RICE UNIVERSITY

A Narrow Linewidth Diode Laser System for Strontium Laser Cooling Applications by Sarah B. Nagel

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE

Approved, Thesis Committee:

Thomas C. Killian , Chair Assistant Professor of Physics and Astronomy

Randall G. Hulet Fayez Sarofim Professor of Physics and Astronomy

Jason H. Hafner Assistant Professor of Physics and Astronomy

Houston, Texas April, 2004 ABSTRACT

A Narrow Linewidth Diode Laser System for Strontium Laser Cooling Applications

by

Sarah B. Nagel

1 3 The diode laser system for laser cooling on the S0 → P1 intercombination line of strontium discussed in this thesis allows us to cool and trap an atomic strontium sample to 15 µK. Samples in this temperature range are useful for the development of the next generation of atomic frequency standards, cold collision studies, and as a step towards quantum degeneracy. This laser system consists of a

Littrow configuration external-cavity diode laser, which is frequency locked to a high

finesse cavity. The cavity is subsequently locked to an absorption feature to produce a few mW of tunable, stabilized, single mode power at the target wavelength. We present the design and characterization of this system, including a linewidth measurement of 70 kHz, as well as preliminary results from cooling and trapping. Acknowledgments

While the text of this thesis requires only a few short pages, the list of those I wish to acknowledge has grown to amazing proportions! Without their help, this project would not have been completed, and I will undoubtedly call on them again in the days to come. I can only hope that they will not be offended by the humble acknowledgements given here – wholly inadequate and certainly incommensurate with their contributions.

First, I would like to thank my committee members for their time and energy.

Special thanks go to my advisor, Dr. Tom Killian, for his patience, guidance, and encouragement. They say that first-generation graduate students are the best trained – the fault for any deviation from this trend falls squarely on my shoulders.

The work for this thesis could not have progressed without the support of my labmates, friends and family. For countless reminders not to worry, but to ”just do whatcha gotta do,” special thanks go to Clayton. For myriad late-night conversations and being my Barnabas, I thank Kerry. I could not have done it without you. For phone calls, care packages, and their uncanny ability to joke me out of my blackest funk, I thank my family. Their love and support have carried me through many scrapes and stumbles. I can only love them the way they have loved me: extravagantly. And while they may not know much about lasers and ultracold atoms, they have taught me those things that are most important: to strive for excellence and to live with compassion. I hope to honor them with this work. Contents

Abstract ii

Acknowledgments iii

List of Figures vi

1 Introduction 1

1.1 Laser Cooling and Trapping of Neutral Atoms ...... 1

1.2 Atomic Structure of Strontium ...... 4

1.3 Doppler cooling on a narrow optical transition ...... 6

1.4 Linewidth Concerns ...... 8

1.5 Diode Lasers ...... 9

2 689 nm Diode Laser System 12

2.1 ECDL ...... 12

2.2 ECDL and a High Finesse Cavity ...... 16

2.2.1 PDH Error Signal ...... 16

2.2.2 Cavity Servo Electronics ...... 19

2.2.3 Linewidth Measurement ...... 22

2.3 ECDL+Cavity and Atomic Sample ...... 23

2.3.1 Spectroscopy ...... 24

2.3.2 Servo Electronics ...... 24

2.4 The Entire System ...... 27 v

3 Results 30

3.1 Blue MOT Operation and Diagnostics ...... 30

3.2 Red MOT Operation and Diagnostics ...... 33

3.3 Outlook ...... 35

A Troubleshooting 37

A.1 Replacing a Laser Diode ...... 37

A.1.1 Initial Alignment ...... 38

A.1.2 Threshold Current ...... 39

A.1.3 Target Wavelength ...... 40

A.2 Cavity Error Signal Acquisition and Locking ...... 42

A.2.1 Cavity Error Signal Acquisition ...... 42

A.2.2 Locking to the Cavity ...... 43

A.3 Atomic Error Signal Acquisition and Locking ...... 44

A.3.1 Atomic Error Signal Acquisition ...... 44

A.3.2 Locking to the Atomic Feature ...... 45

References 47 List of Figures

1.1 Partial Strontium Energy Level Diagram ...... 5

1.2 Extended Cavity Diode Configurations ...... 10

2.1 ECDL schematic ...... 13

2.2 Electronic Protection Network ...... 15

2.3 ECDL with Cavity ...... 18

2.4 Cavity Error Signal ...... 19

2.5 Cavity Servo Schematic...... 20

2.6 Fast Path Locked Signal ...... 21

2.7 Locked Cavity Signal ...... 22

2.8 Fourier Transform of Locked Error Signal ...... 23

2.9 Saturated Absorption Schematic ...... 25

2.10 Saturated Absorption Error Signal ...... 26

2.11 Saturated Absorption Servo Schematic ...... 26

2.12 Saturated Absorption Locked Signal ...... 27

2.13 System Schematic ...... 29

3.1 Absorption imaging ...... 31

3.2 Blue MOT Absorption Image ...... 32

3.3 Blue MOT Temperature Determination ...... 32

3.4 Red MOT Absorption Image ...... 34 vii

3.5 Red MOT Temperature Determination ...... 35 Chapter 1 Introduction

This introductory chapter includes discussions of laser cooling and trapping, the atomic structure of strontium, and an introduction to diode lasers, all of which are necessary to motivate the work documented in this thesis: the fabrication, characterization, and use of a diode laser system suitable for laser cooling on the

1 3 S0 → P1 line of strontium.

1.1 Laser Cooling and Trapping of Neutral Atoms

Over the last 30 years, laser cooling and trapping techniques have revolutionized experimental atomic physics. Because these techniques allow a significant reduction in translational energy, these systems approach the ideal ensemble of stationary atoms, allowing us to probe their interactions among themselves as well as interactions with the environment. Laser cooling has become a standard laboratory tool for producing cold (< 1 mK), dense (1010-1011 cm−3) samples of atoms. Magneto-Optical traps [1] are now commonplace and provide a starting point for branching into numerous directions of atomic and quantum physics. The basic mechanics of laser cooling and trapping are discussed in Metcalf and van der Straten’s book Laser Cooling and Trapping [2].

Using resonant radiation pressure to cool atoms was proposed independently by Hansch and Schawlow [4] and by Wineland and Dehmelt [5] in 1975. The basic 2 idea, commonly known as Doppler cooling, is that atoms travelling towards an opposing laser field will preferentially absorb light that is detuned below (to the red of) the center of the atomic resonance. This preferential absorption is due to the

Doppler effect which causes the light to be shifted into resonance with the atoms.

On average, fluorescence is symmetrically distributed in space, which leads to a net atomic momentum loss. Momentum transfer from red-detuned light causes a damping force that opposes the motion of the atom.

Wineland et al. [6]were the first to observe radiation pressure cooling in their experiments with trapped magnesium ions in 1978. Balykin et al. [7] were the first to experimentally observe this effect in 1-D cooling of a sodium atomic beam in

1979. Shortly after, Phillips et al. [8, 9] added a magnetic gradient field to compensate for the changing Doppler shift and to keep the atoms in resonance with the cooling beam as they slowed down. This cooling scheme is often called Zeeman slowing. In 1984 Ertmer et. al [10] used a swept-frequency laser chirp to track the

Na atomic resonance as the atoms were slowed from an initial beam velocity to 600 m/s to a final gas cloud velocity of about 6 m/s (50 mK).

