Atome an der Oberﬂäche, aus dem Atome innerhalb der kurzen Abfal- länge eines evaneszenten Lichtfelds optisch in den Wellenleiter gepumpt werden. Der

Lademechanismus wurde für verschiedene Parameter charakterisiert; hierbei wurde ¿

eine maximale Laderate der Größenordnung ½¼ Atome/s, entsprechend einem Lade-

5 ¾

ﬂuß von ½¼ Atomen/(s cm ) erreicht. Der evaneszente Lademechanismus führte zu

einer etwa ¿¼±igen relativen Besetzung der untersten besetzbaren Wellenleiterschicht, deren mittlerer Abstand von der Oberﬂäche 820 nm betrug.

Manipulation von Atomen im Wellenleiter: integrierte Atomoptik. Auf der Basis des kontinuierlichen Ladeschemas konnte eine lokale Atomquelle in der Wellenleiter- geometrie implementiert werden. In einem schaltbaren, an die Quelle anschließenden linearen Kanal konnte die Propagation von Atomen im Wellenleiter direkt beobachtet werden. Ein im Wellenleiter integrierter Atomdetektor wurde über eine lokale Ver- formung des Wellenleiterpotentials realisiert. Quelle, Kanal und Detekor wurden zu einem integrierten Schaltkreis für ein einfaches miniaturisiertes Atomstrahlexperiment in der untersten Wellenleiterschicht kombiniert. In einem weiteren Experiment konnte die Lokalisierung von Atomen in einem quasi-eindimensionalen Oberﬂächengitter demonstriert werden.

Nachweis metastabiler Atome an einer Oberfläche. Der Nachweis der metastabilen Atome an der Oberfläche erfolgte durch die elektronenoptische Abbildung von Sekundärelektronen, die bei der Abregung einzelner Atome an der Oberfläche aus- gelöst werden. Der Oberflächenatomdetektor wurde mit atomoptischen Methoden

charakterisiert und kalibriert. Die Detektionsefﬁzienzen für die in den Experimenten

½× ½× ¿ verwendeten Zustände 5 (MOST) und (Wellenleiter) von Argon wurden be-

stimmt. Dies ermöglichte einen Zugang zu der bisher nicht bekannten Elektronenaus-

½×

lösewahrscheinlichkeit von ¿ an einer Goldoberﬂäche, für die mit einem Wert von

½4± ½×

eine Übereinstimmung mit der für den Zustand 5 gefunden wurde. Basierend auf der räumlichen und zeitlichen Auﬂösung des Detektors konnte eine Methode zur dreidimensionalen Flugzeitspektroskopie demonstriert werden. Danksagung

