Floquet operator engineering for quantum state stroboscopic stabilization

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.Comment: (10 pages, 3 figures

Optimal control strategies for parameter estimation of quantum systems

Optimal control theory is an effective tool to improve parameter estimation of quantum systems. Different methods can be employed for the design of the control protocol. They can be based either on Quantum Fischer Information (QFI) maximization or selective control processes. We describe the similarities, differences, and advantages of these two approaches. A detailed comparative study is presented for estimating the parameters of a spin$-\tfrac{1}{2}$ system coupled to a bosonic bath. We show that the control mechanisms are generally equivalent, except when the decoherence is not negligible or when the experimental setup is not adapted to the QFI. In this latter case, the precision achieved with selective controls can be several orders of magnitude better than that given by the QFI

Characterization of a Driven Two-Level Quantum System by Supervised Learning

International audienceWe investigate the extent to which a two-level quantum systemsubjected to an external time-dependent drive can be characterizedby supervised learning. We apply this approach to the case ofbang-bang control and the estimation of the offset and the finaldistance to a given target state. For any control protocol, thegoal is to find the mapping between the offset and the distance.This mapping is interpolated using a neural network. The estimateis global in the sense that no a priori knowledge is required onthe relation to be determined. Different neural network algorithmsare tested on a series of data sets. We show that the mapping canbe reproduced with very high precision in the direct case when theoffset is known, while obstacles appear in the indirect casestarting from the distance to the target. We point out the limitsof the estimation procedure with respect to the properties of themapping to be interpolated. We discuss the physical relevance ofthe different results

Characterization of a Driven Two-Level Quantum System by Supervised Learning

International audienceWe investigate the extent to which a two-level quantum systemsubjected to an external time-dependent drive can be characterizedby supervised learning. We apply this approach to the case ofbang-bang control and the estimation of the offset and the finaldistance to a given target state. For any control protocol, thegoal is to find the mapping between the offset and the distance.This mapping is interpolated using a neural network. The estimateis global in the sense that no a priori knowledge is required onthe relation to be determined. Different neural network algorithmsare tested on a series of data sets. We show that the mapping canbe reproduced with very high precision in the direct case when theoffset is known, while obstacles appear in the indirect casestarting from the distance to the target. We point out the limitsof the estimation procedure with respect to the properties of themapping to be interpolated. We discuss the physical relevance ofthe different results

Optimal Floquet Engineering for Large Scale Atom Interferometers

The effective control of atomic coherence with cold atoms has made atom interferometry an essential tool for quantum sensors and precision measurements. The performance of these interferometers is closely related to the operation of large wave packet separations. We present here a novel approach for atomic beam splitters based on the stroboscopic stabilization of quantum states in an accelerated optical lattice. The corresponding Floquet state is generated by optimal control protocols. In this way, we demonstrate an unprecedented Large Momentum Transfer (LMT) interferometer, with a momentum separation of 600 photon recoils ($600\hbar k$) between its two arms. Each LMT beam splitter is realized in a remarkably short time (2 ms) and is highly robust against the initial velocity dispersion of the wave packet and lattice depth fluctuations. Our study shows that Floquet engineering is a promising tool for exploring new frontiers in quantum physics at large scales, with applications in quantum sensing and testing fundamental physics

Ingénierie d’opérateur de Floquet pour la stabilisation stroboscopique d’état quantique

(13 pages, 3 figures)International audienceOptimal 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.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 opérateur de Floquet stabilisant un état cible. Les optimisations de contrôle numériques mettent en évidence l’existence d’une vitesse quantique limite pour ce processus de stabilisation, et nos résultats expérimentaux montrent la stabilisation efficace d’une large gamme d’états quantiques dans le réseau

Reprise de la discussion sur le projet de décret concernant l'ordre de travaux de l'Assemblée, lors de la séance du 1er janvier 1791

Lameth Alexandre Théodore Victor, chevalier de, Cottin Jacques Edme, Dionis du Séjour Achille-Pierre, Boussion Pierre, Populus Marc Etienne, Folleville Antoine-Charles, marquis de, André Antoine Balthazar d'. Reprise de la discussion sur le projet de décret concernant l'ordre de travaux de l'Assemblée, lors de la séance du 1er janvier 1791. In: Archives Parlementaires de 1787 à 1860 - Première série (1787-1799) Tome XXI - Du 26 novembre 1790 au 2 janvier 1791. Paris : Librairie Administrative P. Dupont, 1885. pp. 749-750

Reprise de la discussion sur le projet de décret concernant l'ordre de travaux de l'Assemblée, lors de la séance du 1er janvier 1791

Lameth Alexandre Théodore Victor, chevalier de, Cottin Jacques Edme, Dionis du Séjour Achille Pierre, Boussion Pierre, Populus Marc Etienne, Folleville Antoine Charles Gabriel, marquis de, André Antoine Balthazar d'. Reprise de la discussion sur le projet de décret concernant l'ordre de travaux de l'Assemblée, lors de la séance du 1er janvier 1791. In: Archives Parlementaires de 1787 à 1860 - Première série (1787-1799) Tome XXI - Du 26 novembre 1790 au 2 janvier 1791. Paris : Librairie Administrative P. Dupont, 1885. pp. 749-750