Squeezed Light from a Silicon Micromechanical Resonator

Total Page:16

File Type:pdf, Size:1020Kb

Squeezed Light from a Silicon Micromechanical Resonator LETTER doi:10.1038/nature12307 Squeezed light from a silicon micromechanical resonator Amir H. Safavi-Naeini1,2*, Simon Gro¨blacher1,2*, Jeff T. Hill1,2*, Jasper Chan1, Markus Aspelmeyer3 & Oskar Painter1,2,4 Monitoring a mechanical object’s motion, even with the gentle electromechanical elements20, solid-state mechanical elements21–23 and touch of light, fundamentally alters its dynamics. The experimental ultracold gas-phase atoms6,24 integrated with or comprising Fabry–Pe´rot manifestation of this basic principle of quantum mechanics, its cavities, and on-chip nanophotonic cavities sensitive to mechanical link to the quantum nature of light and the extension of quantum deformations25,26. measurement to the macroscopic realm have all received extensive The canonical cavity-optomechanical system consists of an optical attention over the past half-century1,2. The use of squeezed light, with cavity resonance that is dispersively coupled to the position of a mech- quantum fluctuations below that of the vacuum field, was proposed anical resonance. The Hamiltonian describing the interaction between 3 ~ { ~ ^{z^ nearly three decades ago as a means of reducing the optical read-out light and mechanics is Hint Bgp0a^ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia^^x xzpf , where ^x xzpf (b b) is noise in precision force measurements. Conversely, it has also been the mechanical position, xzpf ~ B=2meff vm is the zero-point fluc- proposed that a continuous measurement of a mirror’s position with tuation amplitude, vm is the mechanical resonance frequency, meff is light may itself give rise to squeezed light4,5. Such squeezed-light the effective motional mass of the resonator, g0 is the frequency shift of generation has recently been demonstrated in a system of ultracold the optical resonance for a mechanical amplitude of x , B is Planck’s 6 zpf gas-phase atoms whose centre-of-mass motion is analogous to the constant divided by 2p, a^ and ^a{ are respectively the annihilation and motion of a mirror. Here we describe the continuous position mea- creation operators for optical excitations, and ^b and ^b{ are the analog- surement of a solid-state, optomechanical system fabricated from a ous operators for mechanical excitations. The optical cavity decay rate, silicon microchip and comprising a micromechanical resonator k, is the loss rate of photons from the cavity and the rate at which coupled to a nanophotonic cavity. Laser light sent into the cavity is optical vacuum fluctuations are coupled into the optical resonance27. used to measure the fluctuations in the position of the mechanical Similarly, the mechanical damping rate, ci, is the rate at which thermal resonator at a measurement rate comparable to its resonance fre- bath fluctuations couple to the mechanical system. In all experimental quency and greater than its thermal decoherence rate. Despite the realizations of solid-state optomechanics so far, including that pre- mechanical resonator’s highly excited thermal state (104 phonons), sented here, the optomechanical coupling rate, g0, has been much we observe, through homodyne detection, squeezing of the reflected smaller than k. As such, without a strong coherent drive, the inter- light’s fluctuation spectrum at a level 4.5 6 0.2 per cent below that of action of the vacuum fluctuations with the mechanics is negligible. vacuum noise over a bandwidth of a few megahertz around the Under the effect of a coherent laser drive, the cavity is populated with mechanical resonance frequency of 28 megahertz. With further a mean intracavity photon number Æncæ, and wep considerffiffiffiffiffiffiffiffi the optical fluc- device improvements, on-chip squeezing at significant levels should tuations about the classical steady state, ^a? hnciza^. This modifies be possible, making such integrated microscale devices well suited the optomechanical interaction, resulting in a linear coupling between for precision metrology applications. { the fluctuations of the intracavity optical field, X^0~^aza^ , and the The generation of states of light with fluctuations below that position fluctuations of the mechanical system, ^x: H ~BGX^ ^x x . 