index - Atomes Froids

In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive the van der Pol oscillator with an external time-dependent force to reach the limit cycle in a given finite time. Specifically, we are interested in minimising the non-conservative contribution to the work when driving the system from a given initial point on the phase plane to any final point belonging to the limit cycle. There appears a speed limit inequality, which expresses a trade-off between the connection time and cost -- in terms of the non-conservative work. We show how the above results can be { generalized to the broader family of non-linear oscillators given by} the Liénard equation. Finally, we also look into the problem of minimising the total work done by the external force.

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The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach equilibrium except for highly specific initial conditions: it generically evolves toward and stays in a breathing mode. This state is periodic in time, with a Gaussian velocity distribution, an oscillating temperature, and a density profile that oscillates as well. We characterize this breather in terms of initial conditions and constants of the motion. For low but finite densities, the analysis requires taking into account the finite size of the particles. Under well-controlled approximations, a closed description is provided, which shows how equilibrium is reached at long times. The (weak) dissipation at work erodes the breather's amplitude, while concomitantly shifting its oscillation frequency. An excellent agreement is found between molecular dynamics simulation results and the theoretical predictions for the frequency shift. For the damping time, the agreement is not as accurate as for the frequency and the origin of the discrepancies is discussed.

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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.

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The monochromatic driving of a quantum system is a successful technique in quantum simulations, well captured by an effective Hamiltonian approach, and with applications in artificial gauge fields and topological engineering. Here, we investigate multichromatic Floquet driving for quantum simulation. Within a well-defined range of parameters, we show that the time coarse-grained dynamics of such a driven closed quantum system is encapsulated in an effective master equation for the time-averaged density matrix, that evolves under the action of an effective Hamiltonian and tunable Lindblad-type dissipation or quantum gain terms. As an application, we emulate the dissipation induced by phase noise and incoherent emission or absorption processes in the bichromatic driving of a two-level system, and reproduce the phase decoherence in a harmonic oscillator model.

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[...]

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Derniers dépôts, tout type de documents

[hal-04769566] Optimal synchronization to a limit cycle (2024-11-06)

[hal-04767690] Fate of Boltzmann's breathers: Kinetic theory perspective (2024-11-05)

[hal-04761378] Optimal Floquet Engineering for Large Scale Atom Interferometers (2024-10-31)

[hal-04707751] Multichromatic Floquet engineering of quantum dissipation (2024-09-24)

[hal-04701036] Shortcut to synchronization in classical and quantum systems (2024-09-18)

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