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arXiv:2212.12602 · Atoms

Robust Optimized Pulse Schemes for Atomic Fountain Interferometry

Michael H. Goerz, Mark A. Kasevich, Vladimir S. Malinovsky

Published Feb 10, 2023• 18 citations
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Abstract

The robustness of an atomic fountain interferometer with respect to variations in the initial velocity of the atoms and deviations from the optimal pulse amplitude is examined. We numerically simulate the dynamics of an interferometer in momentum space with a maximum separation of 20ℏk and map out the expected signal contrast depending on the variance of the initial velocity distribution and the value of the laser field amplitude. We show that an excitation scheme based on rapid adiabatic passage significantly enhances the expected signal contrast, compared to the commonly used scheme consisting of a series of π/2 and π pulses. We demonstrate further substantial increase of the robustness by using optimal control theory to identify splitting and swapping pulses that perform well on an ensemble average of pulse amplitudes and velocities. Our results demonstrate the ability of optimal control to significantly enhance future implementations of atomic fountain interferometry.

DOI
10.3390/atoms11020036

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We present an analysis of the robustness of existing analytic schemes for the implementation of an atomic fountain interferometer, and develop concepts for improving this robustness through the use of optimal control theory. For an interferometer operating in the Raman regime, we consider an implementation that manipulates the atomic momentum states with a series of Rabi pulses, and analyze how robust the population dynamics are with respect to variations in the effective pulse amplitude seen by the atoms in the atomic clouds, and variations in the initial velocity of the atoms relative to the rest frame. We then show that using rapid adiabatic passage to implement momentum transfer can significantly improve this robustness. Finally, we formulate the most general control conditions for an atomic fountain interferometer and design a functional that can be used for an ensemble optimization over the robustness landscape. We show preliminary results of optimizing the system using Krotov's method, suggesting that optimal control may be able to significantly enhance the robustness of atom interferometers.
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.
We present designs for the augmentation ``mirror'' pulses of large-momentum-transfer atom interferometers that maintain their fidelity as the wave-packet momentum difference is increased. These biselective pulses, tailored using optimal control methods to the evolving bimodal momentum distribution, should allow greater interferometer areas and hence increased inertial measurement sensitivity, without requiring elevated Rabi frequencies or extended frequency chirps. Using an experimentally validated model, we have simulated the application of our pulse designs to large-momentum-transfer atom interferometry using stimulated Raman transitions in a laser-cooled atomic sample of 85Rb^{85}\mathrm{Rb}85Rb at 1 $\ensuremath{\mu}\mathrm{K}$. After the wave packets have separated by 42 photon recoil momenta, our pulses maintain a fringe contrast of 90%, whereas, for adiabatic rapid passage and conventional $\ensuremath{\pi}$ pulses, the contrast is less than 10%. Furthermore, we show how these pulses may be adapted to be robust to laser intensity variations between pulses and to suppress the detrimental off-resonant excitation that limits other broadband pulse schemes.
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.