3,7–9 int 0 zpf of vacuum has been of great theoretical interest since the 1970s . Thep parametricffiffiffiffiffiffiffiffi linear coupling occurs at an effective interaction rate of Early experimental work demonstrated squeezing of a few per cent G: hncig0, and the mechanical motion is coupled to the intracavity below the vacuum noise level in a large variety of different nonlinear optical field at a rate of C ; 4G2/k. Through this interaction, the 10 11 meas systems, such as neutral atoms in a cavity , optical fibres and crystals intensity fluctuations of the vacuum field, X^ (in) (t), entering the cavity 12,13 h~0 with bulk optical nonlinearities . Modern experiments demonstrate impart a force on the mechanical system: squeezing of almost 13 dB (ref. 14). Initial research was mainly pursued pffiffiffiffiffiffiffiffiffiffiffi B C as a strategy to mitigate the effects of shot-noise, the manifestation ^ ~ meas ^ (in) FBA(t) Xh~0(t) ð1Þ of vacuum noise in the intensity detection of light, given the possi- xzpf bility of improved optical communication7 and better sensitivity in This radiation-pressure shot-noise (RPSN) force has previously been gravitational-wave detectors3,8. In recent years, in addition to being measured in an ultracold atomic gas24 and, more recently, on a mac- used in gravitational-wave detectors15, squeezed light has enhanced roscopic silicon nitride nanomembrane28. The mechanical motion is in metrology in more applied settings16,17. turn recorded in the phase of the light leaving the cavity: The vacuum fluctuations arising from the quantum nature of light pffiffiffiffiffiffiffiffiffiffiffi C determine our ability to resolve mechanical motion optically, and set ^ (out) ~{^ (in) { meas 18 Xh (t) Xh (t) 2 ^x(t) sin (h) ð2Þ limits on the perturbation caused by the act of measurement .A xzpf system well suited to studying quantum measurement experimentally ^ (j)~ {ihz { ih is that of cavity optomechanics, in which an optical cavity’s resonance Here Xh ^aje ^aj e , a^in and ^aout are respectively the operators of frequency is designed to be sensitive to the position of a mechanical the input and reflected optical fields from the cavity, and h is the quad- system. By monitoring the phase and intensity of the reflected light rature angle with h 5 0 and h 5 p/2 corresponding respectively to the from such a cavity, a continuous measurement of mechanical displace- intensity and phase quadratures. In such a measurement, the optical ment can be made. Systems operating on this simple principle have cavity has the role of the position detector, measuring the observable ^x been realized in a variety of experimental settings, such as in large-scale at a rate Cmeas, and the RPSN imposes a measurement back-action force laser gravitational-wave interferometers19, microwave circuits with on the mechanical system2. In addition to this back-action noise, thermal 1Kavli Nanoscience Institute and Thomas J. Watson, Sr, Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA. 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA. 3Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, A-1090 Wien, Austria. 