By using three pairs of intersecting, orthogonal, counterpropogating red-detuned laser beams Chu et al. [11] extended Doppler cooling into three dimensions in 1985. Atoms with speeds below a certain capture velocity were rapidly cooled to a remarkable temperature of 240 µK. Although there was no position-dependent force, and thus the sample was not trapped, the overlap region 3 of the laser beams confined the atoms for 100 ms. This configuration is known as optical molasses.

Without any position-dependent restoring force, the atoms eventually random walk out of the cooling beams. The temperature limit of this molasses is found by balancing the cooling due to the damping force and the heating from the statistical

fluctuations of the force caused by random absorption and emission of photons.

Using a Fokker-Planck semiclassical model, several theoretical treatments

[12, 13, 14, 15, 16] yield the well-known Doppler limit for laser cooling, given by

h¯Γ k T = cool , (1.1) B d 2 where Td is the Doppler-limited temperature, and Γcool is the linewidth of the atomic transition used for cooling. This limit says that the minimum kinetic energy of the atoms is equal to the energy width of the cooling transition. It is interesting to compare this limit to the recoil-limited temperature, which occurs when the kinetic energy of the atom is equal to the recoil energy imparted to the atom when it absorbs a single photon: h¯2k2 k T = . (1.2) b r M

Here, k is the wavenumber of the light and M is the mass of the atom. For most experiments, this is the hard limit for laser cooling since it involves the minimum interaction with the laser field. For typical cooling transitions, the Doppler-limited temperature is 100 − 1000 times greater than the recoil-limited temperature.

By adding a magnetic quadrupole gradient field whose zero coincides with the 4 optical molasses center, Raab et al. [1] utilized the internal structure of the atom to produce a 3-D restoring force that trapped the atoms for long periods of time. By using orthogonal circular light polarizations to distinguish each counterpropogating beam, spatially-preferred absorption in three dimensions is caused by Zeeman level shifts as the atoms move away from the zero of the magnetic field gradient. This gradient field is easily generated by an anti-Helmholtz coil pair — a Helmholtz configuration with opposite circulating currents in each coil. The damping force of the optical molasses simultaneously exists with the restoring force. This apparatus, known commonly as a magneto-optical trap (MOT), provides a convenient way not only to cool atoms to very low velocities, but also to confine them to a very small volume (1 mm3), producing dense, ultracold atomic samples.

1.2 Atomic Structure of Strontium

The most commonly trapped atoms are the alkali metals, but there has been considerable interest in expanding the range of laser-trapped elements. The alkaline earth metal atoms possess an atomic and nuclear structure which makes them appealing for laser cooling studies. The most abundant alkaline earth atoms have no nuclear spin (I = 0) and therefore no complicating hyperfine structure.

Furthermore, the two valence electrons can couple together anti-parallel (S = 0) to produce a singlet state or parallel (S = 1) to make a triplet state. As a consequence the ground state is a single J = 0 state, and the alkaline earth atoms approach the ideal J = 0 → J = 1 system which is commonly used to theoretically describe many 5

Figure 1.1 Partial Strontium Energy Level Diagram. Decay rates (s−1) and selected excitation wavelengths are given. Taken from Nagel et al. [17] laser cooling experiments. The level diagram for strontium displayed in Figure 1.1 shows this simple atomic structure [17]. Levels for the other alkaline earth atoms have a similar structure.

All alkaline earth atoms offer strong cycling transitions from the singlet ground state to the first excited singlet P state. In the case of strontium, the upper

1 1 state of the S0 → P1 461 nm cycling transition has a 5 ns lifetime[18] and allows rapid laser cooling of the atoms. The branching ratio to the lower singlet D state is small enough that atoms can be brought to near zero velocity before decaying out of the cycling transition.

An important property of the structure of the alkaline earth atoms is the division of all atomic states into either singlets or triplets. From selection rules, we know that the electric dipole (E1) operator does not connect ∆S = ±1 transitions, 6 and thus we are justified in separating the singlet from the triplet states as we have done in Figure 1.1. That is, E1 transitions can occur only between states of the same S. This picture is strictly true for low mass atoms in which Russell-Saunders

LS-coupling holds[19]. However, as an atom’s mass increases, there is a progressive breakdown of LS-coupling, and spin-orbit effects will mix singlet and triplet states of the same electronic term. Thus, E1 transitions with ∆S = 1 are possible and become increasingly stronger for heavier atoms. These ∆S = 1 transitions, commonly referred to as intercombination lines, are generally much weaker than their ∆S = 0 counterparts. Because of their narrow linewidths, intercombination transitions are useful as potential optical frequency standards.

1.3 Doppler cooling on a narrow optical transition

In an alkali atom MOT, temperatures below the Doppler limit are routinely obtained using polarization gradient cooling processes[20, 21]. These cooling mechanisms arise from optical pumping effects between ground state Zeeman levels which produce a damping force stronger than that of Doppler cooling, resulting in temperatures that approach the recoil limit. Because the even-isotope alkaline earth atoms have no nuclear spin, and thus, no ground state structure, sub-Doppler cooling does not occur and the MOT has a Doppler-limited temperature (Td). The

1 1 situation is further aggravated by the broad S0 → P1 cooling transition (Γ = 32

MHz for Sr and Ca; 80 MHz for Mg) which cools atoms only to a Doppler limit of a few mK (Td ∝ Γcool), in contrast with the alkali atoms which reach MOT 7 temperatures < 50µK with polarization gradient cooling.

Because of the linear dependence of the Doppler temperature on the cooling linewidth, the advantage of cooling on an intercombination line is readily apparent.

For strontium, the scattering rate of the 7.6 kHz intercombination line at 689 nm is just large enough to make it feasible to trap on this narrow transition. A trap operating on this transition can capture atoms that have been pre-cooled on the 461 nm transition. Trapping on this transition has been the subject of study for the last few years. In 1999, Katori et al. [27] reported cooling a sample to the recoil limit of

400 nK. More recently in 2004, Loftus et al. [28] reported an extensive study of narrow line cooling, including cooling below the recoil temperature to 250 nK.

These efforts have been towards the goal of quantum degeneracy, but it has yet to be achieved.

Thus, laser cooling on the 7.6 kHz intercombination line of strontium will provide samples in the sub-µK temperature range. In the short term, these samples will be useful for collision studies. Long term goals include transferring this sample to a dipole trap, achieving strontium Bose Einstein condensation, and developing a strontium optical frequency standard. In order to achieve these goals, it is necessary to develop a 689 nm laser system suitable for these applications. The remainder of this chapter focuses in more detail on linewidth concerns and an introduction to diode lasers. 8

1.4 Linewidth Concerns

Typical laser linewidths are on the order of 1 MHz. Lasers have been narrowed by several means. J.L. Hall [22] pioneered the field with his work on dye lasers.

Recent achievements include those by the Hollberg group [23], the Hemmerich group

[24] and others. The record is currently held by the Bergquist group[25], who have narrowed a visible laser linewidth to the sub-Hz regime. So, while achieving a linewidth of 100 kHz is a bit challenging, it is well within the reach of current technology.

The temperature limits discussed above rely on the linewidth of the cooling transition, Γcool being the largest linewidth in the system. Therefore, the achievement of any of the above goals requires the linewidth of the laser to be under

7.6 kHz. A laser linewidth of 1 kHz would be ideal.

