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Optical and Quantum Sensing and Precision Metrology

Limitations on maximum achievable enhancement in sensitivity using large momentum transfer for point source atom interferometry

Jinyang Li, Gregório R. M. da Silva, Wayne Huang, Mohamed F. Fouda, Jason Bonacum, Tim Kovachy, M. S. Shahriar

Published Mar 4, 2021• 0 citations
Publisher

Abstract

A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses. During the pulse sequence, an initially trapped cloud of cold atoms is released and allowed to expand, behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. Contrary to typical approaches used for describing a PSI, we employ a model under which the motion of the center of mass of each atom is described quantum mechanically. We show how increasing Doppler shifts lead to imperfections, thereby limiting the visibility of the signal fringes, and identify ways to suppress this effect by increasing the effective, two-photon Rabi frequencies of the Raman pulses. Considering the effect of spontaneous emission, we show that for a given value of the one-photon Rabi frequency, there is an optimum value for the number of pulses employed, beyond which the net enhancement in sensitivity begins to decrease. For a one-photon Rabi frequency of 200 MHz, for example, the peak value of the factor of enhancement in sensitivity is ~39, for a momentum transfer that is ~69 times as large as that for a conventional PSI. We also find that this peak value scales as the one-photon Rabi frequency to the power of 4/5.

DOI
10.1117/12.2588300

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A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses. During the pulse sequence, an initially trapped cloud of cold atoms is released and allowed to expand, behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. Contrary to typical approaches used for describing a PSI, we employ a model under which the motion of the center of mass of each atom is described quantum mechanically. We show how increasing Doppler shifts lead to imperfections, thereby limiting the visibility of the signal fringes, and identify ways to suppress this effect by increasing the effective, two-photon Rabi frequencies of the Raman pulses. Considering the effect of spontaneous emission, we show that for a given value of the one-photon Rabi frequency, there is an optimum value for the number of pulses employed, beyond which the net enhancement in sensitivity begins to decrease. For a one-photon Rabi frequency of 200 MHz, for example, the peak value of the factor of enhancement in sensitivity is ~39, for a momentum transfer that is ~69 times as large as that for a conventional PSI. We also find that this peak value scales as the one-photon Rabi frequency to the power of 4/5.
A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from the rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possible to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. We analyze how factors such as Doppler detuning, spontaneous emission, and the finite initial size of the atomic cloud compromise the advantage of LMT and how to find the optimal momentum transfer under these limitations, with both the semi-classical model and a model under which the motion of the center of mass of each atom is described quantum mechanically. We identify a set of realistic parameters for which LMT can improve the PSI by a factor of nearly 40.
Large-momentum-transfer (LMT) atom interferometry provides a route toward enhanced inertial sensitivity in compact quantum sensors, but its scalability is limited by the accumulation of pulse-transfer errors across long Raman pulse sequences. We investigate theoretically the use of stimulated Raman shortcut-to-adiabatic passage (STIRSAP) for high-fidelity LMT atom optics in a Mach--Zehnder interferometer geometry. The counterdiabatic correction is encoded directly into the Raman pulse envelopes, eliminating the need for auxiliary microwave or radio-frequency control fields. Numerical simulations based on an effective Raman model show that 1 μs1~μ\mathrm{s}1 μs STIRSAP pulses achieve single-pulse transfer fidelities of Fπ=0.99902F_π= 0.99902Fπ​=0.99902 while maintaining negligible pulse-time overhead even at high momentum order. We analyze the resulting tradeoff between interferometric phase enhancement and compound contrast decay and identify an unconstrained shot-noise optimum near n≈270n\approx270n≈270. The analysis further shows that practical operation at extreme LMT order is constrained by wave-packet separation, vibration noise, Doppler detuning, and accumulated systematic effects rather than by pulse duration itself. These results establish superadiabatic Raman control as a promising approach for scalable high-fidelity atom optics and clarify the physical limitations governing compact high-order atom interferometers.
Large momentum transfer (LMT) enhances the gravitational phase of a light-pulse atom interferometer by a factor nnn, while mirrorless operation with momentum-resolved detection can quadruple the phase-carrying quantum Fisher information. These gains compete in practice because the momentum-space fringe period scales as 1/n1/n1/n, making the fringe signal increasingly vulnerable to finite detector resolution. We analyze this trade-off in a solvable model with instantaneous lossless nnn-photon pulses, a Gaussian source, and Gaussian detection blur, allowing continuous interpolation between Kasevich--Chu and mirrorless geometries. Closed-form expressions for the blurred output distributions and classical Fisher information are obtained, with a fringe-phase averaging approximation whose error is exponentially suppressed and agrees with numerical simulations at the 10−810^{-8}10−8 level. We find that mirrorless operation surpasses a conventional interferometer with the same momentum transfer only when σp<0.91 m/(nk0T)σ_p < 0.91\,m/(n k_0 T)σp​<0.91m/(nk0​T). Fringe-based readout exhibits an optimal momentum transfer n∗≃0.93 m/(σpk0T)n^* \simeq 0.93\,m/(σ_p k_0 T)n∗≃0.93m/(σp​k0​T) and a resolution-limited sensitivity floor Δg≃4.4 σp/(mTN)Δg \simeq 4.4\,σ_p/(mT\sqrt{N})Δg≃4.4σp​/(mTN​), independent of photon momentum. When this criterion is not satisfied, partial mirror asymmetry can recover part of the enhancement, whereas population-based readout remains insensitive to detector blur and ultimately favors the conventional sequence at sufficiently large nnn. Estimates for 87^{87}87Rb sensors show that the mirrorless advantage is primarily restricted to short-baseline instruments.
We analyze theoretically the sensitivity of accelerometry and rotation sensing with a point source interferometer employing large momentum transfer (LMT) and present a design of an inertial measurement unit (IMU) that can measure rotation around and acceleration along each of the three axes. In this design, the launching technique is used to realize the LMT process without the need to physically change directions of the Raman pulses, thus significantly simplifying the apparatus. We also describe an explicit scheme for such an IMU.
Abstract Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage pulses in simulated LMT Mach–Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of ℏ k momentum separation and offer more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
Using the technique of point source atom interferometry, we characterize the sensitivity of a multi-axis gyroscope based on free-space Raman interrogation of a single source of cold atoms in a glass vacuum cell. The instrument simultaneously measures the acceleration in the direction of the Raman laser beams and the component of the rotation vector in the plane perpendicular to that direction. We characterize the sensitivities for the magnitude and direction of the rotation vector measurement, which are 0.033 ∘/s^{\circ}/\mathrm{s}∘/s and 0.27 ∘^{\circ}∘ with one second averaging time, respectively. The sensitivity could be improved by increasing the Raman interrogation time, allowing the cold-atom cloud to expand further, correcting the fluctuations in the initial cloud shape, and reducing sources of technical noise. The unique ability of the PSI technique to measure the rotation vector in a plane may permit applications of atom interferometry such as tracking the precession of a rotation vector and gyrocompassing.