Controlling phase separation of a two-component Bose-Einstein condensate by confinement

TL;DR

This paper demonstrates that kinetic energy and confinement significantly influence phase separation in two-component Bose-Einstein condensates, challenging traditional criteria and enabling control via confinement parameters instead of interaction strengths.

Contribution

It reveals that confinement and kinetic energy can suppress or modify phase separation, turning the transition from first to second order, offering a new method to control condensate miscibility.

Findings

Kinetic energy opposes phase separation predicted by traditional criteria.

Confinement size L influences phase separation regardless of interaction parameters.

Transition changes from first-order to second-order due to kinetic energy effects.

Abstract

We point out that the widely accepted condition g11g22<g122 for phase separation of a two-component Bose-Einstein condensate is insufficient if kinetic energy is taken into account, which competes against the intercomponent interaction and favors phase mixing. Here g11, g22, and g12 are the intra- and intercomponent interaction strengths, respectively. Taking a d-dimensional infinitely deep square well potential of width L as an example, a simple scaling analysis shows that if d=1 (d=3), phase separation will be suppressed as L\rightarrow0 (L\rightarrow\infty) whether the condition g11g22<g122 is satisfied or not. In the intermediate case of d=2, the width L is irrelevant but again phase separation can be partially or even completely suppressed even if g11g22<g122. Moreover, the miscibility-immiscibility transition is turned from a first-order one into a second-order one by the kinetic energy. All these results carry over to d-dimensional harmonic potentials, where the harmonic oscillator length {\xi}ho plays the role of L. Our finding provides a scenario of controlling the miscibility-immiscibility transition of a two-component condensate by changing the confinement, instead of the conventional approach of changing the values of the g's.