Sound speed of a Bose-Einstein condensate in an optical lattice

TL;DR

This paper investigates how the speed of sound in a Bose-Einstein condensate varies with optical lattice strength across different dimensions, revealing complex behaviors influenced by lattice geometry and interactions.

Contribution

It provides a comprehensive analytical and numerical analysis of sound speed dependence on lattice strength in 1D, 2D, and 3D optical lattices, highlighting new complex behaviors.

Findings

Sound speed decreases monotonically in 1D with increasing lattice strength.

In 2D, sound speed first increases then decreases as lattice strength increases.

In 3D, sound speed can oscillate with lattice strength.

Abstract

The speed of sound of a Bose-Einstein condensate in an optical lattice is studied both analytically and numerically in all three dimensions. Our investigation shows that the sound speed depends strongly on the strength of the lattice. In the one-dimensional case, the speed of sound falls monotonically with increasing lattice strength. The dependence on lattice strength becomes much richer in two and three dimensions. In the two-dimensional case, when the interaction is weak, the sound speed first increases then decreases as the lattice strength increases. For the three dimensional lattice, the sound speed can even oscillate with the lattice strength. These rich behaviors can be understood in terms of compressibility and effective mass. Our analytical results at the limit of weak lattices also offer an interesting perspective to the understanding: they show the lattice component perpendicular to the sound propagation increases the sound speed while the lattice components parallel to the propagation decreases the sound speed. The various dependence of the sound speed on the lattice strength is the result of this competition.