As a first step, we have narrowed the linewidth of our laser to ∼100 kHz. This has enabled us to cool a sample to ∼ 10µK. While this is not the ideal laser linewidth or temperature, it is a beginning. Even with a 100 kHz laser, it is necessary to artificially broaden the 689 nm laser as the first stage of cooling. This broadening is more thoroughly discussed in section 3.2. So, while a 1 kHz laser linewidth would yield sub-µK temperatures, we are able to trap and cool a large fraction of the 461 nm atoms in a red MOT with a laser linewidth on the order of

100 kHz. 9

1.5 Diode Lasers

The temperature limits discussed in Section 1.1 can be reached using any coherent light source with sufficiently narrow linewidth and sufficiently high power; an easy way to do this is by using diode lasers. Diode lasers are a good choice because they are relatively inexpensive, possess large tuning ranges, and can be spectrally narrowed by external means[26].

The frequency of light produced by a diode laser source depends on temperature and drive current, as well as optical feedback. As the temperature increases, the frequency decreases. This is not a smooth tuning; it is subject to mode hops. Likewise, as the drive current increases, the frequency decreases. This, too, is not a smooth tuning; it subject to mode hops. These two factors yield very high

flexibility, and when working together can yield tuning ranges of hundreds of GHz.

As mentioned above, laser diodes are extremely sensitive to optical feedback.

We can use this sensitivity to our advantage by coupling the laser to an external wavelength selective element such that only a desired frequency is returned to the laser diode. Because lasers work on amplification principles, the one frequency that is fed back gains power, and eventually becomes the dominant mode. This reduces the threshold current, narrows the linewidth, and provides a broad tuning range.

There are several wavelength selective elements to choose from: gratings, etalons, and high finesse cavities[32]. We have chosen to use a grating to form an extended cavity diode laser (ECDL). 10

a) b)

Figure 1.2 Extended Cavity Diode Configurations. a) In the Littrow configuration, up to 80% of the power is coupled out of the ECDL. b) In the Littman-Metcalf configuration, the output beam does not wander as the wavelength changes.

ECDLs exist in many configurations. Two common optical configurations, the

Littrow, and Littman-Metcalf are described below and illustrated in Figure 1.2.

In the Littrow configuration, the grating is aligned such that the first order diffraction returns directly to the laser diode. The coarse lasing wavelength is then determined by the angle of the grating with respect to the laser. Wavelength tunes with this angle. The output is the zeroth order reflected beam, which can be as high as 80% of the original output power of the diode. The advantages of this configuration are simplicity and output power. The disadvantage is that the angle of the output beam changes slightly as the angle of the grating changes.

In the Littman-Metcalf configuration, the output beam from the laser diode is aligned at grazing incidence with the grating. The first order diffracted beam is then sent to a mirror which reflects the beam back on itself. This reflected beam then hits the grating and the first-order diffracted beam couples back into the diode.

Here, wavelength tuning is accomplished by varying the angle of the mirror, which changes the wavelength that the diode receives as optical feedback. The output is the zeroth order reflected beam off the grating. Since the grating in this configuration does not move, the output beam angle does not change as the 11 wavelength is tuned. That’s the advantage. However, since the light coupled back into the laser is be diffracted twice by the grating, a larger fraction of the power must be diffracted, which leaves less power available for the output.[33]

The Littman-Metcalf configuration is useful because the beam does not wander as you change the angle of the grating. However, we have chosen the

Littrow configuration because of simplicity and power considerations. Also, the change in output beam angle that results from sweeping the laser over the wavelength region of interest is very small.

The next chapter contains a discussion of the 689 nm ECDL system. Chapter 2 689 nm Diode Laser System

This chapter describes the present design for the 689 nm system. The following sections describe and characterize the mechanical and electronic setups.

Section 2.1 is a discussion and characterization of the 689 nm extended cavity diode laser (ECDL). Section 2.2 describes the interaction of the laser with a high finesse cavity and our methods of controlling the laser frequency such that it tracks the transmission peak of that cavity. Section 2.3 describes saturated absorption spectroscopy and our methods of locking the cavity transmission mode to the atomic resonance. Finally, section 2.4 is an overview of the entire system.

The most challenging part of this process was devising servo loops with the proper characteristics. In order for the laser wavelength to be stable on the order of kilohertz, the lock circuitry needed to be good to well past 1 MHz in frequency space. This sort of circuitry has been done most notably by the Hollberg Group

[23], and the Hemmerich group [24].

2.1 ECDL

As mentioned in Chapter 1, the frequency output of a laser diode is dependent upon temperature, current, and optical feedback. Both the temperature and optical feedback concerns are addressed in the mechanical setup of the ECDL, shown in

Figure 2.1. 13

Thermistor Laser Diode TEC

PZT

Figure 2.1 ECDL schematic. TEC, thermistor, pzt, and current driver leads are shown. The placement of the collimating lens is crucial. 14

The temperature of the ECDL is set and maintained by a commercial temperature control unit from Wavelength Electronics, which uses a thermistor and a thermoelectric cooler (TEC). To keep the temperature stable over long periods of time, it is useful to have a fairly large heatsink. In this design, the entire aluminum box acts a heatsink. With this precaution and a hermetically sealed box, temperature stability is good enough for the laser to remain locked for several hours. The free running ECDL drifts .01 cm−1/hour, which corresponds to 300 MHz per hour. This is not impressive performance, but it is sufficient for our purposes.

We have the option of temperature controlling the entire aluminum box. To allow this capability, the aluminum housing is separated from the optical table by four

G-10 blocks. However, we have not found it necessary to temperature control the aluminum housing.

The current through the laser diode is set by a commercial laser diode driver from ILX Lightwave. Because of the susceptibility of laser diodes to electrostatic discharge, there is a protection network across the diode, shown in Figure 2.2.

The output beam from a free running laser diode is both elliptical and highly divergent. The placement of the collimating lens in this system is critical. In order to have a collimated beam, the laser diode facet must be placed at the focal length of the lens. In practice, we adjust the position of the lens to minimize the spotsize in the far field. Also, outside the housing, we use a cylindrical lens to correct for an astigmatism in the beam. 15

1000 H ILX Current Driver ¡ 10 K 1 nF Fast Path

¡ Laser ¡ 50 Diode 10 K

1 nF

Figure 2.2 Electronic Protection Network. There are two connections to the laser diode. The ILX Lightwave is always connected through a 1000 µH inductor; the fast path is capacitively coupled to the laser diode, current limited by the 10 KΩ resistor, and terminated by the 50Ω resistor. Adapted from Hollberg et al. [23].

In order for this design to work well, the grating must be isolated from mechanical vibrations. In order to accomplish this isolation, the grating is glued to a brass mount which is mechanically anchored to the aluminum box. The box is anchored to the optics table, which floats, to isolate the system from mechanical vibrations.

In order to reduce unwanted optical feedback to the diode from scattered light from subsequent optics, we use two OFR optical isolators in series immediately after the grating, which provide 80 dB of attenuation. Thus, both vibrational stability concerns and optical feedback concerns are addressed in the mechanical setup of this system.

