Phase Separation and Dynamics of Two-component Bose-Einstein Condensates

TL;DR

This paper investigates the phase separation, oscillatory dynamics, and stability of two-component Bose-Einstein condensates using a variational approach, deriving conditions for miscibility and analyzing bifurcations and symmetry-breaking states.

Contribution

It introduces a simplified classical model for two-component BEC dynamics and provides explicit phase diagrams for miscibility based on trap and interspecies coupling parameters.

Findings

Derived explicit miscibility conditions and phase diagrams.

Identified bifurcation scenarios leading to phase separation.

Analyzed symmetry-breaking dynamical states.

Abstract

We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady state solutions and their stability. By employing a variational approach for a quasi one-dimensional, two-atomic species, condensate we obtain equations of motion for the parameters of each species: amplitude, width, position and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies species coupling parameter. We numerically illustrate the bifurcation scenario whereby non-topological, phase-separated states of increasing complexity emerge out of a symmetric state, as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.