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

TL;DR

This work addresses the challenge of achieving robust, high-fidelity mirror pulses in cold-atom interferometers under inhomogeneous broadening and finite phase-modulator response. It introduces a GRAPE-based slice-phase optimization that discretizes the control into non-uniform time slices with central symmetry, and explicitly models a finite phase response time to reflect experimental constraints. The optimized, step-like phase profiles substantially improve ensemble-averaged fidelity and robustness to detuning, Rabi-frequency variations, and longitudinal temperature, outperforming conventional rectangular pulses even under realistic limitations. The approach provides a minimalistic yet scalable strategy for quantum optimal control in high-precision AI experiments, with potential impact on precision measurements of gravity, rotation, fundamental constants, and gravitational-wave detection.

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.

Figures (6)

• Figure 1: (a) Spatial distribution of the atomic cloud in the $x-y$ plane, assumed as an ideal Gaussian profile in our numerical model. (b) Velocity distribution of atoms in the $z$-direction follows a Gaussian profile. (c) The combined probability distribution constructed from the assumed spatial and velocity Gaussian profiles. (d) Schematic of the three-level Raman system. Two counter-propagating laser beams with frequencies $\omega_1$ and $\omega_2$ couple the two hyperfine ground states $|g\rangle$ and $|e\rangle$ via the intermediate excited state $|i\rangle$. The single-photon detuning $\Delta$ and the two-photon detuning $\delta$ are labeled.
• Figure 2: Sketch of the GRAPE optimal control algorithm. An initial control field $\hat{H}(0)$ is applied to a numerically simulated system and iteratively optimized under physical constraints. The optimization maximizes a figure of merit $\cal{F}$ after time evolution, yielding the final control field $\hat{H}^{\rm{OPT}}(T)$.
• Figure 3: (a) Phase profile $\phi_L(t)$ for GRAPE pulse optimized to maximize $\cal{F}_{\rm{ave}}$ under the constraint of $N=20$ slices ($\tau_{\rm{resp}}=0~\mu$s). (b) Excited state population as a function of the two-photon detuning $\delta$, with the Rabi frequency fixed at $\Omega_0=2\pi \times 25$ kHz. Results for the optimized pulse phase (red curve) and the rectangular pulse phase (blue curve) are compared. (c) The ensemble averaged fidelity ${\cal{F}}_{ave}$ as a function of the longitudinal temperature $T_z$.
• Figure 4: (a) and (c) show the excited state population in the parameter space of two photon detuning and Rabi frequency, for the rectangular phase pulse and optimized phase pulse, respectively. The contours are at 0.3, 0.5, 0.8, 0.9, and 0.96. (b) and (d) present the time evolution of the ${\cal{F}}_{ave}$ under the rectangular phase pulse and the optimized phase pulse, respectively. All results are obtained assuming $\tau_{\rm{resp}}=0~\mu$s.
• Figure 5: (a) Time evolution of the optimized phase pulse with a response time of $\tau_{\rm{resp}}=1~\mu$s. (b) Zoom of the red dashed box in panel (a), where the phase transition between two adjacent slices is treated as a linear transition with duration $\tau_{\rm{resp}}$. During the remaining interval $\Delta t_i-\tau_{\rm{resp}}$, the pulse phase is kept at the optimized value. (c) Excited state population of the system in the parameter space of Rabi frequency $\Omega$ and two-photon detuning $\delta$, taking into account the finite response time. (d) Final ensemble-averaged fidelity ${\cal{F}}_{ave}(T)$ versus the response time, the optimized pulse (red) outperforms the rectangular pulse (blue) for $\tau_{\rm{resp}}\leq 1.6~\mu$s.