Long range interaction induced density modulated state in a Bose-Einstein condensate

TL;DR

This paper investigates how long-range s-wave interactions in a one-dimensional Bose-Einstein condensate lead to a density modulated state, using a perturbative approach to solve the non-local Gross-Pitaevskii equation.

Contribution

It introduces a perturbative method to find density modulated states in a non-local BEC model, showing these states are energetically favorable over uniform states.

Findings

Density modulated states are energetically favorable under long-range s-wave scattering.

The density modulated state is obtained directly as a solution to the non-local GP equation.

The approach differs from the traditional amplitude modulation method.

Abstract

We consider a Gross-Pitaevskii model of BEC with non-local s-wave scattering to study the density modulated state in 1D. We resort to a perturbative Taylor series expansion for the order parameter. By perturbative calculations, we show that under long range s-wave scattering a density modulated state is energetically favourable as compared to the uniform density state. We obtain density modulated state as a solution to the perturbative non-local GP equation, rather than the conventional approach of introducing amplitude modulations on top of the uniform density state and lowering the roton minimum.