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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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We discuss the emulation of non-Hermitian dynamics during a given time window using a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an unstable state and map the quasi-continuum parameters, enabling the precise approximation of non-Hermitian dynamics. The limitations of this model, including in particular short- and long-time deviations, are extensively discussed. We then consider a driven two-level system and establish criteria for non-Hermitian dynamics emulation with a finite quasi-continuum. We quantitatively analyze the signatures of the finiteness of the effective continuum, addressing the possible emergence of non-Markovian behavior during the time interval considered. Finally, we investigate the emulation of dissipative dynamics using a finite quasi-continuum with a tailored density of states. We show through the example of a two-level system that such a continuum can reproduce non-Hermitian dynamics more efficiently than the usual equidistant quasi-continuum model.

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Sujets

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

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75