Shock waves in a quasi one-dimensional Bose-Einstein condensate

TL;DR

This paper investigates shock wave formation in a quasi-one-dimensional Bose-Einstein condensate using an advanced equation that accounts for transverse density variations, revealing quantitative differences from traditional models.

Contribution

It introduces a 1D nonpolynomial Schrödinger equation to better model shock wave dynamics in BECs, extending beyond the standard 1D GPE.

Findings

Quantitative differences in shock wave velocity and formation time between models.

Dispersive ripple wavelengths differ when using the 1D NPSE.

Enhanced understanding of shock wave behavior in ultracold atomic gases.

Abstract

We study analytically and numerically the generation of shock waves in a quasi one-dimensional Bose-Einstein condensate (BEC) made of dilute and ultracold alkali-metal atoms. For the BEC we use an equation of state based on a 1D nonpolynomial Schrodinger equation (1D NPSE), which takes into account density modulations in the transverse direction and generalizes the familiar 1D Gross-Pitaevskii equation (1D GPE). Comparing 1D NPSE with 1D GPE we find quantitative differences in the dynamics of shock waves regarding the velocity of propagation, the time of formation of the shock, and the wavelength of after-shock dispersive ripples.