Bose einstein condensation and atom cavity interactions

COLLECTIVE DISPERSIVE INTERACTION OF ATOMS AND LIGHT IN A HIGH FINESSE CAVITY KYLE JOSEPH ARNOLD B.S. Eng. Physics, University of Illinois Urbana-Champaign B.S. Mathematics, University of Illinois Urbana-Champaign A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE 2012 ii Declaration I herewith declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. The thesis has also not been submitted for any degree in any university previously. Kyle Joseph Arnold December 2012 Acknowledgements First and foremost, I would like to thank my supervisor, Dr. Murray Barrett. We have worked closely over the years and without the wealth of atomic physics, optics, and electronics knowledge I have received from him, the work in the thesis would not have been possible. Next I would like to thank Markus Baden, my partner on the cavity experiments. In particular, for many fruitful physics discussions and taking the time to proof read my thesis. Also, for introducing me to python, my go-to tool for scientific computing and source of many quality plots in this thesis. Many thanks to my other fellow PhD students, Arpan Roy, Chuah BoonLeng, and Nick Lewty, who, though not directly involved in my experiments, have all contributed to our common efforts in developing the lab. Thanks also to the many RAs who have helped out in the lab, in particular Andrew Bah who produced the 3D-rendered experiment schematics for my thesis. I’m grateful for work of our CQT support staff, especially our procurement officer, Chin Pei Pei, our electronics support staff, Joven Kwek and Gan Eng Swee, and our machinists, Bob and Teo, who have made numerous parts for me on short order. Finally, I would like to thank my wife, Vicky, for her continuous love and support during these years, and my parents who having always been supportive of my chosen path even though it has taken me to distant lands far from home. Contents List of Tables ix List of Figures xi Introduction 1.1 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dipole Trapping and All-Optical Bose-Einstein Condensation 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Dipole traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Laser cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.3 Evaporative cooling . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.4 Scaling laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.5 Atom losses due to inelastic collisions . . . . . . . . . . . . . . . 15 Discussion of crossed beam traps . . . . . . . . . . . . . . . . . . . . . . 16 2.3.1 General thermal distribution of a trapped gas . . . . . . . . . . . 17 2.3.2 Crossed beam distribution: numeric solution . . . . . . . . . . . 18 2.3.3 Crossed beam distribution: approximate analytic solution . . . . 18 2.3.4 Thermalization in crossed beam traps . . . . . . . . . . . . . . . 21 2.3.5 Analysis of a recent cross-beam result . . . . . . . . . . . . . . . 23 2.3.6 Elliptical beams . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.7 Basics of Bose-Einstein condensates . . . . . . . . . . . . . . . . 25 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.1 Cooling lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.2 Imaging diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3 2.4 iii CONTENTS 2.5 2.6 2.4.3 MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4.4 Dipole trap loading . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.5 Trap lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4.6 Hyperfine changing collisions . . . . . . . . . . . . . . . . . . . . 35 2.4.7 Measuring trap frequencies . . . . . . . . . . . . . . . . . . . . . 36 2.4.8 Thermal lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Bose-Einstein condensation experiment . . . . . . . . . . . . . . . . . . . 38 2.5.1 Primary beam geometry . . . . . . . . . . . . . . . . . . . . . . . 38 2.5.2 Primary beam free evaporation . . . . . . . . . . . . . . . . . . . 39 2.5.3 Primary beam forced evaporation . . . . . . . . . . . . . . . . . . 39 2.5.4 Secondary beam geometry . . . . . . . . . . . . . . . . . . . . . . 41 2.5.5 Cross-beam compression . . . . . . . . . . . . . . . . . . . . . . . 41 2.5.6 Observation of a condensate . . . . . . . . . . . . . . . . . . . . . 43 2.5.7 Comments of observing a bi-modal distribution . . . . . . . . . . 46 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Collective Cavity Quantum Electrodynamics with Multiple Atom Levels 49 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 Cavity quantum electrodynamics . . . . . . . . . . . . . . . . . . . . . . 