4Max Planck Institute for the Science of Light, Gu¨ nther-Scharowsky-Straße 1/Bldg 24, D-91058 Erlangen, Germany. *These authors contributed equally to this work. 8 AUGUST 2013 | VOL 500 | NATURE | 185 ©2013 Macmillan Publishers Limited. All rights reserved RESEARCH LETTER fluctuations from the bath also drive the mechanical motion, with motion of the zipper cavity. A wavelength scan of the reflected signal their magnitudes becoming comparable as Cmeas approaches the ther- from the cavity is plotted in Fig. 2b, showing an optical resonance malization rate, Cthermal(v):cin(v),wheren(v) is the thermal bath with a linewidth k/2p 5 3.42 GHz at a wavelength of lc 5 1,540 nm. occupancy. Inefficiencies in the collection and detection of light result in addi- Formally, the output noise power spectral density (PSD) of the tional uncorrelated shot-noise in the measured signal and can reduce homodyne detector photocurrent, I, normalized to the shot-noise level the squeezing to undetectable levels. For the device studied here, the is found by taking the Fourier transform of the autocorrelation of cavity coupling efficiency, corresponding to the percentage of photons equation (2): sent into the cavity which are reflected, is determined to be gk 5 0.54. The g 5 C B fibre-to-chip coupling efficiency is measured at CP 0.90. A homodyne out ~ z 4 meas 2 z SII (v) 1 2 Sxx sin (h) Refxmg sin (2h) ð3Þ detection scheme allows for high-efficiency detection of arbitrary quad- xzpf 2 ratures of the optical signal field. Characterization and optimization of the efficiency of the entire optical signal path and homodyne detection where Sxx(v) is the noise PSD of the mechanical position fluctuations { g 5 of the resonator and x (v)~(m (v2 {v2{ic v )) 1 is the mech- system yielded an overall set-up efficiency of set-up 0.48, correspond- m eff m i m g 5 g g 5 anical susceptibility characterizing the response of the mechanical ing to a total signal detection efficiency of tot set-up k 0.26. Figure 2c shows the noise spectrum of the thermal motion of the system to an applied force. The PSD S (v) contains noise stemming xx mechanical resonator obtained by setting the laser frequency near from coupling to the thermal bath, quantum back-action noise from the cavity resonance and tuning the relative local-oscillator phase the light field and any other technical laser noise driving the mechanics of the homodyne detector, h , to measure the quadrature of the (Supplementary Information). The three terms in Sout(v) in equa- lock II reflected signal in which mechanical motion is imprinted.
Recommended publications
  • Polarization Squeezing of Light by Single Passage Through an Atomic Vapor
    PHYSICAL REVIEW A 84, 033851 (2011) Polarization squeezing of light by single passage through an atomic vapor S. Barreiro, P. Valente, H. Failache, and A. Lezama* Instituto de F´ısica, Facultad de Ingenier´ıa, Universidad de la Republica,´ J. Herrera y Reissig 565, 11300 Montevideo, Uruguay (Received 8 June 2011; published 28 September 2011) We have studied relative-intensity fluctuations for a variable set of orthogonal elliptic polarization components of a linearly polarized laser beam traversing a resonant 87Rb vapor cell. Significant polarization squeezing at the threshold level (−3dB) required for the implementation of several continuous-variable quantum protocols was observed. The extreme simplicity of the setup, which is based on standard polarization components, makes it particularly convenient for quantum information applications. DOI: 10.1103/PhysRevA.84.033851 PACS number(s): 42.50.Ct, 42.50.Dv, 32.80.Qk, 42.50.Lc In recent years, significant attention has been given to vapor cell results in squeezing of the polarization orthogonal to the use of continuous variables for quantum information that of the pump (vacuum squeezing) [14–17] as a consequence processing. A foreseen goal is the distribution of entanglement of the nonlinear optical mechanism known as polarization self- between distant nodes. For this, quantum correlated light rotation (PSR) [18–20]. Vacuum squeezing via PSR has been 87 beams are to interact with separate atomic systems in order observed for the D1 [15–17] and D2 [14] transitions using Rb to build quantum mechanical correlations between them [1,2]. vapor. As noted in [9], the existence of polarization squeezing A particular kind of quantum correlation between two light can be inferred from these results.
