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