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

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 $[-\Omega_0,\Omega_0]$ and Rabi frequency $[0.1\times\Omega_0,1.9\times\Omega_0]$ ($\Omega_0=2\pi\times25$ kHz), while maintaining high transfer efficiency even when the response-time delays up to 1.6 $\rm{\mu s}$. 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.