    [Show full text]
  • Multichannel Cavity Optomechanics for All-Optical Amplification of Radio Frequency Signals
    ARTICLE Received 6 Jul 2012 | Accepted 30 Aug 2012 | Published 2 Oct 2012 DOI: 10.1038/ncomms2103 Multichannel cavity optomechanics for all-optical amplification of radio frequency signals Huan Li1, Yu Chen1, Jong Noh1, Semere Tadesse1 & Mo Li1 Optomechanical phenomena in photonic devices provide a new means of light–light interaction mediated by optical force actuated mechanical motion. In cavity optomechanics, this interaction can be enhanced significantly to achieve strong interaction between optical signals in chip-scale systems, enabling all-optical signal processing without resorting to electro-optical conversion or nonlinear materials. However, current implementation of cavity optomechanics achieves both excitation and detection only in a narrow band at the cavity resonance. This bandwidth limitation would hinder the prospect of integrating cavity optomechanical devices in broadband photonic systems. Here we demonstrate a new configuration of cavity optomechanics that includes two separate optical channels and allows broadband readout of optomechanical effects. The optomechanical interaction achieved in this device can induce strong but controllable nonlinear effects, which can completely dominate the device’s intrinsic mechanical properties. Utilizing the device’s strong optomechanical interaction and its multichannel configuration, we further demonstrate all-optical, wavelength- multiplexed amplification of radio-frequency signals. 1 Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota
    [Show full text]
  • Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology Aaron Hankin
    University of New Mexico UNM Digital Repository Physics & Astronomy ETDs Electronic Theses and Dissertations 1-28-2015 Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology Aaron Hankin Follow this and additional works at: https://digitalrepository.unm.edu/phyc_etds Recommended Citation Hankin, Aaron. "Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology." (2015). https://digitalrepository.unm.edu/phyc_etds/23 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at UNM Digital Repository. It has been accepted for inclusion in Physics & Astronomy ETDs by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected]. Aaron Hankin Candidate Physics and Astronomy Department This dissertation is approved, and it is acceptable in quality and form for publication: Approved by the Dissertation Committee: Ivan Deutsch , Chairperson Carlton Caves Keith Lidke Grant Biedermann Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology by Aaron Michael Hankin B.A., Physics, North Central College, 2007 M.S., Physics, Central Michigan Univeristy, 2009 DISSERATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Physics The University of New Mexico Albuquerque, New Mexico December 2014 iii c 2014, Aaron Michael Hankin iv Dedication To Maiko and our unborn daughter. \There are wonders enough out there without our inventing any." { Carl Sagan v Acknowledgments The experiment detailed in this manuscript evolved rapidly from an empty lab nearly four years ago to its current state. Needless to say, this is not something a graduate student could have accomplished so quickly by him or herself.
    [Show full text]
  • Travis Dissertation
    Experimental Generation and Manipulation of Quantum Squeezed Vacuum via Polarization Self-Rotation in Rb Vapor Travis Scott Horrom Scaggsville, MD Master of Science, College of William and Mary, 2010 Bachelor of Arts, St. Mary’s College of Maryland, 2008 A Dissertation presented to the Graduate Faculty of the College of William and Mary in Candidacy for the Degree of Doctor of Philosophy Department of Physics The College of William and Mary May 2013 c 2013 Travis Scott Horrom All rights reserved. APPROVAL PAGE This Dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Travis Scott Horrom Approved by the Committee, March, 2013 Committee Chair Research Assistant Professor Eugeniy E. Mikhailov, Physics The College of William and Mary Associate Professor Irina Novikova, Physics The College of William and Mary Assistant Professor Seth Aubin, Physics The College of William and Mary Professor John B. Delos, Physics The College of William and Mary Professor and Eminent Scholar Mark D. Havey, Physics Old Dominion University ABSTRACT Nonclassical states of light are of increasing interest due to their applications in the emerging field of quantum information processing and communication. Squeezed light is such a state of the electromagnetic field in which the quantum noise properties are altered compared with those of coherent light. Squeezed light and squeezed vacuum states are potentially useful for quantum information protocols as well as optical measurements, where sensitivities can be limited by quantum noise. We experimentally study a source of squeezed vacuum resulting from the interaction of near-resonant light with both cold and hot Rb atoms via the nonlinear polarization self-rotation effect (PSR).