In the Littrow configured ECDL, the angle at which the incident beam strikes 16 the grating sets the wavelength of the output, given by

λ = 2d sin(θ), (2.1) where λ is the wavelength of light, d is the distance between grooves of the grating, and θ is the angle the incident beam makes with the grating normal. The wavelength tunes with the angle θ. In our configuration, this angle is varied by changing the voltage over a piezo electric transducer (PZT). As the voltage increases, θ decreases, and so wavelength decreases. In the lab, we find it more useful to work in wavenumbers (cm−1), and the dependence of wavelength on this pzt voltage is approximately 0.01cm−1/1.5V. Although we have not measured the linewidth of the free running ECDL we estimate from the sweep (following) that it is on the order of 1 MHz.

2.2 ECDL and a High Finesse Cavity

For this laser to be useful in cooling and trapping experiments, its linewidth must be reduced further. This section describes tracking the transmission mode of a high finesse cavity using electronic feedback.

2.2.1 PDH Error Signal

A standard technique for narrowing the linewidth of a laser is the

Pound-Drever-Hall (PDH) method [29]. This technique involves writing phase modulation sidebands onto the laser frequency. When the laser beam interacts with high finesse Fabry-Perot cavity, only those wavelengths which meet the resonance 17 requirement

nλ = L (2.2) 2 are transmitted. Here, λ is the wavelength of the light incident on the cavity, n is an integer, and L is the length of the cavity. The cavity used in this setup was designed and built by Y.N. Martinez. This cavity has a finesse of 1920 and a linewidth of 460 kHz. A schematic of the setup is shown in Figure 2.3. The laser beam is transmitted through the EOM, driven at 50 MHz, and through a polarizing beam splitter cube (PBS3). The beam passes through a quarter wave plate (QWP), which makes the polarization circular. If the light is on resonance with the cavity, it is transmitted and picked up by a photodiode (PD3). If, however, the light is not on resonance, it is reflected, and passes through the quarter waveplate again, which makes the polarization linear, and perpendicular to its original polarization. Now, when the beam interacts with the PBS cube, it is rejected and propagates to a mirror (M16), and is then focused by a lens (L8) onto a photodiode (PD2). When this photodiode signal is demodulated, we observe the error signal.

Figure 2.4 shows typical curves for both the error signal and the transmission signal. This error signal can be generated by sweeping the laser PZT and thus changing the wavelength of light (λ) – or by sweeping the cavity PZT and thereby changing the length of the cavity (L). We have found it better in practice to scan the cavity PZT, which simplifies the implementation of further frequency locks.

The sidebands on this signal are spaced by the modulation frequency (50 18

Transmission Sig nal PD3

RF Mixer Cavity Error Signal HFC PD2

L8

QWP M16 PBS3

EOM 50 MHz

M1

Figure 2.3 ECDL with Cavity. If the laser is on resonance with the cavity, light is transmitted to PD3; otherwise it is reflected to PD2. As we scan through the resonance, demodulation of the PD2 signal yields an error signal. 19

0.5 error monitor ramp/50 0.4 transmission signal*10−.4V

0.3

0.2

0.1

0 Signal(V)

−0.1

−0.2

−0.3

−0.4

−0.5 −60 −40 −20 0 20 40 60 Frequency (MHz)

Figure 2.4 Cavity Error Signal. Note that the laser frequency is held fixed while the cavity is scanned. In the 3 ms it takes to scan the cavity, the laser frequency has moved such that the sidebands are no longer equally spaced.

MHz); looking closely one finds that the sideband features are not equidistant from the central feature. This discrepancy can be traced to the laser frequency drifting as the cavity is scanned through resonance. Also, the error signal has a small offset; that is, the error signal is not centered about zero volts. This offset is a result of amplitude modulation rather than phase modulation by the EOM; it can be corrected by tweaking the alignment of the EOM (see Section A.2.2). If the offset is very large, this can be problematic in subsequent frequency locks; if the offset is under 35 mV, however, it is not a problem.

2.2.2 Cavity Servo Electronics

Given the above error signal, we use feedback electronics to both the current through the laser diode and the grating PZT to keep the laser frequency locked to 20

Figure 2.5 Cavity Servo Schematic. The fast path goes directly to the laser diode; the slow path goes through a Thorlabs pzt driver to the cavity pzt. the transmission mode of the cavity. A schematic of this circuitry is given in Figure

2.5. There are two paths to this circuit: a fast path, which goes directly to the diode, and a slow path, which controls the laser PZT. In this circuit the gain of the fast path goes through unity at ∼1 MHz; the gain of the slow path is around

∼1kHz. In the fast path, note that the error signal is amplified by a factor of 10 and sent directly to the diode.

Figure 2.6 shows the a PZT scan with and without the fast path of the lock circuit enabled. Since the transmission is held at the peak value, one can see that the fast path acquires the lock signal; because of low gain at DC, the fast path cannot maintain the lock. The necessarily high gain at DC is accomplished in the 21

0.5 0.5

0.25 0.25

0 0 Signal(V) Signal(V)

−0.25 −0.25

−0.5 −0.5 −20 −10 0 10 20 −20 −10 0 10 20 Frequency (MHz) Frequency (MHz)

error monitor error monitor ramp/50 ramp/50 transmission signal*10−.4V transmission signal*10−.4V

Figure 2.6 Fast Path Locked Signal. The trace on the left is without the fast path locked; the trace on the right shows the signal with the fast path locked. In both cases, the upper trace is the error signal monitor, the lower trace is the transmission signal. On the right, note the sustained maximum value of the transmission signal. The fast path is able to acquire a lock, but not hold it. integrator stage of the slow path of this circuit. Along the slow path, the capacitor across chip F is either shorted or not. This translates to infinite gain at DC or not.

In practice, the fast path is always closed and the slow path is closed only when the error signal is centered in the ramp.

After the fast path has been closed, we enable the integrator stage; that is, the capacitor is taken from short to not short. When this is successfully done, the transmission signal is held at its maximum level, and the error signal trace remains centered around zero. This is illustrated in Figure 2.7. The transmission trace is relatively flat; the characteristics of the cavity imply that this signal will not respond to changes in intensity that occur at frequencies higher than ∼600 kHz.

The noise on the error signal is significant. This noise indicates a linewidth, which is further discussed in Section 2.2.3.

A Fourier transform of the locked error signal can provide useful information 22

0.5 error monitor transmission signal*10−.4 0.4

0.3

0.2

0.1

0 Signal(V)

−0.1

−0.2

−0.3

−0.4

−0.5 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 −3 time (s) x 10 Figure 2.7 Locked Cavity Signal. The slow path working with the fast path locks the laser to the transmission mode of the cavity. Noise on the error signal is indicative of laser linewidth. on the frequency components of the noise in the system. The fourier transform in

Figure 2.8 shows that the major noise component occurs at ∼1MHz. This is consistent with the flat signal from the transmission monitor. It is unclear whether this is noise on the laser or noise resulting from poor electronics design. Future work includes modification of the fast path circuitry to yield higher gain out to 10 MHz, and thus narrow the linewidth considerably. A more in-depth discussion follows.

2.2.3 Linewidth Measurement

By looking at the excursion of the locked error signal, see Figure 2.7, (that is, the amplitude of the noise on the error signal) we can estimate the stability of the laser. Given that the sidebands are 100 MHz apart, we measure the slope of the error signal as 1MHz/400mV (see Figure 2.6A). The rms noise on the error signal is 23

−5 noise on locked error signal

−10

−15

−20

−25

−30

−35

FFT of noise on locked error signal (dB(V)) −40

−45

−50 2 3 4 5 6 7 10 10 10 10 10 10 Frequency (Hz) Figure 2.8 Fourier Transform of Locked Error Signal. The major noise components come in at 1 MHz. This noise could be on the laser or be due to poor circuit design.