50 3.2.1 Jaynes-Cummings model . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.2 Real systems: dissipation . . . . . . . . . . . . . . . . . . . . . . 55 3.2.3 Cavity QED for N multi-level atoms . . . . . . . . . . . . . . . . 58 3.2.4 Semi-classical model for multi-level atoms . . . . . . . . . . . . . 63 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3.1 High finesse cavity . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3.2 Cavity laser system . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.3 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.4 Optical lattice transport . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.5 808 nm intra-cavity FORT . . . . . . . . . . . . . . . . . . . . . 72 3.3.6 Optical pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Experimental results: cavity transmission spectra . . . . . . . . . . . . . 74 3.4.1 75 3.3 3.4 Experiment procedure . . . . . . . . . . . . . . . . . . . . . . . . iv CONTENTS 3.5 3.4.2 Two-level atoms: the cycling transition . . . . . . . . . . . . . . 76 3.4.3 Multi-level atoms: π-probing . . . . . . . . . . . . . . . . . . . . 77 3.4.4 Driving both cavity modes . . . . . . . . . . . . . . . . . . . . . 78 3.4.5 Optical pumping by the cavity field . . . . . . . . . . . . . . . . 79 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Self-Organization of Thermal Atoms Coupled to a Cavity 83 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 Derivation of the threshold equations . . . . . . . . . . . . . . . . . . . . 87 4.2.1 Lattice geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.2 Traveling wave geometry . . . . . . . . . . . . . . . . . . . . . . . 94 Experimental set-up and methods . . . . . . . . . . . . . . . . . . . . . . 95 4.3.1 Dual-wavelength high finesse cavity . . . . . . . . . . . . . . . . . 95 4.3.2 Cavity laser system . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.3.3 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.3.4 Atom transport: translation of the dipole trap . . . . . . . . . . 101 4.3.5 1560 nm intra-cavity FORT 4.3 4.4 4.5 4.6 . . . . . . . . . . . . . . . . . . . . 103 Experimental results: self-organization threshold scaling . . . . . . . . . 106 4.4.1 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . 107 4.4.2 Comparison to the threshold equations . . . . . . . . . . . . . . . 107 4.4.3 Lattice geometry threshold results . . . . . . . . . . . . . . . . . 109 4.4.4 Traveling wave geometry threshold results . . . . . . . . . . . . . 110 4.4.5 Discussion of threshold scaling . . . . . . . . . . . . . . . . . . . 111 Experimental results: dynamics of self-organization . . . . . . . . . . . . 113 4.5.1 Lattice geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.5.2 Traveling wave geometry . . . . . . . . . . . . . . . . . . . . . . . 120 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Bragg Scattering, Cavity Cooling, and Future Directions 123 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2 Bragg scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.2.1 5.3 Future Bragg scattering related experiments . . . . . . . . . . . . 127 Cavity cooling of atomic ensembles . . . . . . . . . . . . . . . . . . . . . 128 5.3.1 Cavity cooling via the collective mode . . . . . . . . . . . . . . . 129 v CONTENTS 5.4 5.3.2 Cavity cooling via self-organization . . . . . . . . . . . . . . . . . 134 5.3.3 Conclusions and future experimental directions for cavity cooling 138 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 A High finesse cavities: technical details A.1 ATF mirrors 141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.1.1 Brief History of low-loss mirrors . . . . . . . . . . . . . . . . . . 141 A.1.2 Mirrors from ATF: 2008-2011 . . . . . . . . . . . . . . . . . . . . 142 A.1.3 Mirror handling and cleaning . . . . . . . . . . . . . . . . . . . . 144 A.2 Contamination of mirrors by Rb . . . . . . . . . . . . . . . . . . . . . . 