Atom Interferometry with Laser-Cooled Lithium by Kayleigh Cassella Doctor of Philosophy in Physics University of California, Berkeley Professor Holger M¨Uller,Chair
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Hot Beats and Tune Outs: Atom Interferometry with Laser-cooled Lithium by Kayleigh Cassella A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Holger M¨uller,Chair Professor Dan Stamper-Kurn Professor Jeffrey Bokor Spring 2018 Hot Beats and Tune Outs: Atom Interferometry with Laser-cooled Lithium Copyright 2018 by Kayleigh Cassella 1 Abstract Hot Beats and Tune Outs: Atom Interferometry with Laser-cooled Lithium by Kayleigh Cassella Doctor of Philosophy in Physics University of California, Berkeley Professor Holger M¨uller,Chair Ushered forth by advances in time and frequency metrology, atom interferometry remains an indispensable measurement tool in atomic physics due to its precision and versatility. A sequence of four π=2 beam splitter pulses can create either an interferometer sensitive to the atom's recoil frequency when the momentum imparted by the light reverses direction between pulse pairs or, when constructed from pulses without such reversal, sensitive to the perturbing potential from an external optical field. Here, we demonstrate the first atom interferometer with laser-cooled lithium, advantageous for its low mass and simple atomic structure. We study both a recoil-sensitive Ramsey-Bord´einterferometer and interferometry sensitive to the dynamic polarizability of the ground state of lithium. Recoil-sensitive Ramsey-Bord´einterferometry benefits from lithium's high recoil fre- quency, a consequence of its low mass. At an interrogation time of 10 ms, a Ramsey-Bord´e lithium interferometer could achieve sensitivities comparable to those realized at much longer times with heavier alkali atoms. However, in contrast with other atoms that are used for atom interferometry, lithium's unresolved excited-state hyperfine structure precludes the the cycling transition necessary for efficient cooling. Without sub-Doppler cooling techniques. As as result, a lithium atomic gas is typically laser cooled to temperatures around 300 µK, above the Doppler limit, and well above the recoil temperature of 6 µK. This higher tem- perature gas expands rapidly during the operation of an atom interferometer, limiting the experimental interrogation time and preventing spatially resolved detection. In this work, a light-pulse lithium matter-wave interferometer is demonstrated in spite of these limitation. Two-photon Raman interferometer pulses coherently couple the atom's spin and momentum and are thus able to spectrally resolve the outputs. These fast pulses drive conjugate interferometers simultaneously which beat with a fast frequency component proportional to the atomic recoil frequency and an envelope modulated by the two-photon detuning of the Raman transition. We detect the summed signal at short experimental times, preventing perturbation of the signal from vibration noise. This demonstration of a sub-recoil measurement with a super-recoil sample opens the door to similar scheme with other particles that are difficult to trap and cool well, like electrons. 2 An interferometer instead composed of π=2-pulses with a single direction of momentum transfer, can be sensitive to the dynamic polarizability of the atomic ground state. By scanning the frequency of an external driving field, such a measurement can be used to determine the atom's tune-out wavelength. This is the wavelength at which the frequency- dependent polarizability vanishes due to compensating ac-Stark shifts from other atomic states. Lithium's simple atomic structure allows for a precise computation of properties with only ab initio wave functions and spectroscopic data. A direct interferometric measurement of lithium's red tune-out wavelength at 670.971626(1) nm, is a precise comparison to existing `all-order' atomic theory computations. It also provides another way to experimentally determine the S− to P − transitions matrix elements, for which large correlations and small values complicate computations. Finally, a future measurement of lithium's ultraviolet tune- out wavelength of at 324.192(2) nm would be sensitive to relativistic approximations in the atomic structure description. Atom interferometry