∼56.57 mV. At first glance, this implies a linewidth of 140 kHz. Going one step further in the analysis, we fit this curve to a dispersion lineshape [30], and find that the slope at the center of the line is in fact 1 MHz/800mV. This implies a linewdith of 70 kHz. A laser with this linewidth is useful to cool and trap atoms. We plan to continue to improve the system to get a linewidth of ∼1kHz.

2.3 ECDL+Cavity and Atomic Sample

This laser-cavity system is useful only if we lock the cavity mode to the atomic transition. This section discusses the means by which we observe the atomic resonance and lock the cavity mode to it. 24

2.3.1 Spectroscopy

Now that the laser is locked to the cavity, we slowly scan the cavity PZT , which scans the transmission mode and thus the wavelength of the laser over an atomic absorption feature. We employ standard saturated absorption techniques

[31]. A schematic of the setup is shown in Figure 2.9. In absorption, as the laser scans over the atomic resonance, we see a dip in the power transmitted through the atomic sample. In saturated absorption, the pump and probe beam counterpropagate through the atomic sample. The pump beam is 10X more intense than the probe beam. When these two beams interact with the same velocity group, the pump beam has bleached the population in the ground state, and there are fewer atoms for the probe beam to excite. Thus, there is a small peak in the broader absorption dip.

By modulating the pump beam and using RF techniques to demodulate the absorption feature, we obtain an error signal. A typical error signal is shown in

Figure 2.10.

2.3.2 Servo Electronics

Using this error signal, and the servo circuitry shown in Figure 2.11, we lock the laser frequency to the atomic absorption feature. There is one path in this circuit – it is to the cavity PZT. There are two switches. The first is the switch from ramp to lock. The second from short to integrate. The following figure is the signature of a locked system. This lock circuit has a bandwidth of ∼1 kHz. It does 25

a) PD1

> >

probe

b)

PD1 > > > probe pump

Figure 2.9 Saturated Absorption Schematic. a)As the laser frequency sweeps through an atomic resonance, the power of the probe beam transmitted to the photodiode decreases. b) With the addition of a pump beam, the number of atoms available to absorb on resonance decreases; thus exactly on resonance, there is a peak in the absorption dip. 26

2

1.5

1

0.5

0 Volts

−0.5

−1

−1.5

−2 −10 −5 0 5 10 Freq (MHz) Figure 2.10 Saturated Absorption Error Signal. Modulating the probe beam and demodulating the photodiode signal yield this error signal.

Figure 2.11 Saturated Absorption Servo Schematic. There is a single path in this circuit, which has a bandwidth of 1 kHz. 27

2

1.5

1

0.5

0 Volts

−0.5

−1

−1.5

−2 −10 −5 0 5 10 Freq (MHz) Figure 2.12 Saturated Absorption Locked Signal. The noise on the locked signal is indicative of a frequency stability of 200 kHz within a 1 kHz bandwidth. not affect the linewidth of the laser, but determines how close the laser frequency is to the atomic transition. The slope of the error signal is .828 MHz/V. The noise on the locked error signal is equivalent to the noise on the zero portion of the unlocked error signal. This indicates a frequency stability of 200 kHz within a bandwidth of

1kHz, but is an extreme upper limit. We suspect the frequency stability is much better. If, for example, the laser frequency were stable to 1 kHz, the locked absorption error signal would look exactly the same, implying the same 200 kHz stability.

2.4 The Entire System

In summary, this is a two-stage lock. First, the laser is locked to a transmission mode of a high-finesse optical cavity. Next, the transmission mode of this cavity is 28 locked to a saturated absorption feature. When both locks are working, we have a narrow, stable, on resonance laser with which to do atomic physics.

An entire system schematic is shown in Figure 2.13; a basic description follows. A fraction of the ECDL output goes through a fiber to the high finesse cavity, which generates the cavity error signal; another fraction goes to the saturated absorption cell, which generates the atomic error signal. When the laser is locked to the cavity, and the cavity to the atoms, the system is locked and yet another fraction of the power goes through a polarization preserving optical fiber to the experimental setup. Preliminary laser cooling and trapping results with the 70 kHz linewidth laser follow in Chapter 3. 29

M6 M7 PD3 M10 M13 PBS2 L6 PD1 To MOT M11 FC2 HFC PD2 L7

L4 L8 M8 EOM SAC

QWP M16 PBS3 M12 L5 M15 M14

M9 AOM2

OI1 L1 OI2 AOM1 M3 L3 M2 FC1 M6 HWP1 HWP2 PBS1 M1 M4 M5 L2

Figure 2.13 System Schematic. This is an accurate layout of the 689 nm system on the optics table. Those elements labelled with M are mirrors, L are lenses, PBS are polarizing beam splitters, QWP are quarter wave plates, HWP are half waveplates, PD are photodiodes, OI are optical isolators, FC are fiber couplers, and AO are acousto-optic modulators. The EOM is an electro-optic modulator, SAC is the saturated absorption cell, and HFC is the high finesse cavity. Chapter 3 Results

With the ECDL locked to the cavity, and the cavity locked to the atomic transition, cooling and trapping experiments are possible. This section includes a discussion of experimental operation of the 461 nm (blue) MOT and absorption imaging, as well as preliminary results from the 689 nm (red) MOT.

3.1 Blue MOT Operation and Diagnostics

1 1 The magneto-optical trap on the S0 → P1 transition in strontium has been working in our lab for almost two years[17]. In this setup, atoms are slowed by a

Zeeman beam and trapped by three orthogonal retro-reflected beams. The current in the anti-Helmholtz coils is 40A. We measure the number of atoms and sample temperature using absorption imaging techniques, illustrated in Figure 3.1. These techniques involve illuminating the sample with a collimated, near-resonant beam that falls on a CCD camera. The atoms absorb the beam, casting a shadow.

Recall, if either the trapping lasers or the magnetic field gradient is not present, the atoms are not trapped. Starting with a cold trapped sample, we turn off the trapping lasers at a time t=0, wait a time t, and then apply the imaging beam. During this time t, the atoms expand ballistically. The ccd camera records a laser intensity pattern with atoms present I(x, y)atoms, and without I(x, y)back. 31

CCD camera

Image

Figure 3.1 Absorption imaging. A collimated near-resonant beam illuminates the atomic sample and falls on a ccd camera. The atoms absorb a fraction of the incident power, thus casting a shadow. From Beer’s law, we define optical depth (OD) in the following manner:

Z ∞ I(x, y) n σ 2 2 2 2 back 0 abs −x /2σx−y /2σy OD(x, y) = ln[ ] = σabs dzn(x, y, z) = √ e , (3.1) I(x, y)atoms −∞ 2πσz where n0 is the peak atom density, and σabs is the absorption cross section. We have inserted a Gaussian density distribution for the atoms in the last line, which leads to the function used to fit the data. This fitting routine is identical to the one used in the Killian group’s most recent paper[35]. Figure 3.2 shows a typical absorption image taken after a delay time of 3 ms. The number of atoms in the blue MOT is typically 3x108.

This optical density fitting routine yields σx and σy, the rms widths of the cloud. These widths expand according to the following equation:

2 2 2 2 σ = σ0 + v t , (3.2)

q where v is given by kbT/M [34].