    [Show full text]
  • Optical Binding with Cold Atoms
    Optical binding with cold atoms C. E. M´aximo,1 R. Bachelard,1 and R. Kaiser2 1Instituto de F´ısica de S~aoCarlos, Universidade de S~aoPaulo, 13560-970 S~aoCarlos, SP, Brazil 2Universit´eC^oted'Azur, CNRS, INPHYNI, 06560 Valbonne, France (Dated: November 16, 2017) Optical binding is a form of light-mediated forces between elements of matter which emerge in response to the collective scattering of light. Such phenomenon has been studied mainly in the context of equilibrium stability of dielectric spheres arrays which move amid dissipative media. In this letter, we demonstrate that optically bounded states of a pair of cold atoms can exist, in the absence of non-radiative damping. We study the scaling laws for the unstable-stable phase transition at negative detuning and the unstable-metastable one for positive detuning. In addition, we show that angular momentum can lead to dynamical stabilisation with infinite range scaling. The interaction of light with atoms, from the micro- pairs and discuss the increased range of such a dynami- scopic to the macroscopic scale, is one of the most fun- cally stabilized pair of atoms. damental mechanisms in nature. After the advent of the laser, new techniques were developed to manipulate pre- cisely objects of very different sizes with light, ranging from individual atoms [1] to macrosopic objects in opti- cal tweezers [2]. It is convenient to distinguish two kinds of optical forces which are of fundamental importance: the radiation pressure force, which pushes the particles in the direction of the light propagation, and the dipole force, which tends to trap them into intensity extrema, as for example in optical lattices.
    [Show full text]
  • Phase Steps and Resonator Detuning Measurements in Microresonator Frequency Combs
    ARTICLE Received 23 May 2014 | Accepted 27 Oct 2014 | Published 7 Jan 2015 DOI: 10.1038/ncomms6668 Phase steps and resonator detuning measurements in microresonator frequency combs Pascal Del’Haye1, Aure´lien Coillet1, William Loh1, Katja Beha1, Scott B. Papp1 & Scott A. Diddams1 Experiments and theoretical modelling yielded significant progress toward understanding of Kerr-effect induced optical frequency comb generation in microresonators. However, the simultaneous Kerr-mediated interaction of hundreds or thousands of optical comb frequencies with the same number of resonator modes leads to complicated nonlinear dynamics that are far from fully understood. An important prerequisite for modelling the comb formation process is the knowledge of phase and amplitude of the comb modes as well as the detuning from their respective microresonator modes. Here, we present comprehensive measurements that fully characterize optical microcomb states. We introduce a way of measuring resonator dispersion and detuning of comb modes in a hot resonator while generating an optical frequency comb. The presented phase measurements show unpredicted comb states with discrete p and p/2 steps in the comb phases that are not observed in conventional optical frequency combs. 1 National Institute of Standards and Technology (NIST), Boulder, Colorado 80305, USA. Correspondence and requests for materials should be addressedto P.D. (email: [email protected]). NATURE COMMUNICATIONS | 6:5668 | DOI: 10.1038/ncomms6668 | www.nature.com/naturecommunications 1 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6668 ptical frequency combs have proven to be powerful a liquid crystal array-based waveshaper that allows independent metrology tools for a variety of applications, as well as for control of both the phase and amplitude of each comb mode.
    [Show full text]
  • 1 Quantum Optomechanics
    1 Quantum optomechanics Florian Marquardt University of Erlangen-Nuremberg, Institute of Theoretical Physics, Staudtstr. 7, 91058 Erlangen, Germany; and Max Planck Institute for the Science of Light, Günther- Scharowsky-Straÿe 1/Bau 24, 91058 Erlangen, Germany 1.1 Introduction These lectures are a basic introduction to what is now known as (cavity) optome- chanics, a eld at the intersection of nanophysics and quantum optics which has de- veloped over the past few years. This eld deals with the interaction between light and micro- or nanomechanical motion. A typical setup may involve a laser-driven optical cavity with a vibrating end-mirror, but many dierent setups exist by now, even in superconducting microwave circuits (see Konrad Lehnert's lectures) and cold atom experiments. The eld has developed rapidly during the past few years, starting with demonstrations of laser-cooling and sensitive displacement detection. For short reviews with many relevant references, see (Kippenberg and Vahala, 2008; Marquardt and Girvin, 2009; Favero and Karrai, 2009; Genes, Mari, Vitali and Tombesi, 2009). In the present lecture notes, I have only picked a few illustrative references, but the dis- cussion is hopefully more didactic and also covers some very recent material not found in those reviews. I will emphasize the quantum aspects of optomechanical systems, which are now becoming important. Related lectures are those by Konrad Lehnert (specic implementation in superconducting circuits, direct classical calculation) and Aashish Clerk (quantum limits to measurement), as well as Jack Harris. Right now (2011), the rst experiments have reported laser-cooling down to near the quantum ground state of a nanomechanical resonator.
