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The wave nature of matter remains one of the most striking aspects of quantum mechanics. Since its inception, a wealth of experiments has demonstrated the interference, diffraction or scattering of massive particles. More recently, experiments with ever increasing control and resolution have allowed imaging the wavefunction of individual atoms. Here, we use quantum gas microscopy to image the in-situ spatial distribution of deterministically prepared single-atom wave packets as they expand in a plane. We achieve this by controllably projecting the expanding wavefunction onto the sites of a deep optical lattice and subsequently performing single-atom imaging. The protocol established here for imaging extended wave packets via quantum gas microscopy is readily applicable to the wavefunction of interacting many-body systems in continuous space, promising a direct access to their microscopic properties, including spatial correlation functions up to high order and large distances.

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Boltzmann showed that in spite of momentum and energy redistribution through collisions, a rarefied gas confined in a isotropic harmonic trapping potential does not reach equilibrium; it evolves instead into a breathing mode where density, velocity, and temperature oscillate. This counterintuitive prediction is upheld by cold atoms experiments. Yet, are the breathers eternal solutions of the dynamics even in an idealized and isolated system? We show by a combination of hydrodynamic arguments and molecular dynamics simulations that an original dissipative mechanism is at work, where the minute and often neglected bulk viscosity eventually thermalizes the system, which thus reaches equilibrium.

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Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results.

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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.

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Control of stochastic systems is a challenging open problem in statistical physics, with potential applications in a wealth of systems from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional Active Brownian Particles model in a harmonic potential, a paradigm for the study of self-propelled bacteria. We search for protocols for the driving parameters (stiffness of the potential and activity of the particles) bringing the system from an initial passive-like stationary state to a final active-like one, within a chosen time interval. The exact analytical results found for this prototypical system of self-propelled particles brings control techniques to a wider class of out-of-equilibrium systems.

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Sujets

Condensat Bose-Einstein Lentille de Fresnel Field equations stochastic Cold atoms Quantum gases Fluorescence microscopy Nano-lithographie Engineering Quantum simulator Fresnel lens Chaos Bose-Einstein Condensate Quantum chaos Initial state Effet rochet Collisions ultrafroides Current constraint Mirror-magneto-optical trap Beam splitter Bragg scattering Matter wave Optical lattice Entropy production Masques matériels nanométriques Bose-Einstein Condensates Espace des phases Couches mono-moléculaire auto assemblées Optimal control theory Jet atomique Nano-lithography Bragg Diffraction Bose-Einstein condensates Chaos-assisted tunneling Diffraction de Bragg Gaz quantiques Bose–Einstein condensates Plasmon polariton de surface Condensation de bose-Einstein Bose-Einstein Gaz quantique Contrôle optimal Effet tunnel dynamique Bose-Einstein condensates Coherent control Cold atoms and matter waves Cold gases in optical lattices Maxwell's demon Quantum control Optique atomique Quantum simulation Lattice optical Hamiltonian Microscopie de fluorescence Effet tunnel Quantum gas Piège magnéto-optique à miroir Matter waves Césium Contrôle optimal quantique Physique quantique Théorie de Floquet Dimension 1 Atom chip Réseaux optiques Condensat de Bose-Einstein Quantum physics Fluid Bose-Einstein condensate Mechanics Quantum optimal control Ouvertures métalliques sub-longueur d'onde Puce atomique Condensation Phase space Chaos quantique Condensats de Bose-Einstein Mélasse optique Dynamical tunneling Atom laser Non-adiabatic regime Condensats de Bose– Einstein Experimental results Approximation semi-classique et variationnelle Bose Einstein Condensation Ultracold atoms Floquet theory Levitodynamics Atom optics Periodic potentials Numerical methods Onde de matière Réseau optique Atomes froids Quantum collisions Effet tunnel assisté par le chaos Electromagnetic field time dependence Optical tweezers Condensats de Bose Einstein Atomes ultrafroids dans un réseau optique Bose Einstein condensate Atomic beam Optical lattices Optical molasses

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