Self-localized state and solitons in a Bose-Einstein-condensate-impurity mixture at finite temperature

TL;DR

This paper investigates the behavior of a Bose-Einstein condensate-impurity mixture at finite temperature using TDHFB theory, revealing how thermal effects influence localization, self-trapping, and soliton formation.

Contribution

It introduces a coupled nonlinear framework to analyze finite-temperature effects on BEC-impurity mixtures, including soliton formation and self-trapping thresholds.

Findings

Thermal cloud and anomalous density deform with temperature.

Impurity becomes less localized at higher temperatures.

Solitons can form in the mixture at finite temperature.

Abstract

We study the properties of a Bose-Einstein condensate (BEC)-impurity mixture at finite temperature employing the time dependent Hartree-Fock Bogoliubov (TDHFB) theory which is a set of coupled nonlinear equations of motion for the condensate and its normal and anomalous fluctuations on the one hand, and for impurity on the other. The numerical solutions of these equations in the static quasi-1D regime show that the thermal cloud and the anomalous density are deformed as happens to the condensate and the impurity becomes less localized at nonzero temperatures. Effects of the BEC fluctuations on the self-trapping state are studied in homogeneous weakly interacting BEC-impurity at low temperature. The self-trapping threshold is also determined in such a system. The formation of solitons in the BEC-impurity mixture at finite temperature is investigated. Our formalism shows several new pictures.