An dieser Stelle möchte ich mich bei allen bedanken, die zum Gelingen dieser Arbeit beigetragen haben. Ich danke Professor Jürgen Mlynek für die Möglichkeit, mich in der stimulierenden Atmosphäre seines Konstanzer Lehrstuhls mit Atomoptik beschäftigen zu können, und insbesondere für die uneingeschränkte und vertrauensvolle Unterstützung meiner Ar- beit, die mir immer ein großer Ansporn zum Erfolg war. Ich danke weiterhin Professor Tilman Pfau (Universität Stuttgart) für viele gemeinsame Überlegungen und Diskussio- nen in seiner Zeit als Leiter der Konstanzer Atomoptik-Gruppe, sowie seinem Nachfol- ger Dr. Markus Oberthaler für klärende Diskussionen, sein Interesse und seine Geduld bis zum Abschluß der Arbeit. Bei der täglichen Arbeit an der nun Geschichte gewordenen Strahlmaschine ISABEL danke ich zunächst meinen Vorgängern Michael Hartl und Harald Gauck für die in vieler Hinsicht interessante gemeinsame Zeit. Harald Schnitzler schuf mit seiner Kamerasoftware während seiner Diplomarbeit eine extrem zuverlässige Voraussetzung für die Durchführung unserer Experimente, hierfür nochmals vielen Dank. Kay Orgassa danke ich für seinen großen Einsatz während seiner Diplomandenzeit, die vom gemein- samen harten Ringen um die Reproduzierbarkeit der MOST geprägt war. Ein großer Dank gilt Dr. Masahiro Hasuo (Gastwissenschaftler von der Universität Kyoto) und Thomas Anker, zunächst HiWi und dann Diplomand, für die exzellente Zusammen- arbeit während des letzten experimentellen Jahres, in dem eine Vielzahl von Ergebnis- sen entstanden sind. Schließlich danke ich Dr. Richard Adams, Postdoc an der Nachbar- maschine, für seinen unnachahmlichen Humor, der viel zu einem heiteren Arbeitsklima im Labor beigetragen hat. Die Optimierung der Oberberﬂäche war eine wichtige Voraussetzung für unsere Ex- perimente. Ich danke Professor Paul Leiderer und Dr. Clemens Bechinger für wertvolle Informationen zu Oberﬂächenplasmonen und Schichtsystemen, sowie Stefan Walheim und Erik Schäffer für die Hilfe bei der Charakterisierung unserer aufgedampften Gold- schichten mit dem AFM, und nochmals Stefan Walheim für einen überaus wertvollen Tip zur Behandlung unserer Glasprismen. Jean-Philippe Deschamps (Ecole Polytech- nique, Paris) danke ich für Experimente zum optimierten Aufdampfen von Schichten während eines Praktikums in unserer Gruppe und Dr. Vahid Sandoghdar und seiner Nanooptik-Gruppe am Lehrstuhl für das Bereitstellen von Infrastruktur in ihrem Labor. Weiterhin danke ich Dr. Carsten Henkel (Universität Potsdam) für die Zusammenarbeit

121 122 DANKSAGUNG bei der Steulicht-Charakterisierung und -Modellierung. Dr. Peter Marzlin danke ich für wertvolle Hinweise zur störungstheoretischen Behandlung des Zweifarbenproblems der MOST. Der Atomoptikgruppe und allen Kollegen auf P8 danke ich für das freundschaftliche und hilfsbereite Miteinander, und insbesondere auch den ”Chromis” Jürgen Stuhler, Piet Schmidt und Sven Hensler für den Erfahrungsaustausch von MO(S)T zu MOT. Un- serem Elektronik-Guru Stefan Eggert danke ich für seine bewundernswert schnellen Lösungsvorschläge und für seine Engelsgeduld bei der Feinjustage von Schaltkreisen. Stefan Hahn war nicht nur Ansprechpartner für verzwickte mechanische Fragen, son- dern hat auch als Infrastrukturspezialist nicht unerheblich zum reibungslosen Ablauf der Arbeit beigetragen, hierfür vielen Dank. Ute Hentzen und Waltraud Heinzen danke ich für ihre große Hilfsbereitschaft bei organisatorischen Dingen und den Werkstätten der Uni Konstanz für die schnelle und hochwertige Bearbeitung zahlreicher Aufträge. Beim Verfassen der schriftlichen Arbeit konnte ich von hilfreichen Anmerkungen der Probeleser Dr. Björn Brezger, Dr. Masahiro Hasuo, Dr. Markus Oberthaler, Dr. Jo Bellanca und Thomas Anker proﬁtieren, denen ich hierfür herzlich danke. Ein großer Dank gilt hier auch Professor Wolfgang Ketterle und Professor David Pritchard, in deren Gruppe am Massachusetts Institute of Technology ich die schriftliche Arbeit zu Ende bringen durfte. Den Mitmusikern der Lehrstuhl-Jazzcombo, darunter Hannes Schniepp, Peter Marzlin, Stefan Eggert, sowie als Very Special Guests Tilman Pfau und Jürgen Mlynek, danke ich für musikalische Sternstunden rund um die Konstanzer Physik... Schließlich, aber nicht zuletzt, danke ich von Herzen meiner Familie und meiner Frau Elisa, die meinetwegen den Sprung über den Atlantik hin und wieder zurück gewagt hat, für die unbeschreibliche Unterstützung und Rückendeckung während all der Jahre.