Temperatures are not useful to characterise bright-soliton experiments for ultra-cold atoms

TL;DR

This paper argues that temperature is not a useful parameter for describing bright-soliton experiments in ultra-cold atoms, due to ensemble inequivalence and observed coexistence phenomena.

Contribution

It demonstrates the non-equivalence of canonical and micro-canonical ensembles for quantum bright solitons and highlights the limitations of temperature-based descriptions in experiments.

Findings

Canonical ensemble predicts anomalous energy fluctuations.

Micro-canonical ensemble shows coexistence of atoms and solitons.

Temperature is not a reliable descriptor for bright-soliton states.

Abstract

Contrary to many other translationally invariant one-dimensional models, the low-temperature phase for an attractively interacting one-dimensional Bose-gas (a quantum bright soliton) is stable against thermal fluctuations. However, treating the thermal properties of quantum bright solitons within the canonical ensemble leads to anomalous fluctuations of the total energy that indicate that canonical and micro-canonical ensembles are not equivalent. State-of-the-art experiments are best described by the micro-canonical ensemble, within which we predict a co-existence between single atoms and solitons even in the thermodynamic limit - contrary to strong predictions based on both the Landau hypothesis and the canonical ensemble. This questions the use of temperatures to describe state-of-the-art bright soliton experiments that currently load Bose-Einstein condensates into quasi-one-dimensional wave guides without adding contact to a heat bath.