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arXiv:2302.10737 · Physical Review A

Quantum kinetics of quenched two-dimensional Bose superfluids

Clément Duval, Nicolas Cherroret

Published Apr 6, 2023• 10 citations
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Abstract

We study theoretically the nonequilibrium dynamics of a two-dimensional (2D) uniform Bose superfluid following a quantum quench, from its short-time (prethermal) coherent dynamics to its long-time thermalization. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system and characterize both their normal and anomalous momentum distributions. We apply this formalism to the interaction quench of a 2D Bose gas and study the ensuing dynamics of its quantum structure factor and coherence function, both recently measured experimentally. Our results indicate that, in two dimensions, a description in terms of independent quasiparticles becomes quickly inaccurate and should be systematically questioned when dealing with nonequilibrium scenarios.

DOI
10.1103/physreva.107.043305

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We study theoretically the nonequilibrium dynamics of a two-dimensional (2D) uniform Bose superfluid following a quantum quench, from its short-time (prethermal) coherent dynamics to its long-time thermalization. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system and characterize both their normal and anomalous momentum distributions. We apply this formalism to the interaction quench of a 2D Bose gas and study the ensuing dynamics of its quantum structure factor and coherence function, both recently measured experimentally. Our results indicate that, in two dimensions, a description in terms of independent quasiparticles becomes quickly inaccurate and should be systematically questioned when dealing with nonequilibrium scenarios.
While the mechanisms governing the equilibrium properties of quantum gases are today relatively well understood, their non-equilibrium counterparts remain largely unknown. In this thesis, we theoretically explore the non-equilibrium physics of low-dimensional, interacting Bose gases in two representative configurations. In the first one, we consider an isolated Bose superfluid in two dimensions following a quench of the coupling constant. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system. This enables us to describe the system's evolution from its short-time (prethermal) coherent dynamics to its long-time thermalization. In particular, we derive and discuss the Landau-Beliaev damping rates both in the standard perturbative approach and within a self-consistent extension of the theory. The results are also discussed in the light of recent experiments. Our second study explores a one-dimensional, periodically-driven quantum system, a Bose gas subjected to periodically-kicked interactions. In the limit of infinitely short kicks, this system was previously shown to exhibit a fast exponential spreading of the wave function. By revisiting this problem for kicks of arbitrary duration, we demonstrate that, in this case, the spreading is not exponential but sub-diffusive at long time. Our findings indicate that the breakdown of exponential spreading occurs at very short times even for extremely short kicks, suggesting that sub-diffusion is more the rule than the exception in that system.
The coherence and tunability of Feshbach-resonant gasses enable the experimental studies of highly nonequiblirum quantum many-body states, with a particular focus on the dynamics following a quantum Hamiltonian quench Hi to Hf. These have raised numerous fundamental questions on thermalization under unitary time evolution of a closed quantum system. In my dissertation, I studied the dynamics of two specific systems following a quantum quench: 3d Rb85 resonant Bose gas and 1d spin-imbalanced Fermi-Hubbard model. Using self-consistent Bogoliubov theory and Bosonization formalism, I identify rich post quench dynamics, which lead to thermal or prethermal states that depend strongly on initial state properties. My finding helps better understand the intriguing physics of unitary Bose gas as well as the elusive inhomogeneous superconductivity.
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The understanding of nonequilibrium dynamics in many-body quantum systems is a fundamental issue in statistical physics. Experiments that probe universal properties of these systems can address such foundational questions. In this study, we report the measurement of universal dynamics triggered by a quench from the superfluid to normal phase across the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional (2D) Bose gas. We reduced the density by splitting the 2D gas in two, realizing a quench across the critical point. The subsequent relaxation dynamics were probed with matter-wave interferometry to measure the local phase fluctuations. We show that the time evolution of both the phase correlation function and vortex density obeys universal scaling laws. This conclusion is supported by classical-field simulations and interpreted by means of real-time renormalization group theory.
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After a sudden disruption, weakly interacting quantum systems first relax to a prethermalized state that can be described by perturbation theory and a generalized Gibbs ensemble. Using these properties of the prethermalized state we perturbatively derive a kinetic equation which becomes a quantum Boltzmann equation in the scaling limit of vanishing interaction. Applying this to interaction quenches in the fermionic Hubbard model we find that the momentum distribution relaxes to the thermal prediction of statistical mechanics. For not too large interaction, this two-stage scenario provides a quantitative understanding of the time evolution leading from the initial pure via a metastable prethermal to the final thermal state.