145 A.3 Cavity construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 B Self-organization threshold equations 149 B.1 Lattice geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 B.2 Traveling wave geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 C Self-organization: temperature, entropy and phase space density 153 References 163 vi Summary This thesis details experimental investigations into the interaction of an ultracold atomic ensemble with a single mode high finesse optical cavity. To this end, simple and efficient experimental methods are developed to cool and transport atoms. These include the all-optical production of a Bose-Einstein condensate in a µm wavelength crossed beam dipole trap and direct mechanical translation of cold atoms into a high finesse cavity over ∼ cm. First, we study the cavity transmission spectra for weak driving of a single mode cavity coupled to a cold ensemble of rubidium atoms. The multi-level structure of the atoms together with the collective coupling to the cavity mode leads to complex spectra which depend on atom number and probe polarization. We model the linear response of the system as collective spin with multiple levels coupled to a single mode of the cavity. The observed spectra are in good agreement with this reduced model. Second, we study transverse pumping of a thermal ensemble of atoms coupled to a cavity which results in self-organization. The differences between probing with a traveling wave and a retro-reflected lattice are investigated. We derive threshold conditions for self-organization in both scenarios and verify a threshold scaling consistent with the mean field prediction over a range of atom numbers and cavity detunings. Most recently, a 2D lattice potential is used to organize the atoms into a Bragg crystal, and coherent scattering into the cavity is observed without threshold. This configuration is ideal for future investigations into either cavity sideband cooling of the collective motion or simulation of Dicke model via the collective spin. CONTENTS viii It can be shown that lim∗ µ→µ dβ lim∗ µ→µ dµ = dβ dµ = lim∗ µ→µ lim dβ dµ µ→µ∗ We note that 2µ b2 µLT b0 dC = −A, from which dµ lim µ→µ∗ lim∗ µ→µ 2A dβ dµ 3A B (C.48) 2µ b2 µLT b0 µ = (C.47) −A + B dβ dµ lim µ→µ∗ 3µ µLT − µLT 2µ 2µ b2 µLT b0 2µ b2 µLT b0 µ µLT −4 − 2µ b4 µLT b0 . (C.49) b4 b0 = is exactly the threshold condition from Eq. C.27, which together with the limit lim∗ µ→µ 1 2µ b4 , =1− ∗ + µLT b0 µ µLT (C.50) yields the result dβ lim∗ = µ→µ dµ 1+ 3µ∗ µLT −2 µ∗ µLT µLT − µLT 2µ∗ 1− µ∗ . + (C.51) µLT Plugging this result into Eq. C.36, we find the change in entropy at the phase transition, ∆S ∗ = kb −3 (µ∗ )2 µLT ∗ µµLT − ∗ + ( µµLT )2 − µ∗ µLT 1− µ∗ µ∗ + . (C.52) µLT Temperature and phase space density above threshold To find the final temperature above threshold, Tf , we again consider the initial and final entropy, ln kb T0 ω S0< + ∆S ∗ = S > ∆S ∗ kb Tf +1+ = ln kb ω Tf T0 exp = µb2 b0 b0 + ln b0 + − µ exp b2 − b0 2µ µ2 dβ β + µLT µLT dµ 2µ µ2 dβ ∆S ∗ β + + . µLT µLT dµ kb (C.53) Here the first exponential determines the temperature rise prior to organization, and the second exponential, what happens after self-organization. Thus by setting β = 0, ∆S ∗ = 0, and dβ dµ = 0, we recover Eq. C.24, the temperature below threshold. 159 C. SELF-ORGANIZATION: TEMPERATURE, ENTROPY AND PHASE SPACE DENSITY Figure C.1: Entropy and phase space density change across threshold. The blue line is entropy change calculated from Eq. C.52. The red line is phase space density gain calculated from Eq. C.59. The dotted red line is the contribution from of the entropy term only (Eq. C.60). Given the partition function above threshold, Z> = = kb Tf b0 ω kb T0 exp µ ω (C.54) b2 2β + b0 µLT + µ2 dβ ∆S ∗ + µLT dµ kb (C.55) we can determine the peak phase space density again from Eq. C.25, > ρ = = e µ 1+ µ2β LT (C.56) Z> ω b2 2β 2β exp µ − + − kb T0 b0 µLT µLT − µ2 dβ ∆S ∗ − . µLT dµ kb If we consider the phase density far above threshold (µ → ∞), there β → 1, and dβ dµ (C.57) b2 b0 → 1, → 0. We find this limit, verified numerically, to be ρ∞ = ω µLT ∆S ∗ exp − . kb T0 2(1 + µLT ) kb (C.58) Thus the gain in phase space density from just below threshold, ρ∗ , to far above threshold is ρ∞ µLT µLT ∆S ∗ ∗ − µ + − . = exp ρ∗ 2(1 + µLT ) kb In both limiting cases of µ∗ and µ∗ (C.59) 1, this reduces to simply ∗ ρ∞ − ∆S kb = e . ρ∗ 160 (C.60) Both Eq. C.59 and Eq. C.60 are plotted in Fig. C.1 for comparison, note the additional terms in Eq. C.59 contribute only a small correction in the intermediate regime. 161 C. SELF-ORGANIZATION: TEMPERATURE, ENTROPY AND PHASE SPACE DENSITY 162 References ¨ nsch and A.L. Schawlow. Cooling of gases by laser radiation. Optics [1] T.W. Ha Communications, 13(1):68 – 69, 1975. [2] D. J. Wineland and Wayne M. Itano. Laser cooling of atoms. Phys. Rev. A, 20:1521–1540, Oct 1979. [3] J. Dalibard and C. Cohen-Tannoudji. Laser cooling below the Doppler limit by polarization gradients: simple theoretical models. J. Opt. Soc. Am. 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Lett., 12(11):876–878, Nov 1987. 174 [...]