simultaneously verifies existing atomic theory with measurements of atomic properties and searches for exotic physics lurking in plain sight. The techniques devel- oped here broaden the applicability of interferometry and increase measurement sensitivity by simplifying cooling, increasing atom number and reducing the cycle time. Overcom- ing the current experimental limitations on interrogation time would allow for ultra-precise measurements of both the tune-out wavelength and the fine structure constant. i To my mom and step-dad, who filled me with enough resolve to do hard things. To my sisters, who grew with me and tethered me to real things. To my husband, who unfolded all the crumpled parts of me, again and again. To my children, my greatest teachers, who sprinkled light in all the dark places. I dedicate this work to you. ii Contents Contents ii List of Figures vi List of Tables viii 1 Outward bound 1 1.1 Corpuscular and undulatory . 2 1.1.1 Waves of matter . 4 1.2 α, the fine structure constant . 5 h 1.2.1 M measurement . 8 1.3 α, the polarizability . 8 1.3.1 Dynamic polarizability . 10 1.4 Previous measurements . 12 1.4.1 λto measurement . 13 1.5 Overview of this thesis . 15 2 Atom interferometry 16 2.1 Light off . 19 2.1.1 The free evolution phase . 22 2.2 Light on . 23 2.2.1 Raman scattering . 23 2.2.1.1 Dressed states . 28 2.2.2 The interaction phase . 30 2.2.3 The separation phase . 31 2.3 The total phase . 31 π π π π 2.4 Conjugate interferometers with the 2 - 2 - 2 - 2 . 33 2.5 The Ramsey-Bord´einterferometer . 33 2.5.1 cRBI phase computation . 36 2.6 The copropagating interferometer . 38 2.6.1 cCPI phase computation . 41 iii 3 Lithium, the smallest alkali 42 3.1 Lithium, the lightest alkali . 42 3.2 Lithium, the simplest alkali . 45 3.2.1 The Hylleraas basis . 46 3.3 Dynamic polarizability . 48 3.4 Lukewarm Lithium . 50 3.4.1 Lithium atom interferometry in the space domain . 53 3.5 Advantages of light-pulsed interferometry with lithium . 54 4 Experimental Methods 56 4.1 Lithium Spectroscopy . 58 4.1.1 Modulation Transfer Spectroscopy . 59 4.1.2 The cascade of frequency generation . 62 4.1.2.1 Tapered amplifiers . 63 4.2 Cooling and trapping . 64 4.2.1 2D MOT frequency generation . 67 4.2.2 3D MOT frequency generation . 67 4.2.3 Vacuum system and optics . 68 4.2.3.1 2D MOT chamber . 70 4.2.3.2 3D MOT chamber . 72 4.2.4 Experimental sequence . 73 4.3 State preparation . 74 4.3.1 Frequency generation for optical pumping light . 76 4.3.2 Optical pumping optics . 78 4.3.2.1 Quantization axis . 78 4.4 Interferometry . 78 4.4.1 Frequency generation for Raman beams . 78 4.4.2 Raman optics . 82 4.5 Detection . 83 4.5.1 Absorption imaging . 83 4.5.2 Wollaston prism technique . 84 4.5.3 Time-of-flight imaging . 84 5 Hot Beats 87 5.1 Super-recoil lithium . 87 5.1.1 Large bandwidth pulses . 88 5.1.2 k-reversal . 88 5.2 Simultaneous and conjugate . 89 5.3 Overlapped, simultaneous and conjugate . 91 5.3.1 Hot beats . 92 5.3.2 Time-domain fitting . 92 5.3.3 Frequency-domain fitting . 94 iv 5.4 Phase noise . 95 5.5 Outlook . 97 5.5.1 Vibration immunity . 98 6 Tune-outs 100 6.1 Previous polarizability measurements . 101 6.1.1 The differential Stark shift . 101 6.1.2 Space-domain atom interferometry . 102 6.2 Light-pulsed interferometric lithium tune outs . 103 6.2.1 φto, the tune-out phase . 103 6.2.2 The tune-out beam . 106 6.2.3 Experimental Sequence . 106 6.2.4 Detection & Analysis . 108 6.2.4.1 Principal component analysis . 110 6.3 Towards tune-out . 111 6.3.1 Precision . 111 6.3.1.1 Single-photon scattering . 112 6.3.1.2 Beam shaping . 113 6.3.2 Accuracy . 113 6.4 Hyperfine dynamic polarizabilities . 113 7 Conclusion 117 7.1 Outlook for recoil-sensitive interferometry with super-recoil samples . 117 7.1.1 h=me measurement . 117 7.2 Outlook for tune-out interferometric measurements in lithium . 119 7.2.1 Beyond the red . 119 7.2.2 Investigation of nuclear structure between isotopes . 121 7.3 Atom interferometry with lukewarm lithium . 122 7.3.1 Sisyphus cooling . 123 7.3.2 Gray molasses . 123 7.4 Onward . 123 A Properties of lithium 125 A.1 The level spectrum . 129 A.2 Interaction with static fields . 129 A.3 Interaction with dynamic fields . 131 A.3.1 Reduced Matrix Elements in Atomic Transitions . 131 A.4 Clebsch-Gordan coefficients for D{line transitions . ..