    [Show full text]
  • A Tunable Doppler-Free Dichroic Lock for Laser Frequency Stabilization
    my journal manuscript No. (will be inserted by the editor) A tunable Doppler-free dichroic lock for laser frequency stabilization Vivek Singh, V. B. Tiwari, S. R. Mishra and H. S. Rawat Laser Physics Applications Section, Raja Ramanna Center for Advanced Technology, Indore-452013, India. Received: date / Revised version: date Abstract We propose and demonstrate a laser fre- resolution spectroscopy [2], precision measurements [3] quency stabilization scheme which generates a dispersion- etc. A setup for laser cooling and trapping of atoms re- like tunable Doppler-free dichroic lock (TDFDL) signal. quires several lasers which are actively frequency sta- This signal offers a wide tuning range for lock point bilized and locked at few line-widths detuned from the (i.e. zero-crossing) without compromising on the slope peak of atomic absorption. In the laser cooling experi- of the locking signal. The method involves measurement ments, the active frequency stabilization is achieved by of magnetically induced dichroism in an atomic vapour generating a reference signal which is based on absorp- for a weak probe laser beam in presence of a counter tion profile of atom around the resonance. The refer- propagating strong pump laser beam. A simple model is ence locking signal can be either Doppler-broadened with presented to explain the basic principles of this method wide tuning range or Doppler-free with comparatively to generate the TDFDL signal. The spectral shift in the much steeper slope but with limited tuning range. The locking signal is achieved by tuning the frequency of the most commonly used technique for frequency locking pump beam.
    [Show full text]
  • Quantum Effects in Optomechanical Systems
    Quantum effects in optomechanical systems C. Genes a, A. Mari b, D. Vitali c, and P. Tombesi c aInstitute for Theoretical Physics, University of Innsbruck, and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstrasse 25, A-6020 Innsbruck, Austria bInstitute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany cDipartimento di Fisica, Universit`adi Camerino, via Madonna delle Carceri, I-62032, Camerino (MC) Italy Abstract The search for experimental demonstrations of the quantum behavior of macroscopic mechanical resonators is a fastly growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state, and the generation of entanglement involving mechanical, optical and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiation pressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantum communication networks. Key words: radiation pressure,
    [Show full text]
  • Introduction to Optical Resonators
    Quantum optics and cavity QED with quantum dots in photonic crystals Jelena Vučković, Stanford University Lectures given at Les Houches 101th summer school on “Quantum Optics and Nanophotonics", August 2013 (to be published by Oxford University Press) This chapter will primarily focus on the studies of quantum optics with semiconductor, epitaxially grown quantum dots (QDs) embedded in photonic crystal (PC) cavities. Therefore, we will start by giving brief introductions into photonic crystals and quantum dots, although the reader is advised to refer to other references (John D. Joannopoulos 2008) (Michler 2009) for more detailed studies of these topics. We will then proceed with the introduction to cavity quantum electrodynamics (QED) effects (Kimble, Cavity Quantum Electrodynamics 1994) (Haroche 2013), with a particular emphasis on the demonstration of these effects on the quantum dot-photonic crystal platform. Finally, we will focus on the applications of such cavity QED effects. 1. Photonic crystals and microcavities 1.1. Photonic crystals Photonic crystals are media with periodic modulation of dielectric constant in up to three dimensions (John D. Joannopoulos 2008) (Yablonovitch 1987) (John 1987). In the literature, the name “photonic crystals” usually refers to the structures with dielectric constant periodic in two and three dimensions, while one-dimensional periodic media are referred to as the distributed Bragg reflectors (DBRs). Let us consider a non-magnetic periodic medium (the permeability is equal to µ ), 0 described with a periodic dielectric constant ε (r ) = ε (r + a), where a is an arbitrary lattice vector. The allowed electromagnetic modes in such a medium can be obtained as the solutions of the wave equation: ∇ × ∇ × E = ω2ε (r )µ E , 0 where the dielectric constant is periodic ε (r ) = ε (r + a), as described above.
