Displaced dynamics of binary mixtures in linear and nonlinear optical lattices

TL;DR

This paper investigates the oscillatory behavior of two-component Bose-Einstein condensates in optical lattices, combining analytical and numerical methods to understand their dynamics and potential for measuring BEC properties.

Contribution

It introduces a variational effective potential approach to analyze displaced soliton dynamics in BEC mixtures within optical lattices, providing analytical expressions for mode frequencies.

Findings

Analytical expressions for symmetric and anti-symmetric mode frequencies.

Good agreement between analytical predictions and numerical simulations.

Displaced dynamics can be used to measure BEC characteristics indirectly.

Abstract

The dynamical behavior of matter wave solitons of two-component Bose-Einstein condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is investigated. In particular, the dependence of the frequency of the oscillating dynamics resulting from initially slightly displaced components is investigated both analytically, by means of a variational effective potential approach for the reduced collective coordinate dynamics of the soliton, and numerically, by direct integrations of the mean field equations of the BEC mixture. We show that for small initial displacements binary solitons can be viewed as point masses connected by elastic springs of strengths related to the amplitude of the OL and to the intra and inter-species interactions. Analytical expressions of symmetric and anti-symmetric mode frequencies, are derived and occurrence of beatings phenomena in the displaced dynamics is predicted. These expressions are shown to give a very good estimation of the oscillation frequencies for different values of the intra-species interatomic scattering length, as confirmed by direct numerical integrations of the mean field Gross-Pitaevskii equations (GPE) of the mixture. The possibility to use displaced dynamics for indirect measurements of BEC mixture characteristics such as number of atoms and interatomic interactions is also suggested.