By fitting our data to this equation, we extract a temperature. Figure 3.2 shows a typical blue MOT temperature of 1.9 mK. 32

1.2

1.4

1.2 1

1

0.8 0.8 0.6

0.4 Optical Depth 0.6 0.2

0 0.4 −0.2 1.5

1.5 1 0.2 −3 x 10 1 0.5 −3 0.5 x 10 0 Y (m) 0 0 X (m)

Figure 3.2 Blue MOT Absorption Image. This image shows the spatial distribution of the atomic sample after a delay time of 3 ms.

−3 x 10 1.8

1.7

1.6

1.5

Sigma Y (m) 1.4

1.3

data 1.2 fit

1.1 500 1000 1500 2000 2500 3000 delay (us) Figure 3.3 Blue MOT Temperature Determination. The fit to the data indicates a temperature of 1.9 mK. 33

3.2 Red MOT Operation and Diagnostics

The typical blue MOT sample discussed above has a temperature on the order of a few mK, which results in a Doppler broadening (3-4 MHz) of the intercombination line resonance. As mentioned earlier, in order to transfer an appreciable fraction of the atoms from the blue MOT to the red MOT, it is necessary to artificially broaden the 689 nm laser. Otherwise, the laser would be on resonance with a very small fraction of the trapped atoms and the transfer efficiency would be likewise very small (few percent). We broaden the laser by modulating the frequency of an acousto-optic modulator (AOM) by 1.6 MHz at a modulation frequency of 10 kHz. The fact that we have a 100 kHz wide laser, rather than 1 kHz, thus has no effect on the initial capture dynamics.

The experimental setup is very similar to the blue MOT setup; in fact, the red

MOT beams follow the same three retro-reflected paths as the blue MOT beams.

This beam overlap and the use of the same anti-helmholtz coils ensure that the centers of the two MOTs overlap. The red MOT is significantly more susceptible to stray magnetic fields than the blue, and we use trim coils to counteract those stray

fields.

Experimentally, the sequence of events is as follows: we start by trapping atoms in the blue MOT. The field gradient here is 115 G/cm. Then, we switch off the blue MOT beams, ramp down the magnetic field gradient (for the red MOT we need only 3 G/cm), and switch on the red MOT beams. After cooling for 35 ms, we 34

0.25

0.3

0.25 0.2

0.2

0.15 0.15

0.1 Optical Depth 0.05 0.1 0

−0.05 1.5 0.05 1.5 1 −3 x 10 1 0.5 −3 0.5 x 10 0

Y (m) 0 0 X (m)

Figure 3.4 Red MOT Absorption Image. This image shows the spatial distribution of the atomic sample after a delay time of 20 ms. Note that this distribution is much narrower than the blue MOT absorption image, indicating a much lower temperature.

turn off the red MOT beams. This is our new t = 0. After waiting a time t, the same imaging procedure is followed. Figure 1.4 shows an image taken after a delay time of 20 ms. When comparing to the blue absorption image, it is readily apparent that even though the delay time has increased by a factor of 7, the atoms have not spread out as far. The number of atoms in this red MOT is around 4x107. These numbers imply a transfer efficiency of around 13%.

We already know that the temperature of this sample is much lower than with the blue MOT. This figure illustrates that the same fitting routine yields a temperature of 15.3 µK. Thus, we have cooled a few x107 atoms to the µK regime with a MOT size of under 1 mm. 35

−4 x 10 9

8

7

6 Sigma Y (m)

5

data 4 fit

3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 4 delay (us) x 10 Figure 3.5 Red MOT Temperature Determination. The fit to the data indicates a temperature of 15.3 µK.

3.3 Outlook

This result is consistent with the findings of Katori[27] and more recently, the work of Loftus et al. at JILA[28]. These groups have done more detailed studies with narrower lasers. Their maximum transfer efficiency was ∼30%, yielding samples on the order of 107 atoms with temperatures on the order of 1 µK. These efforts have been towards quantum degeneracy, but it has not yet been achieved.

The limitations of this system as it stands are the laser linewidth and our technology to control the amplitude of the broadening of the laser. Also, these results are recent and we have not optimized the trapping and cooling. In both the

Katori and JILA experiments, the amplitude of the broadening of the laser was varied over time to yield colder samples and higher transfer efficiency. We have 36 recently purchased a higher resolution DAC card to control this dither amplitude, and we will be making improvements in the locking electronics (specifically, the fast path of the cavity lock). I am confident that with these improvements, we, too, will be able to cool to sub-µK temperatures.

In the meantime, we will transfer this 15 µK sample into a dipole trap. This trap will be ideal for collision studies, as well as for evaporative cooling studies towards quantum degeneracy. Appendix A Troubleshooting

This system exhibits a number of clearly recognizable failure modes. The first such failure mode discussed below, and the most drastic, occurs when a laser diode has been damaged and must be replaced and aligned. In six months, this has happened once and was traced to a mechanical failure: one of the solder joints in the cable from the current driver to the diode came undone. In similar experiments, unperturbed diode lifetimes range from 2-4 years. The second topic discussed is

finding and locking the cavity error signal. After replacing the diode, or in day-to-day experimental work, it is sometimes difficult to acquire and lock to an error signal from the cavity, the atomic resonance, or both. The third topic discussed is finding and locking to the atomic error signal. Finally, an overall system schematic is given.

A.1 Replacing a Laser Diode

In the unfortunate event that a laser diode becomes damaged, it must be replaced and the replacement aligned. The signatures of a damaged laser diode are as follows: reduced output power, poor mode quality, or (worst of all) no light at all.

Replacing a diode is a rather drastic procedure – be sure it is absolutely necessary.

The first check is to unplug the small plastic connector from the back of the laser diode and use a cheap Thorlabs diode to replace it. If the Thorlabs diode works, the 38 problem is the laser diode. If the Thorlabs diode does not work, the problem is not with the laser diode. Make sure you check the connections to the current driver. As a last resort, check the resistance of the diode. If the resistance is infinite in both directions, the diode has blown and must be replaced. Be very careful with the new diode; it is very susceptible to electrostatic discharge. Once the laser is safely mounted in its housing, and connected to the current driver, the following procedures must be followed: initial alignment, threshold current determination, and scanning through the target wavelength.

A.1.1 Initial Alignment

As mentioned in Chapter 1, initial alignment is critical. Make sure that the plane defined by the anode and cathode pins of the laser diode is vertical and parallel to the grooves on the grating, as this produces the correct polarization of the beam. Then turn on the power. Align the grating such that the first order beam is reflected back into the diode first with gross rotation of the brass mount, then with the small adjustment screws. Be careful! The horizontal adjustment screw is in contact with the cavity pzt. You can break this pzt with too much pressure. Also, be careful not to strip the vertical adjustment screw; there are only three or four turns available to you. For more drastic vertical alignment changes, remove the screw altogether and use pliers and/or a screwdriver to reset the zero of this adjustment by squeezing or prying apart this part of the brass mount. Here, too, be careful of the pzt and squeeze the mount on the pivot side of center. 39

Now, check the wavelength. Your target wavelength is 689.45 nm. Testing this requires getting the light to the other table. Here’s how: adjust the initial steering mirrors (M1 in the schematic from Chapter 2) to get some power coupled into the

fiber to go to the other table – you usually need about 5 mW into the fiber and decent coupling to get a reading from the wavemeter. If the wavelength is more than one tenth of a nanometer off, change the grating angle by adjusting the horizontal axis set screw in the grating mount [clockwise for higher wavelength; counterclockwise for lower]. These horizontal adjustments will adversely affect your alignment to the fiber; a correction with the first steering mirror is all that is required to regain proper alignment. Once you are within a tenth of a nanometer,

finer tuning can be accomplished by making small changes in the temperature and current (See Section 2.1). Before making finer adjustments, however, it is useful to measure the threshold current and adjust the vertical alignment.