    [Show full text]
  • Arxiv:2004.02848V3 [Physics.Atom-Ph] 10 Nov 2020 4 and 3 Vibrational Manifolds and Repump Them Back Into and Spontaneous Emission Events
    Direct Laser Cooling of a Symmetric Top Molecule Debayan Mitra,1, 2, ∗ Nathaniel B. Vilas,1, 2, ∗ Christian Hallas,1, 2 Loïc Anderegg,1, 2 Benjamin L. Augenbraun,1, 2 Louis Baum,1, 2 Calder Miller,1, 2 Shivam Raval,1, 2 and John M. Doyle1, 2 1Harvard-MIT Center for Ultracold Atoms, Cambridge, MA 02138, USA 2Department of Physics, Harvard University, Cambridge, MA 02138, USA (Dated: November 11, 2020) We report direct laser cooling of a symmetric top molecule, reducing the transverse temperature of a beam of calcium monomethoxide (CaOCH3) to 1:8 ± 0:7 mK while addressing two distinct nuclear spin isomers. These results open a path to efficient production of ultracold chiral molecules and conclusively demonstrate that by using proper rovibronic optical transitions, both photon cycling and laser cooling of complex molecules can be as efficient as for much simpler linear species. Laser cooling of atomic systems has enabled extraordinary ultracold molecules, including those proposed for symmetric progress in quantum simulation, precision clocks, and quan- top molecules [5,6]. tum many-body physics [1–4]. Extending laser cooling to The established recipe for achieving optical cycling and a diversity of complex polyatomic molecules would provide laser cooling of molecules requires three key ingredients: qualitatively new and improved platforms for these fields. strong electronic transitions between two fully bound molec- The parity doublets that result from rotations of a molecule ular states; diagonal Franck-Condon factors (FCFs), which around its principal axis, a general feature of symmetric top limit branching to excited vibrational levels; and rotationally molecules, give rise to highly polarized states with structural closed transitions.
    [Show full text]
  • Atom Optics Using an Optical Waveguide- Based Evanescent Field
    ATOM OPTICS USING AN OPTICAL WAVEGUIDE- BASED EVANESCENT FIELD DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Rajani Ayachitula Physics The Ohio State University 2010 Dissertation Committee: Professor Gregory P. Lafyatis, Advisor Professor Richard Furnstahl Professor Eric Herbst Professor Linn VanWoerkem Copyright by Rajani Ayachitula 2010 ABSTRACT The storage and manipulation of cold atoms near surfaces is of growing interest for applications like atom optics, the measurement of atom-surface interactions, and quantum information processing. In this work, we have constructed an apparatus to study cold atom physics above an optical waveguide. A two dimensional array of atoms trapped above our optical waveguide surface could serve as a quantum register, allowing for the individual addressing of single atoms from above or below using laser light. The first application of our system on the path to creating an addressable quantum register was to create a large area atom mirror. To realize our atom mirror, we had two main tasks: creating the cold atom source to drop onto the surface and creating the atom mirror out of our waveguide. We designed our apparatus to move magnetically trapped cold atoms from the Rb source to the region above the optical waveguide to conduct the dropping experiment. Several cooling and trapping steps are necessary to create our cold atom sample that will be dropped on our waveguide surface. We show that we have successfully created a 3mK cold atom sample of 3 ! 108 atoms to drop onto our surface to realize an atom mirror.
    [Show full text]