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Physical Review A

Amplitude-modulated mirror pulses for improved cold-atom gravimetry

Yida Wang, Jinshuo Cheng, Yujuan Liu, Tingting Lin

Published May 2, 2024• 4 citations
Publisher

Abstract

Cold-atom gravimetry is susceptible to environmental factors and noise resulting from the expansion of the atom cloud, thereby impacting the quality of gravity signals. An amplitude-modulated mirror-pulse scheme for cold-atom gravimeters is proposed to enhance the stability of the gravity measurement. The amplitude-modulated pulse is calculated based on the combined optimal control method of differential evolution and gradient ascent pulse engineering. This combination imparts high robustness to the amplitude-modulated pulse against detuning and coupling strength. Numerical modeling of the atom gravimeter with a cloud of 3 $\mathrm{\textmu{}}\mathrm{K}\phantom{\rule{4pt}{0ex}}^{87}\mathrm{Rb}$ atoms suggests that, compared with the rectangular pulse, the amplitude-modulated mirror pulse reduces the uncertainty of the gravity value extracted from a single interference fringe, increases the contrast of the interference fringe by about 1.5 times, and improves the stability of the gravity measurement. Additionally, by imposing constraints on pulse-shape smoothness, the phase-noise transfer function of the gravimeter using the amplitude-modulated mirror pulse closely approximates the performance of the rectangular pulse.