A.1.2 Threshold Current

The threshold current for lasing is an indication of good vertical grating alignment and indicates that the grating is controlling the output of the laser diode.

At low current, the diode does not lase without feedback – and if you see lasing, you know you’ve got feedback and the alignment is good. The lower the threshold, the better your alignment, and the better the grating is controlling the output of the laser diode. First, take the current to some low value, around 50 mA. As you turn this vertical adjustment screw on the grating mount, watch the laser output on a 40 card. Again, be careful not to strip this screw. As you tune through good alignment, the spot will be dim, brighten, and be dim again. The goal here is to zero in on the bright spot. If you reduce the current and sweep through again, the brightening will not last as long – you have better resolution and can sweep a smaller range of values.

Using this method of reducing the current and twiddling the vertical adjustment screw, zero in on the bright spot. Make the current and the adjustment as small as you can. N.B. If the current is too low, you will not see the brightening at all.

Now, you have found the threshold current, that drive current for which the brightening just barely occurs and which assures good vertical alignment. Typical values for threshold current with this setup are between 41 and 44 mA, depending on the diode.

A.1.3 Target Wavelength

Now, for the tricky part. You know the vertical grating alignment is good, because the threshold current is at a minimum. And you know that the horizontal grating alignment is in the ballpark, because the wavelength is close to within .1nm.

The next step is to find a good mode (scanning with the grating pzt) near the target wavelength. The best way to see this is with the wavemeter in the wavenumber setting rather than wavelength. The atomic resonance is located at or near 14504.33 cm−1. So, what do you do? First examine where you are right now: how far can you scan with the pzt? Don’t worry too much about the absolute numbers, but see how far you can travel without hopping. If it’s under .06 cm−1, 41 you need to look for a better mode. If it’s between .06 and .08 cm−1 the mode is acceptable, but not great. If it’s between .08 and .10 cm−1 the mode is good, and if the scan is greater than that – this is the mode for you! If the reading is too low

−1 (14504.2 cm ) you want to bring it up with temperature (Tmon voltage up by .1V) or with current(down 2mA) – this is definitely the art part of working with this system. Sometimes you will be closing in on the resonance, and the laser will jump modes. Don’t be discouraged. Just play around with the pzt voltage to find your mode and try again. It takes some work, but you’ll get there.

A note on boundaries for temperature, current, and pzt voltage. If the temperature goes below 160C water will begin to condense on the diode; if the temperature goes above 280C the lifetime of the diode will be reduced significantly.

So, you want to keep the voltage on the temperature monitor between 1.5V (cold) and .95V(hot). If the current goes below 65 mA, you will have a significant reduction of output power; the maximum operating current for this diode is 85 mA, the supply is set to not go over 80 mA. So, the current is limited to 65-80 mA. The pzt used in the extended cavity mount is polarized: can take -15V to +200V. In practice, we like to keep the voltage on this pzt between 20 and 80 V, which allows for large excursions if necessary for locking.

With these guidelines, and some time, you should be able to scan from

14504.29-14504.36 cm−1 at a minimum. Equipped with this scan, and the proper alignment, you will be able to observe the cavity error signal and the atomic error 42 signal in the straightforward manner described in the following section.

A.2 Cavity Error Signal Acquisition and Locking

In order to observe an error signal, there must be a modulation present as well as a resonance. In the cavity system, the modulation is provided by an EOM; the resonance arises as discussed in the classic PDH paper [29]. In this section, we discuss error signal acquisition and locking.

A.2.1 Cavity Error Signal Acquisition

There are a number of things that can go wrong with the cavity error signal.

The first is that you see no signal at all. The second is that the signal has more than a 5% offset – or that it is off center. Before you go any further, make sure all the switches in both circuits are in the ”unlocked” position. Also during this process, monitor the transmission signal as well as the error signal.

So, if you see absolutely no error signal, the cavity fiber alignment could be poor, the pzt settings could be wrong, the EO could be malfunctioning, or the laser could be multimode. Check the alignment to the cavity fiber. In general, the coupling is around 60% with 180 µ W input power. This gives you a DC voltage of around 45mV on the PD monitor. If the efficiency is poor, improve your coupling by adjusting the beamsplitter and the mirror before the EO. Once the power through is good, look for the error signal again. If there is still no signal, check the cavity pzt scan width and offset – the offset should be between 40 and 80 V with a scan width greater than 20V. This will assure at least one cavity mode in the scan. If the fiber 43 coupling is good and the cavity pzt scan is on target and you still see no signal, check the frequency of the EO – it should be around 48.87 MHz. If none of these are the problem, the laser could be multi-mode. Try hopping the cavity mode by adjusting current and/or temperature. You may not be on the target wavelength, but you should see something. If you see a transmission signal, but no error signal, the problem is with the EO or the RF electronics. Use the SRS lock in amplifier instead of the mixer assembly to see the error signal. If, however, you see no transmission as well as no error signal, you may need to realign the cavity.

Once you have regained an error signal, it may have a significant offset or deviation from center. In order to correct for the offset, adjust the horizontal screw on the EO mount. This is a sensitive adjustment: if you go too far, you will cut down your signal significantly; if not enough, you will have difficulty locking. To correct for a deviation of the central feature from the center of the scan, simply change the cavity pzt offset voltage.

A.2.2 Locking to the Cavity

Now that you have an error signal, why can’t you lock the to the cavity? Make sure your offset is small – the best place to check this is at TP3. Also, make sure that the switches are initially set to ”short” and not locked. Get the error signal to the center of the ramp by adjusting the laser pzt offset. Narrow the range of the cavity sweep until neither sideband is visible, and only the central zero-crossing feature is visible. Now lock the fast path. If you are still in the error signal, switch 44 the pzt path from not locked to locked. Then switch from short to integrate. This may take a few tries, but you’ll get there.

A.3 Atomic Error Signal Acquisition and Locking

In the atom system, the modulation is provided by sweeping the frequency on an AOM. The atomic resonance is canonical doppler-free saturated absorption spectroscopy [31].

A.3.1 Atomic Error Signal Acquisition

There are a number of things that can go wrong with the atomic error signal.

The first is that you see no signal at all. The second is that the signal has more than a 5% offset – or that it is off center. In order to see the atomic error signal, though, the laser must be locked to the cavity, which is scanning over the atomic resonance.

So, before proceeding, make sure the laser is locked to the cavity, and that it’s the right mode. Also, you want to monitor the absorption signal as well as the error signal during this process. So, if you see neither the error signal nor the absorption signal, the saturated absorption alignment could be poor, the pzt settings could be wrong, the AO could be malfunctioning, or the laser could be on the wrong cavity mode. Check the saturated absorption alignment to the photodiodes: the probe beam falls on a fast photodiode; the pump falls on a monitor. The monitor photodiode is usually around 35 mV. If the alignment is poor, improve it using the four satabs steering mirrors[M6,7,8,9]. Once the alignment is good, look for the error signal again. If there is still no signal, check the cavity pzt scan width and 45 offset – The offset should be between 40 and 80 V with a scan width greater than

20V. Check that the wavelength is at 14504.33-.34 cm−1. If your alignment is good and the cavity pzt scan is on target and you still see no signal, check the frequency and amplitude of the AC voltage to the AO – it should be a 50mV signal at 10kHz.

