Momentum distribution and coherence of a weakly interacting Bose gas after a quench

TL;DR

This paper investigates the dynamics of a weakly interacting Bose gas after a quench, analyzing momentum distribution and coherence, revealing frozen low-momentum modes, adiabatic high-momentum modes, and oscillations at intermediate momenta.

Contribution

It provides an exact analytical solution for the time evolution of a quenched Bose gas with time-dependent interactions, highlighting the behavior of different momentum modes and coherence properties.

Findings

Low-momentum modes remain frozen during evolution.

High-momentum modes follow the interaction change adiabatically.

Oscillations occur at intermediate momenta, similar to Sakharov oscillations.

Abstract

We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth "light-cone effect," with typically no prethermalization.