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Physical Review Research

Recoil frequency measurement with ppb-level uncertainty by Li6 atom interferometer

Yang Rui, Liang Zhang, Rui Li, Xuemei Liu, Chunyang Duan, Pengyue Liu, Yuelong Wu, Haibin Wu

Published Apr 24, 2023• 6 citations
Publisher

Abstract

We report a first realization of cold atom interferometers with the lightest alkali metal $^{6}\mathrm{Li}$ atoms and precisely measure the recoil frequency. The atoms are cooled to approach the half of the photon-recoil limit by using a narrow $2S\ensuremath{\rightarrow}3P$ ultraviolet transition. A ``magic'' magnetically insensitive state, a high-efficiency state preparation, and a frequency-insensitive Raman coupling are developed to overcome the challenges from the half-integer spin and hyperfine interaction of atoms. A conjugated $\text{Ramsey-Bord}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}$ interferometer with crossed Raman beams is realized with a coherence time longer than 2.3 ms. The four sets of interferometers developed using geometric relations greatly eliminate the error from the angle between Raman beams. The measured recoil frequency is ${\ensuremath{\omega}}_{r}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}73\phantom{\rule{0.16em}{0ex}}672.789\phantom{\rule{0.16em}{0ex}}(36)$ Hz, representing the most precise measurement of the recoil frequency of $^{6}\mathrm{Li}$ by using the atom interferometer so far. The realized $^{6}\mathrm{Li}$ cold atom interferometer is not only an effective supplement to the existing interferometers, but also provides a good candidate in precision measurement owing to its low mass and high recoil frequency.

DOI
10.1103/physrevresearch.5.023052

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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 pi/2\\pi/2pi/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\\'e interferometer and interferometry sensitive to the dynamic polarizability of the ground state of lithium. Recoil-sensitive Ramsey-Bord\\'e interferometry benefits from lithium's high recoil frequency, 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 mu\\mumuK, above the Doppler limit, and well above the recoil temperature of 6 mu\\mumuK. This higher temperature 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. An interferometer instead composed of pi/2\\pi/2pi/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 {\\em 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−S-S− to P−P-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 developed here broaden the applicability of interferometry and increase measurement sensitivity by simplifying cooling, increasing atom number and reducing the cycle time. Overcoming the current experimental limitations on interrogation time would allow for ultra-precise measurements of both the tune-out wavelength and the fine structure constant.
We report simultaneous conjugate Ramsey-Borde interferometers with a sample of low-mass (lithium-7) atoms at 50 times the recoil temperature. We optically pump the atoms to a magnetically insensitive state using the 2S1/2−2P1/22S_{1/2} - 2P_{1/2}2S1/2​−2P1/2​ line. Fast stimulated Raman beam splitters address a broad velocity class and unavoidably drive two conjugate interferometers that overlap spatially. We show that detecting the summed interference signals of both interferometers, using state labeling, allows recoil measurements and suppression of phase noise from vibrations. The use of warm atoms allows for simple, efficient, and high-flux atom sources and broadens the applicability of recoil-sensitive interferometry to particles that remain difficult to trap and cool.
We report simultaneous conjugate Ramsey-Bordé interferometers with a sample of low-mass (lithium-7) atoms at 50 times the recoil temperature. We optically pump the atoms to a magnetically insensitive state using the 2S_{1/2}-2P_{1/2} line. Fast stimulated Raman beam splitters address a broad velocity class and unavoidably drive two conjugate interferometers that overlap spatially. We show that detecting the summed interference signals of both interferometers, using state labeling, allows recoil measurements and suppression of phase noise from vibrations. The use of "warm" atoms allows for simple, efficient, and high-flux atom sources and broadens the applicability of recoil-sensitive interferometry to particles that remain difficult to trap and cool.
We describe progress toward a precise measurement of the recoil energy of an atom measured using a modified grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, an additional sw pulse is used to shift the phase of excited momentum states, which produces a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2{\ensuremath{\omega}}_{q}$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures $\ensuremath{\lesssim}$5 $\ensuremath{\mu}$K in a nonmagnetic apparatus. We demonstrate a measurement of ${\ensuremath{\omega}}_{q}$ with a statistical uncertainty of 37 parts per 109{10}^{9}109 (ppb) on a time scale of $\ensuremath{\sim}$45 ms in 14 h. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be $\ensuremath{\sim}$6 parts per 106{10}^{6}106 (ppm). We describe methods of reducing these systematic errors.
Light-pulse atom interferometers have been used as quantum inertial sensors and for precision tests of fundamental laws of physics. For higher contrast, we apply conjugate Ramsey-Borde interferometers to cancel out vibrational noise and top mirror tilting to compensate the Coriolis force. For higher sensitivity, we implement Bragg diffraction and Bloch oscillations for large momentum transfer to increase the enclosed area of our atom interferometer. We also utilize Raman sideband cooling in our experimental setup, which increases the overall signal about twentyfold, and increases the contrast by suppressing the thermal expansion of the atom cloud.By combining measurements of recoil frequency and a frequency comb, we present the first clock referenced to the mass of a single particle. The rest mass of a particle defines its Compton frequency, mc^2/h through relativity and quantum mechanics, and thereby sets a fundamental timescale. Our clock stabilizes a 10 MHz radio frequency signal to a certain fraction of the cesium Compton frequency. Future work could result in an elementary particle (electron) or even antimatter (antihydrogen) clock, opening up new ways to test CPT symmetry and the equivalence principle. We also present our progress towards a new determination of the fine structure constant. The fine structure constant value obtained by our cesium Compton clock measurement is about three times better compared with the earlier cesium recoil frequency result. After combining Bragg diffraction and Bloch oscillations, we achieved 0.33 ppb sensitivity (0.66 ppb uncertainty of the recoil frequency measurement) in 6 hours, which is about two times better than the previous best recoil frequency measurement. The leading systematic effect is also reduced by a factor of 2.75.
Echo atom interferometers have emerged as interesting alternatives to Raman interferometers for the realization of precise measurements of the gravitational acceleration g and the determination of the atomic fine structure through measurements of the atomic recoil frequency ω q . Here we review the development of different configurations of echo interferometers that are best suited to achieve these goals. We describe experiments that utilize near-resonant excitation of laser-cooled rubidium atoms by a sequence of standing wave pulses to measure ω q with a statistical uncertainty of 37 parts per billion (ppb) on a time scale of ∼50 ms and g with a statistical precision of 75 ppb. Related coherent transient techniques that have achieved the most statistically precise measurements of atomic g-factor ratios are also outlined. We discuss the reduction of prominent systematic effects in these experiments using off-resonant excitation by low-cost, high-power lasers.