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arXiv:1401.1986 · Physical Review Letters

Quantum Quench and Prethermalization Dynamics in a Two-Dimensional Fermi Gas with Long-Range Interactions

Nicolás Nessi, Anı́bal Iucci, Miguel A. Cazalilla

Published Nov 17, 2014• 68 citations
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Abstract

We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short- to intermediate-time dynamics is described using the method of bosonization of the Fermi surface. The space-time dependence of the nonequilibrium fermion density matrix as well as the evolution after the quench of the discontinuity at the Fermi momentum of the momentum distribution are computed. We find that the asymptotic state predicted by bosonization is consistent with the existence of a prethermalization plateau, which is also predicted by a perturbative approach in terms of the fermionic degrees of freedom. The bosonized representation, however, explicitly allows for the construction of the generalized Gibbs ensemble describing the prethermalized state.

DOI
10.1103/physrevlett.113.210402

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We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short- to intermediate-time dynamics is described using the method of bosonization of the Fermi surface. The space-time dependence of the nonequilibrium fermion density matrix as well as the evolution after the quench of the discontinuity at the Fermi momentum of the momentum distribution are computed. We find that the asymptotic state predicted by bosonization is consistent with the existence of a prethermalization plateau, which is also predicted by a perturbative approach in terms of the fermionic degrees of freedom. The bosonized representation, however, explicitly allows for the construction of the generalized Gibbs ensemble describing the prethermalized state.
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.
We consider the nonequilibrium dynamics arising after a quench of the transverse magnetic field of a quantum Ising chain, together with the sudden switch-on of a long-range interaction term. The dynamics after the quantum quench is mapped onto a fully connected model of hard-core bosons, after a suitable combination of a Holstein-Primakoff transformation and of a low-density expansion in the quasiparticles injected by the quench. This mapping holds for a broad class of initial states and for quenches which do not cross the critical point of the transverse field Ising model. We then study the algebraic relaxation in time of a number of observables towards a metastable, prethermal state, which becomes the asymptotic steady state in the thermodynamic limit.
The coupling of ultracold quantum gases to an optical cavity provides an ideal system for studying the novel long-range interacting nonequilibrium dynamics. Here we report an experimental observation of the out-of-equilibrium dynamics of a degenerate Fermi gas in the cavity after quenching the pump strength over a superradiant quantum phase transition. The relaxation dynamics exhibits impressively different stages of a delay, violent relaxation, long-lifetime prethermalization, and slowly final thermalization due to the photon-mediated long-range interaction with dissipation. Importantly, we reveal that the lifetime of the system stayed on the prethermalization exhibits the superlinear scaling of the atom number. Furthermore, we show that the backaction of the superradiant cavity field on the gas causes the exchange of atoms between the normal and superradiant state in the early evolution and then induces the prethermalization. This work opens an avenue to explore complex nonequilibrium dynamics of the dissipatively long-range interacting Fermi gases.
Understanding nonequilibrium dynamics of strongly interacting quantum systems represents one of the most challenging problems in many-body physics. Here, quantum thermalization dynamics are explored in real-time in an ultracold Fermi gas suddenly quenched to the BEC-BCS crossover. When quenched to unitarity, it is observed that the cloud size remains unchanged in the early evolution while the momentum distribution emerges two prethermal states with a lifetime difference of two orders of magnitude in the early and intermediate stage before very slowly evolving to the final stationary state. It is revealed that a crossover momentum, at which the momentum distribution remains nearly unchanged, is determined by the thermal wavelength at high temperatures and the Fermi momentum while at low temperatures. It is identified that the universal prethermal dynamics scaling where momentum distributions with different temperatures collapse onto one curve. When quenched to the BEC side, the thermalization rapidly relaxes into a prethermal state and exhibits the low energy oscillation related to the molecular bound states. This work provides benchmarks for the study of quantum thermalization in strongly interacting fermionic many-body systems.
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.
We study thermalization in a one-dimensional quantum system consisting of a noninteracting fermionic chain with each site of the chain coupled to an additional bath site. Using a density matrix renormalization group algorithm we investigate the time evolution of the observables in the chain after a quantum quench. For low densities we show that the intermediate time dynamics can be quantitatively described by a system of coupled equations of motion. For higher densities our numerical results show a prethermalization for the local observables at intermediate times and a full thermalization to the grand canonical ensemble at long times. For the case of a weak bath-chain coupling we find, in particular, a Fermi momentum distribution in the chain in equilibrium in spite of the seemingly oversimplified bath in our model.