Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics

TL;DR

This paper investigates the transition from sudden to adiabatic interaction quenches in the Hubbard model, revealing how ultracold fermionic systems exhibit prethermalization and energy relaxation, facilitating experimental studies of nonequilibrium superconductivity.

Contribution

It demonstrates the role of intrinsic relaxation in ultracold fermions, enabling controlled quenches and clearer observation of nonequilibrium dynamics in the Hubbard model.

Findings

Momentum distribution shows separation of energy relaxation and thermalization.

Prethermalization regime resembles a zero-temperature Fermi liquid.

Ultracold fermions are robust to heating, aiding experimental observation.

Abstract

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: For the particular example of a linear ramp we examine the transient regime of prethermalization [M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime the momentum distribution resembles a zero temperature Fermi liquid as the energy inserted by the ramp remains located in high energy modes. Thus ultracold fermions prove robust to heating which simplifies the observation of nonequilibrium BCS dynamics in optical lattices.