Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement

TL;DR

This paper investigates how transverse confinement affects sound velocity in a Bose-Einstein condensate within an optical lattice, demonstrating that a simplified 1D model accurately captures the full 3D behavior across different regimes.

Contribution

It shows that an effective 1D model based on the equation of state can precisely predict sound velocity in a 3D BEC with optical lattice and transverse confinement.

Findings

Full 3D and 1D models agree across various lattice depths.

The effective 1D model accurately describes the crossover from 1D to 3D regimes.

Results validate the use of simplified models for complex BEC systems.

Abstract

We study the effect of the transverse degrees of freedom on the velocity of sound in a Bose-Einstein condensate immersed in a one-dimensional optical lattice and radially confined by a harmonic trap. We compare the results of full three-dimensional calculations with those of an effective 1D model based on the equation of state of the condensate. The perfect agreement between the two approaches is demonstrated for several optical lattice depths and throughout the full crossover from the 1D mean-field to the Thomas Fermi regime in the radial direction.