DOI
10.1103/physreva.109.053501

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•Dec 1, 2016•1 citation
Cold-atom gravimetry is susceptible to environmental factors and noise resulting from the expansion of the atom cloud, thereby impacting the quality of gravity signals. An amplitude-modulated mirror-pulse scheme for cold-atom gravimeters is proposed to enhance the stability of the gravity measurement. The amplitude-modulated pulse is calculated based on the combined optimal control method of differential evolution and gradient ascent pulse engineering. This combination imparts high robustness to the amplitude-modulated pulse against detuning and coupling strength. Numerical modeling of the atom gravimeter with a cloud of 3 \textmuK87Rb\mathrm{\textmu{}}\mathrm{K}\phantom{\rule{4pt}{0ex}}^{87}\mathrm{Rb}\textmuK87Rb atoms suggests that, compared with the rectangular pulse, the amplitude-modulated mirror pulse reduces the uncertainty of the gravity value extracted from a single interference fringe, increases the contrast of the interference fringe by about 1.5 times, and improves the stability of the gravity measurement. Additionally, by imposing constraints on pulse-shape smoothness, the phase-noise transfer function of the gravimeter using the amplitude-modulated mirror pulse closely approximates the performance of the rectangular pulse.
Dynamic atom gravimeters enable absolute gravity measurements on moving platforms. However, their performance is severely degraded due to the complex dynamic environment. This paper finds that the amplitude-modulation noise (AMN) is a key factor contributing to the degradation of gravity- measurement performance. We find that the AMN is induced by the cold atomic cloud trajectory and velocity variation. We build a model to illustrate the principles and magnitude of AMN arising from various experiment processes. Then we propose a method to fit the normalized AMN with respect to the kinematic parameters of the cold atomic cloud and successfully suppress this noise from 0.11 to 0.038 using the fitting result. With this method, we improve the fringe phase resolution from 0.244 to 0.092 rad and reduce the dynamic gravity-measurement noise from 2.69 to 1.68 mGal. This study finds and suppresses a key noise source in dynamic atom gravimeters, which is useful for further improving their precision. The proposed method can also be applied for precision enhancement for other dynamic atom-interferometer-based sensors, such as atom gradiometers and gyroscopes.
Atom matterwave interferometry requires mirror and beam splitter pulses that are robust to inhomogeneities in field intensity, magnetic environment, atom velocity, and Zeeman substate. We present theoretical results which show that pulse shapes determined using quantum control methods can significantly improve interferometer performance by allowing broader atom distributions, larger interferometer areas, and higher contrast. We have applied gradient ascent pulse engineering (grape) to optimize the design of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom interferometer, with the aim of increasing fringe contrast when averaged over atoms with an experimentally relevant range of velocities, beam intensities, and Zeeman states. Pulses were found to be highly robust to variations in detuning and coupling strength and offer a clear improvement in robustness over the best established composite pulses. The peak mirror fidelity in a cloud of $\ensuremath{\sim}80\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}\phantom{\rule{4pt}{0ex}}^{85}\mathrm{Rb}$ atoms is predicted to be improved by a factor of 2 compared with standard rectangular $\ensuremath{\pi}$ pulses.
Dynamic atom gravimeters enable absolute gravity measurements on moving platforms. However, their performance is severely degraded due to the complex dynamic environment. This paper finds that the amplitude modulation noise (AMN) is a key factor contributing to the degradation of gravity measurement performance. We find that the AMN is induced by the cold atomic cloud trajectory and velocity variation. We build a model to illustrate the principles and magnitude of AMN arising from various experiment processes. Then we propose a method to fit the normalized AMN respect to the kinematic parameters of the cold atomic cloud, and successfully suppress this noise from 0.11 to 0.038 using the fitting result. With this method, we improve the fringe phase resolution from 0.244 rad to 0.092 rad, and reduce the dynamic gravity measurement noise from 2.69 mGal to 1.68 mGal. This study finds and suppresses a key noise source for the dynamic atom gravimeters, which is important for further improving its precision. The proposed method can be also applied for precision enhancement for other dynamic atom interferometer-based sensors, such as the atom gradiometers and gyroscopes.
Atom interferometers require both high efficiency and robust performance in their mirror pulses under experimental inhomogeneities. In this work, we demonstrated that quantum optimal control designed mirror pulse significantly enhance interferometer performance by using novel adaptive sliced structure. Using gradient ascent pulse engineering (GRAPE), optimized mirror pulse for a Mach-Zehnder light-pulse atom interferometer was designed by discretizing the control into non-uniform phase slices. This design broadened the tolerence to experimentally relevant variations in detuning [−Ω0,Ω0][-Ω_0,Ω_0][−Ω0​,Ω0​] and Rabi frequency [0.1×Ω0,1.9×Ω0][0.1\timesΩ_0,1.9\timesΩ_0][0.1×Ω0​,1.9×Ω0​] (Ω0=2π×25Ω_0=2π\times25Ω0​=2π×25 kHz), while maintaining high transfer efficiency even when the response-time delays up to 1.6 μs\rm{μs}μs. The optimized pulse was found to be robust to coupling inhomogeneity and velocity spread, offering a significant improvement in robustness over conventional pulse. The adaptive pulse slicing method provides a minimalist strategy that reduces experimental complexity while enhancing robustness and scalability, offering an innovative scheme for quantum optimal control in high precision atom interferometry.
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.
This work describes the technology developed for the transportable gravity gradiometer, ''GGtop", constructed at the University of Birmingham. The device aims to simultaneously interrogate two physically separated, free-falling cold atom clouds using the technique of Raman interferometry to perform differential gravity measurements. Such a technique will suppress common-mode noise sources, such as vibrations, that otherwise limit classical gravimeters and cold atom interferometers based on single-cloud measurements. The technique is expected to improve speed and sensitivity for field measurements greatly. \nUsing a combination of commercially available components and novel designs, intended to enhance portability and robustness, allowed for demonstration of atomic interference with the apparatus via Ramsey's method of separated oscillatory fields. The achieved fringe contrast of ~2%, defined as the difference in the number of atoms detected in IF = 2>, was limited by drifts stemming from some of the novel designs which prompted continued optimisation of the underpinning subsystems. To address performance issues parts of the experiment were redesigned with the goal of improving reliability at the expense of some portability. Using the retrofitted experiment, interference was once again achieved with fitted fringe spacing of 134.7±2.0 uS in good agreement with the 133.9 uS defined by the experimental control. A factor of 10 improvement in contrast was found with the central fringe demonstrating 18% of the atoms detected in the IF = 2> state when normalised to the total 3D MOT number. The 3.71 ± 0.01 kHz fitted linewidth of the central fringe gives a frequency uncertainty of 5.43 ± 0.01 x 10 - 7. This result leaves the experiment in a good position to begin making measurements of gravity.