Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

TL;DR

This paper analytically investigates the transcritical flow of a Bose-Einstein condensate through a penetrable barrier, revealing the formation of slow dark soliton trains and their dependence on flow parameters, with implications for experiments.

Contribution

It introduces an analytical approach combining hydraulic solutions and Whitham modulation equations to describe dispersive shock structures in BEC flow through barriers, aligning with experimental observations.

Findings

Dispersive shocks form attached to the barrier as slow dark soliton trains.

The soliton emission rate and amplitudes depend on flow velocity and barrier strength.

Good agreement with numerical simulations and experimental relevance is demonstrated.

Abstract

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the localized "hydraulic" solution of the 1D Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train and the drag force are determined in terms of the BEC oncoming flow velocity and the strength of the potential barrier. A good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.