Shock waves in a one-dimensional Bose gas: from a Bose-Einstein condensate to a Tonks gas

TL;DR

This paper investigates shock wave phenomena in a one-dimensional Bose gas, analyzing the transition from Bose-Einstein condensates to Tonks gases, and verifies the accuracy of the Gross-Pitaevskii equation through quantum corrections.

Contribution

It provides a detailed analysis of shock waves in 1D Bose gases and assesses the validity of the Gross-Pitaevskii equation across different interaction regimes.

Findings

Quantum corrections are negligible for typical BEC parameters.

Shock dynamics show signatures of BEC to Tonks crossover.

Results are experimentally verifiable.

Abstract

We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different experimental setups.