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arXiv:2601.15586 · Physical Review A

Optimized Slice-Phase Control of Mirror Pulse in Cold-Atom Interferometry with Finite Response Time

Xueting Fang, Doudou Wang, Kun Yuan, Jie Deng, Qin Luo, Xiaochun Duan, Minkang Zhou, Lushuai Cao, Zhongkun Hu

quant-phphysics.atom-phSubmitted Jan 22, 2026• Announced Jan 23, 2026• 0 citations
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Abstract

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 $[-Ω_0,Ω_0]$ and Rabi frequency $[0.1\timesΩ_0,1.9\timesΩ_0]$ ($Ω_0=2π\times25$ kHz), while maintaining high transfer efficiency even when the response-time delays up to 1.6 $\rm{μs}$. 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.

DOI
10.1103/r62p-d86z

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•Dec 1, 2020•1 citation
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.
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.
Abstract We present the theoretical design and experimental implementation of mirror and beamsplitter pulses that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These pulses are designed using the GRAPE optimal control algorithm and demonstrated experimentally with a cold thermal sample of 85Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional π pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the π pulse fidelity is below 20%, and is thus suitable for large momentum transfer interferometers using thermal atoms or operating in non-ideal environments. We then extend our optimization to all components of a Mach–Zehnder atom interferometer sequence and show that with a highly inhomogeneous atomic sample the fringe visibility is increased threefold over that using conventional π and π/2 pulses.
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 mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of 85^{85}85Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional πππ pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the πππ pulse fidelity is below 20%, and is thus suitable for large momentum transfer interferometers using thermal atoms or operating in non-ideal environments. We then extend our optimization to all components of a Mach-Zehnder atom interferometer sequence and show that with a highly inhomogeneous atomic sample the fringe visibility is increased threefold over that using conventional πππ and π/2π/2π/2 pulses.
The performance of high-precision cold-atom interferometers is often limited by imperfections in the Raman laser fields. We present a reproducible framework for robust Raman mirror-pulse design and compare Krotov, GRAPE, and CRAB under a common normalized peak-amplitude limit of 3.0. The effective two-level model uses a 25-member detuning--amplitude ensemble and a dense out-of-sample grid. In the fixed-budget study, GRAPE attained a terminal ensemble error of 1.224×10−21.224\times10^{-2}1.224×10−2 and projected Krotov attained 1.243×10−21.243\times10^{-2}1.243×10−2; Krotov occupied a slightly larger Pe≥0.9P_e\ge0.9Pe​≥0.9 grid fraction (0.177 versus 0.170). The best of five CRAB seeds gave 3.081×10−23.081\times10^{-2}3.081×10−2. In the interferometer calculation, GRAPE produced the largest contrast, 0.582±0.0190.582\pm0.0190.582±0.019, while Krotov and the selected CRAB pulse gave 0.454±0.0190.454\pm0.0190.454±0.019 and 0.439±0.0230.439\pm0.0230.439±0.023, respectively. These results establish a reproducible comparison of trade-offs, rather than universal superiority of any one optimizer.
Atom interferometric sensors can enable extremely precise measurements of inertial motion and external fields by manipulating and interfering atomic states using pulses of laser light. However, like many experiments that require the coherent control of a quantum system, the interaction fidelity is limited by inhomogeneities in the control fields. Variations in atomic velocity and laser intensity lead different atoms to experience different interactions under the same pulse, reducing the interference fringe contrast, introducing bias, and limiting the sensitivity. We present the theoretical design and experimental demonstration of pulses for atom interferometry which compensate inhomogeneities in atomic velocity and laser intensity. By varying the laser phase throughout a pulse and choosing an appropriate fidelity measure to be maximised, pulses are optimised by adapting optimal control techniques originally designed for nuclear magnetic resonance applications. We show using simulations that optimised pulses significantly improve the fidelity of interferometer operations and verify this experimentally using Raman transitions within a cold sample of 85Rb atoms. We demonstrate a robust state-transfer pulse that achieves a fidelity of 99.8(3)% in a ∼ 35 µK sample and obtain a threefold increase in the fringe contrast using a full sequence of optimised pulses. Many of the pulse shapes found by optimal control are simple and symmetrical, and we show that certain symmetries are integral to error compensation. By systematically exploring the dependence of these solutions on the model and optimisation parameters, we demonstrate a stability which underlines the general applicability of optimised pulses to a range of interferometer configurations. Finally, we introduce and computationally analyse a novel theoretical approach to improve the sensitivity of large-momentum-transfer (LMT) interferometers, whereby “biselective” pulses are optimised to track the changing resonance conditions encountered in extended pulse sequences that are designed to increase the measurement sensitivity. When conventional pulses of steady phase are used, the interference contrast decays rapidly as extra pulses are added because of the change in resonance. Using numerical simulations, we show that bi-selective pulses maintain interaction fidelity throughout extended pulse sequences, allowing significant increases in the sensitivity that may be obtained using LMT.