Amplitude modulated phase in a Bose-Einstein condensate: the role of non-local interactions

TL;DR

This paper investigates a non-local interaction model of Bose-Einstein condensates, revealing that density modulated states can be energetically favorable yet dynamically unstable, highlighting complex stability behavior.

Contribution

It introduces an exact free energy functional for a non-local BEC model and analyzes the stability of density modulated phases in 1D and 2D.

Findings

Density modulated states can have lower energy than uniform states.

Modulated states are inherently dynamically unstable.

The model provides insights into non-local interaction effects.

Abstract

We consider a Gross-Pitaevskii model of BEC with non-local interactions of range of the order of the s-wave scattering length. With this model, we study the density modulated phase in 1D and 2D, which are solutions of this modified model along with the usual uniform density state. We find an exact free energy functional for our model and show that the 1D density modulated state can have lower energy than the uniform density state. Although, the density modulated state can be made to be energetically favourable, we show also that, this state is inherently dynamically unstable due to the coupling of instabilities to the spatial order.