Images of the Dark Soliton in a Depleted Condensate

TL;DR

This paper investigates the quantum mechanical behavior of dark solitons in Bose-Einstein condensates, revealing how single realizations can differ significantly from average predictions due to quantum effects.

Contribution

It applies number-conserving Bogoliubov theory to analyze single experimental realizations of dark solitons, clarifying their possible outcomes beyond average quantum mechanical results.

Findings

Single realizations can show displaced or filled solitons.

Quantum effects lead to different observable outcomes in individual experiments.

Average results align with traditional quantum mechanical predictions.

Abstract

The dark soliton created in a Bose-Einstein condensate becomes grey in course of time evolution because its notch fills up with depleted atoms. This is the result of quantum mechanical calculations which describes output of many experimental repetitions of creation of the stationary soliton, and its time evolution terminated by a destructive density measurement. However, such a description is not suitable to predict the outcome of a single realization of the experiment were two extreme scenarios and many combinations thereof are possible: one will see (1) a displaced dark soliton without any atoms in the notch, but with a randomly displaced position, or (2) a grey soliton with a fixed position, but a random number of atoms filling its notch. In either case the average over many realizations will reproduce the mentioned quantum mechanical result. In this paper we use N-particle wavefunctions, which follow from the number-conserving Bogoliubov theory, to settle this issue.