... practical and fundamental difficulties of cooling trapped atomic ensembles coupled to a single mode cavity 4 Chapter 2 Dipole Trapping and All-Optical Bose- Einstein Condensation This chapter covers the first generation experimental apparatus, pictured in Fig 2.1, and is largely based on ’All-optical Bose- Einstein condensation in a 1.06 µm dipole trap’ K J Arnold and M D Barrett Optics Communications 284, 3288... significantly different and interesting phenomena emerge Coherent scattering into the cavity mode is enhanced by constructive interference only if the atoms are spatially ordered to match the phase of the driving and cavity fields For uniformly distributed atoms, scattering is suppressed by destructive interference 2 1.1 Outline of the Thesis In a standing wave cavity, the backaction on the atoms from the scattered... the photon blockade effect [14] and the vacuum-Rabi splitting due to a single atom [15, 16] For a sufficiently good cavity, an atom can even be trapped by the dispersive backaction from the field of a single photon [17] Unlike a free-space FORT, the intra -cavity optical potential in a driven cavity depends on the position of the atom [18] and thus strongly couples to the atomic motion This coupling can... in the wings relative to the 19 2 DIPOLE TRAPPING AND ALL-OPTICAL BOSE- EINSTEIN CONDENSATION Figure 2.4: Comparison of the fraction of atoms in the wings outside the dimple (blue lines) and the peak density (red lines) as a function of η for 1.06 µm and 10.6 µm traps The red and blue dashed lines are the analytic approximations from equations (2.35) and (2.36) respectively The solid lines result from... cool a single atom [20] Cavity cooling via coherent scattering is of particular interest because it can, in principle, be applied to any polarizable particles [21, 22] Extending cavity cooling schemes to ensembles of particles in a cavity remains a tantalizing possibility and area of active theoretical [23, 24] and experimental research [25, 26] For an ensemble of atoms trapped inside a cavity driven... devoted to each The common thread throughout is the dispersive interaction between light and atomic ensembles First, in free space, where optical potentials are used for the trapping and manipulation of atoms Second, in a cavity, where the collective dispersive interaction with the cavity gives rise to the dispersive shift and dynamic optical potentials Chapter 2 In our first experiment, we all-optically produce... in either a magnetic trap or FORT 11 2 DIPOLE TRAPPING AND ALL-OPTICAL BOSE- EINSTEIN CONDENSATION 2.2.3 Evaporative cooling Evaporation is the natural process by which the highest energy atoms escape the confining potential, thereby lowering the average thermal energy of the remaining trapped atoms Collisions continually redistribute energy between atoms to bring the total distribution towards the Maxwell-Boltzmann... cold atom sources such a Zeeman slower [70] or 2D MOT [71] are able to reach a vacuum of ∼ 10−12 Torr and thus background limited lifetimes exceeding 10 minutes Two-body losses There are two principle mechanisms for two-body losses [72]: light assisted collisions and hyper-fine ground state changing collisions Light-assisted collisions occur when 15 2 DIPOLE TRAPPING AND ALL-OPTICAL BOSE- EINSTEIN CONDENSATION. .. organize the atom into a Bragg crystal by static FORT potentials alone We report our observation of threshold-free coherent scattering into the cavity and discuss potential future research directions with such a system Demonstrating cavity cooling of atomic ensembles has been one of our long standing research objectives, but has thus far produced null results We end on a discussion of the practical and fundamental... both internal and external atomic degrees of freedom has been an essential tool for atom physics research Near to an atomic resonance, scattering of laser light via spontaneous emission is the dominant process Laser cooling harnesses this scattering to cool the motion of atoms down to micro-Kelvin temperatures Additionally, optical pumping [6] methods utilize spontaneous emission to prepare atoms in a . high finesse optical cavity. To this end, simple and efficient experimental methods are developed to cool and transport atoms. These include the all-optical production of a Bose- Einstein condensate. over a range of atom numbers and cavity detunings. Most recently, a 2D lattice potential is used to organize the atoms into a Bragg crystal, and coherent scattering into the cavity is observed. driving and cavity fields. For uniformly distributed atoms, scattering is suppressed by destructive interference. 2 1.1 Outline of the Thesis In a standing wave cavity, the backaction on the atoms