Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

TL;DR

This paper investigates how anisotropic sound and shock waves propagate in dipolar Bose-Einstein condensates across different dimensions, revealing directional dependencies, instabilities, and confirming theoretical predictions through numerical simulations.

Contribution

It provides a comprehensive analysis of anisotropic wave propagation in dipolar BECs in 3D, 2D, and 1D, highlighting stability conditions and validating theoretical models with numerical results.

Findings

Anisotropic sound and shock waves depend on direction relative to dipole axis.

Instability occurs above a critical attraction threshold in 3D and 1D, but not in 2D.

Numerical results match Bogoliubov theory and theoretical Mach angle predictions.

Abstract

We study the propagation of anisotropic sound and shock waves in dipolar Bose-Einstein condensate in three dimensions (3D) as well as in quasi-two (2D, disk shape) and quasi-one (1D, cigar shape) dimensions using the mean-field approach. In 3D, the propagation of sound and shock waves are distinct in directions parallel and perpendicular to dipole axis with the appearance of instability above a critical value corresponding to attraction. Similar instability appears in 1D and not in 2D. The numerical anisotropic Mach angle agrees with theoretical prediction. The numerical sound velocity in all cases agrees with that calculated from Bogoliubov theory. A movie of the anisotropic wave propagation in a dipolar condensate is made available as supplementary material.