Floquet operator engineering for quantum state stroboscopic stabilization

TL;DR

This paper develops a method to engineer Floquet operators for stabilizing quantum states in a Bose-Einstein condensate, combining optimal control and experimental validation to achieve efficient state stabilization.

Contribution

It introduces a novel approach to design Floquet operators for quantum state stabilization using optimal control, applicable to symmetric and general states.

Findings

Existence of a quantum speed limit for stabilization.

Successful experimental stabilization of various quantum states.

Numerical evidence supporting control optimization effectiveness.

Abstract

Optimal control is a valuable tool for quantum simulation, allowing for the optimized preparation, manipulation, and measurement of quantum states. Through the optimization of a time-dependent control parameter, target states can be prepared to initialize or engineer specific quantum dynamics. In this work, we focus on the tailoring of a unitary evolution leading to the stroboscopic stabilization of quantum states of a Bose-Einstein condensate in an optical lattice. We show how, for states with space and time symmetries, such an evolution can be derived from the initial state-preparation controls; while for a general target state we make use of quantum optimal control to directly generate a stabilizing Floquet operator. Numerical optimizations highlight the existence of a quantum speed limit for this stabilization process, and our experimental results demonstrate the efficient stabilization of a broad range of quantum states in the lattice.