Floquet operator engineering for quantum state stroboscopic stabilization

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.Résumé. Le contrôle optimal est un outil précieux pour la simulation quantique, qui permet la préparation, la manipulation et la mesure optimisée d'états quantiques. Par la variation optimale d'un paramètre de contrôle dépendant du temps, des états cibles peuvent être préparés pour initialiser ou façonner des dynamiques quantiques spécifiques. Dans ce travail, nous nous concentrons sur le façonnage d'une évolution unitaire menant à la stabilisation stroboscopique d'états quantiques d'un condensat de Bose-Einstein dans un réseau optique. Nous montrons comment une telle évolution peut être dérivée de contrôles préparant l'état, pour des états avec des symétries d'espace et de temps, puis nous nous consacrons à l'optimisation directe d'un

Introduction to theoretical and experimental aspects of quantum optimal control

“…We propose to demonstrate the different steps of the application of QOC to a specific experimental system, namely the control of a BEC in an optical lattice. We refer the reader to the [137][138][139] for additional theoretical and experimental details on these results.…”

“…In this section, we present some illustrative optimal control results applied to a BEC manipulated in an optical lattice, following the previous formalism. Other examples can be found in [137][138][139]. We focus here on the experimental implementation of the control in a real system, namely the experimental setup at LCAR in Toulouse, the manipulation of the full quantum state of the BEC in the lattice, and a realization of an optimal control in an effective two-level quantum system.…”

“…Again the distribution shows very little evolution, in good agreement with the numerically expected result shown in figure 12(c 2 ). Further examples of state preparation and state characterization can be found in [137][138][139].…”

“…In this paper, we focus on a specific example for which we provide numerical solutions, namely the control of a Bose-Einstein condensate (BEC) in a onedimensional optical lattice [128][129][130]. This system has attracted a lot of interest in recent years from a control point of view [131][132][133][134][135][136][137][138][139][140][141], especially for quantum simulation applications [142][143][144], for which QOC can be used to efficiently prepare the initial state of the system [145]. It allows us to illustrate the implementation of optimal control on an infinite-size system, as well as to emulate a two-level system.…”