Quantum heat waves in a one-dimensional condensate

TL;DR

This paper investigates the non-equilibrium dynamics of phase relaxation in a one-dimensional condensate system, revealing thermalization patterns, propagating sound waves, and extreme temperature effects associated with supersonic splitting.

Contribution

It introduces a detailed analysis of how a finite condensate splits at supersonic speeds, showing the emergence of thermal correlations and the breakdown of generalized Gibbs ensemble descriptions.

Findings

Correlations become locally thermal with different effective temperatures.

Propagating fronts of hot and cold sound waves explain thermalization.

A sonic boom occurs at splitting velocities approaching the speed of sound.

Abstract

We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a bi-directional, supersonic `unzipping' of a finite single condensate. We find that the system fractures into different \emph{extensive} chunks of space-time, within which correlations appear thermal but correspond to different effective temperatures. Coherences between different eigen-modes are crucial for understanding the development of such thermal correlations; at no point in time can our system be described by a generalized Gibbs' ensemble despite nearly always appearing locally thermal. We rationalize a picture of propagating fronts of hot and cold sound waves, populated at effective, relativistically red- and blue-shifted temperatures to intuitively explain our findings. The disparity between these hot and cold temperatures vanishes for the case of instantaneous splitting but diverges in the limit where the splitting velocity approaches the speed of sound; in this limit, a sonic boom occurs wherein the system is excited only along an infinitely narrow, and infinitely hot beam. We expect our findings to apply generally to the study of superluminal perturbations in systems with emergent Lorentz symmetry.