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arXiv:2403.08913

Error analysis in large area multi-Raman pulse atom interferometry due to undesired spontaneous decay

Philip Chrostoski, Scott E. Bisson, D. R. Farley, Frank A. Narducci, Daniel Soh

Published Mar 13, 2024• 0 citations
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Abstract

Despite the fact that atom interferometry has been a successful application of quantum sensing, a major topic of interest is the further improvement of the sensitivity of these devices. In particular, the area enclosed by the interferometer (which controls the sensitivity) can be increased by providing a larger momentum kick to the atom cloud, increasing the extent of the momentum axis. One such atom optics technique involves increasing the number of central $π-$Raman pulses. This technique, while providing the prerequisite additional momentum boost, also causes the atom to remain in the intermediate high energy state for longer periods of time. This additional length of time is often neglected in many treatments due to the adiabatic elimination of the higher energy state enabled by the large optical detuning. The increased time in the intermediate high energy state results in a higher probability of undesired spontaneous decay and a loss of quantum information, thereby adding error to the atom interferometer. In this work, we consider an open quantum system using the Lindblad master equation to devise a model for the atomic state dynamics that includes the undesired spontaneous decay from the intermediate high energy state. We formulate an error figure of merit to analyze limitations of an atom interferometer configured for acceleration measurements. Our theoretical results show the error figure of merit will be dominated by a $N_{R}^{-2}$ scaling factor for low numbers of $π-$Raman pulses, but will be dominated by a monotonic increase in error for high number of $π-$Raman pulses. We determined the number of $π$-Raman pulses that accomplishes maximal momentum transfer with a the minimal error, depending on major system parameters.

DOI
10.48550/arxiv.2403.08913

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Despite the fact that atom interferometry has been a successful application of quantum sensing, a major topic of interest is the further improvement of the sensitivity of these devices. In particular, the area enclosed by the interferometer (which controls the sensitivity) can be increased by providing a larger momentum kick to the atom cloud, increasing the extent of the momentum axis. One such atom optics technique involves increasing the number of central π−π-π−Raman pulses. This technique, while providing the prerequisite additional momentum boost, also causes the atom to remain in the intermediate high energy state for longer periods of time. This additional length of time is often neglected in many treatments due to the adiabatic elimination of the higher energy state enabled by the large optical detuning. The increased time in the intermediate high energy state results in a higher probability of undesired spontaneous decay and a loss of quantum information, thereby adding error to the atom interferometer. In this work, we consider an open quantum system using the Lindblad master equation to devise a model for the atomic state dynamics that includes the undesired spontaneous decay from the intermediate high energy state. We formulate an error figure of merit to analyze limitations of an atom interferometer configured for acceleration measurements. Our theoretical results show the error figure of merit will be dominated by a NR−2N_{R}^{-2}NR−2​ scaling factor for low numbers of π−π-π−Raman pulses, but will be dominated by a monotonic increase in error for high number of π−π-π−Raman pulses. We determined the number of πππ-Raman pulses that accomplishes maximal momentum transfer with a the minimal error, depending on major system parameters.
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.
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.
We demonstrate light-pulse atom interferometry with large-momentum-transfer atom optics based on stimulated Raman transitions and frequency-swept adiabatic rapid passage. Our atom optics have produced momentum splittings of up to 30 photon recoil momenta in an acceleration-sensitive interferometer for laser cooled atoms. We experimentally verify the enhancement of phase shift per unit acceleration and characterize interferometer contrast loss. By forgoing evaporative cooling and velocity selection, this method lowers the atom shot-noise-limited measurement uncertainty and enables large-area atom interferometry at higher data rates.
We report a demonstration of composite Raman pulses that achieve broadband population inversion and are used to increase the momentum splitting of an atom interferometer up to 18ℏk (corresponding to an increase in the inertial signal by a factor of nine). Composite Raman pulses suppress the effects of pulse length and detuning errors, providing higher transfer efficiency and velocity acceptance than single square pulses. We implement two composite pulse sequences, π/20°−π90°−π/20° and π/20°−π180°−3π/20°, and use the latter composite pulse to demonstrate large-area atom interferometry with stimulated Raman transitions. In addition to enabling larger momentum transfer and higher sensitivity, we argue that composite pulses can improve the robustness of atom interferometers operating in dynamic environments.
The mirrors and beamsplitters of atom interferometers often suffer from inhomogeneities in coupling strength and effective detuning because different atoms see different laser intensities, Zeeman and Doppler shifts and are in different Zeeman sub-states. This limits the fringe visibility for a simple interferometer, which falls off rapidly if extra mirrors are added, for example to increase the interferometer area. In practice, one usually therefore filters the atomic velocities/sub-states, thus losing signal, and/or restricting operation to small-area interferometers with low sensitivity. The problem is familiar in the field of NMR, where, instead of using simple pi or pi/2 pulses, the phase and potentially amplitude are modulated during the pulse so as to make the result robust to the inhomogeneities encountered. Despite the similarities with NMR systems, the numbers, correlations and performance measures for atom interferometry are different. We have used optimal control theory to obtain robust high fidelity mirror pulses for atom interferometry. Importantly, while the designs are found by computational simulation, we can validate them experimentally, with remarkably good agreement. We have addressed the optimization of individual mirror pulses, but the eventual aim is to optimize the interferometer as a whole: errors introduced in one pulse can be compensated at a later stage, for example. Our pulses yield high contrast without the need to filter the atomic sample and maintain this even in the case of extended pulse sequences, thus making it possible to achieve significantly larger interferometer areas than with simple pi pulses.