If none of these are the problem, adjust the pzt offset and explore the wavelength region a bit – sometimes the wavemeter can wander. If you see the absorption and not the error signal, the problem is with the AO or the RF electronics. You may need to restart the PerkinElmer lock-in amplifier.

A.3.2 Locking to the Atomic Feature

Locking this circuit is fairly simple. Reduce the amplitude of the cavity pzt scan until you can see only the zero-crossing feature of the error signal. The switch from ramp to lock. Make sure you are still in the error signal by changing the pzt offset slightly and seeing the pzt signal respond in the opposite direction. Then zero up the offset and switch from short to integrate. 46

. 47

References

1. E. L. Raab, M. Prentiss, A. Cable, S. CHu, and D. E. Pritchard. Trapping of neutral sodium atoms with radiation pressure. Phys. Rev. Lett., 59 (23): 2631-2634. 1987. 2. H.J. Metcalf anf P. van der Straten. Laser Cooling and Trapping, Springer-Verlag New York, 1999. 3. K.R. Vogul. Laser Cooling on a Narrow Atomic Transition and Measurement of the Two-Body Cold Collsion loss rate in a Strontium magneto-optical trap. University of Colorado. Boulder, CO 1999. 4. T.W. Hansch and A.L. Schawlow. Cooling of gases by laser radiation. Opt. Commun., 13(1): 68-69, 1975. 5. D. Wineland and H. Dehmelt. Bull. Am. Phys. Soc., 20: 637, 1975. 6. D.J. Wineland, R.E. Drullinger, and F.L. Walls. Radiation-Pressure Cooling of Bound Resonant Absorbers. Phys. Rev. Lett, 40(25): 1639-1643, 1978. 7. V.I. Balykin, V.S. Letokhov, and V.I. Mushin. Observation of the cooling of free sodium atoms in a resonance laser field with a scanning frequency. JETP Lett., 29(10): 560-564, 1979. 8. W.D. Philllips and H. Metcalf. Laser deceleration of an atomic beam. Phys. Rev. Lett., 48(9): 596-599, 1982. 9. J. Prodan, A. Midgall, W.D. Phillips, I. So, H. Metcalf, and J. Dalibard. Stopping atoms with laser light. Phys. Rev. Lett., 54(10): 992-995,1985. 10. W. Ertmer, R. Blatt, J.L. Hall, and M. Zhu. Laser manipualtion of atomic beam velocities:demonstration of stopped atoms and velocity reversal. Phys. Rev. Lett., 54(10): 996-999, 1985. 11. S.Chu, L. Hollberg, J.E. Bjorkholm, A. Cable and A. Ashkin. Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure. Phys. Rev. Lett., 55(1): 48-51, 1985. 12. J.P. Gordon and A. Ashkin. Motion of atoms in a radiation trap. Phys. Rev. A, 21(5): 1606-1617, 1980. 13. R.J. Cook. Quantum-mechaincal fluctuations of the resonance-radiation force. Phys. Rev. Lett, 44(15): 976-979, 1980. 14. S. Stenholm. The semiclassical theory of laser cooling. Rev. Mod. Phys., 58(3): 699-739, 1986. 48

15. P.D. Lett, W.D. Phillips, S.L. Rolston, C.E. Tanner, R.N. Watts, and C.I. Westbrook. Optical Molasses. J. Opt. Soc. Am. B, 6(11): 2084-2107, 1989.

16. D.J. Wineland and W.M. Itano. Laser cooling of atoms. Phys. Rev. A, 20: 1521-1540, 1979.

17. S.B. Nagel, C.E. Simien, S. Laha, P. Gupta, V.S. Ashoka, and T.C. Killian. 3 Magnetic trapping of metastable P2 atomic strontium.Physical Review A, 67, 011401(R), 2003.

18. H. G. C. Werij, C. H. Greene, C.E. Teodosiou, and A. Gallagher. Oscillator strengths and radiative branching ratios in atomic Sr. Phys. Rev.A., 46(3): 1248-1260, 1992.

19. E.U. Condon and G.H. Shortley. Theory of Atomic Sepctra. Cambridge University PRess, London. 1963.

20. P.D. Lett, W.D. Phillips, S.L Rolston, C.E. Tanner, R.N. Watts, and C.I. Westrook. Optical Molasses J. Opt. Soc. Am. B, 6(11): 2084-2107, 1989.

21. J. Dalibardand C. Cohen-Tannoudji. Laser cooling below the Doppler limit by poarization gradients: simple theoretical models. J. Opt. Soc. Am. B, 6(11): 2023-2045, 1989.

22. J.L. Hall and T.W. Hansch. External Dye-laser frequency stabilizer. Optics Lett., 9(11): 502-504, 1984.

23. R.W. Fox, L. Hollberg, and A.S. Zibrov. Semiconductor Diode Lasers. Atomic, Molecular, and Optical Physics: Electromagnetic Radiation,(ed. F.B. Dunning and R.G. Hulet, Academic Press) of 29C series Experimental Methods in the Physical Sciences. 77-102, 1997.

24. A.Schoof, J. Grunert, S.Ritter, and A. Hemmerich, Opt. Soc. of America, 26, 20, 2001.

25. B.C. Young, F.C. Cruz, W.M Itano and J.C. Bergquist. Visible Lasers with subhertz linewidths. Phys. Rev. Lett., 82: 3799-3802, 1999.

26. C.E. Wieman and L. Hollberg.Using Diode Lasers for Atomic Physics,Rev. Sci. Instrum., 62: 1-20, 1991.

27. H.Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami. Magneto-Optical Trapping and Cooling of Stronitum Atoms down to the Photon Recoil Temperature.Phys. Rev. Lett., 82: 1116, 1999. 49

28. T.H. Loftus, T. Ido, A.D. Ludlow, M.M. Boyd, and J.Ye. Narrow Line Cooling:From Semiclassical to Quantum Dynamics. arxiv:physics/0401055, 2004.

29. R.W.P. Drever, J.L. Hall, F.V. Kowalski et al, Applied Phys. B, 31: 97-105, 1983.

30. W.Y.W. Morshidid. Frequency Modulation Spectroscopy for Frequency Stabilization of Dye-Laser. Massachusetts Institute of Technology. May 1994.

31. Demtroder, Atomic Spectroscopy, the whole book

32. B.Dahmani, L. Hollberg, R. Drullinger, Optics Letters, 12: 876-879, 1987.

33. http://www.bldrdoc.gov/timefreq/ofm/lasers/ecdls.htm, accessed 03/16/2004.

34. D.S. Wiess, E. Riis, Y. Shevy, P.J. Ungar, and S. Chu. Optical MOlasses and mulitlevel atoms: experiment.J.Opt. Soc. Am. B, 6(11): 2072-2083, 1989.

35. C.E. Simien, Y.C. Chen, P. Gupta, S. Laha, Y.N. Martinez, P.G. Mickelson, S.B. Nagel, and T.C. Killian. Using Absorption Imaging to Study Ion Dynamics in an Ultracold Neutral Plasma. Phys. Rev. Lett, 92(14): 143001, 2004.