Fluctuating and dissipative dynamics of dark solitons in quasi-condensates

TL;DR

This paper investigates the fluctuating and dissipative behavior of dark solitons in trapped Bose gases, revealing their decay times follow a lognormal distribution and scale with temperature as T^{-4}, aligning with theoretical predictions.

Contribution

It provides a combined numerical and analytical study of dark soliton dynamics at finite temperatures, confirming decay time distributions and temperature scaling laws.

Findings

Soliton decay times are lognormally distributed at each temperature.

Average soliton lifetime scales as T^{-4} in the studied regime.

Model captures the decrease in soliton visibility due to background fluctuations.

Abstract

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long lived soliton trajectories within each ensemble of numerical realizations (S.P. Cockburn {\it et al.}, Phys. Rev. Lett. 104, 174101 (2010)). Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same {\it ab initio} damping). Probing the regime for which $0.8 k_{B}T < \mu < 1.6 k_{B}T$, we find average soliton lifetimes to scale with temperature as $\tau\sim T^{-4}$, in agreement with predictions previously made for the low-temperature regime $k_{B}T\ll\mu$. The model is also shown to capture the experimentally-relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.