Images of the dark soliton in a depleted condensate

Abstract

The dark soliton created in a Bose–Einstein condensate becomes grey in thecourse of time evolution because its notch fills up with depleted atoms. This is theresult of quantum mechanical calculations which describe the outputof 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 singlerealization of the experiment where two extreme scenarios and manycombinations thereof are possible: one will see either (1) a displaced dark solitonwithout 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 atomsfilling its notch. In either case the average over many realizations willreproduce the mentioned quantum mechanical result. In this paper we useN-particlewavefunctions, which follow from the number-conserving Bogoliubov theory, tosettle this issue.