Phase separation of a Bose-Bose mixture: impact of the trap and particle number imbalance

TL;DR

This paper investigates the phase separation in a two-species bosonic mixture confined in quasi-one-dimensional traps, analyzing the effects of trap asymmetry and particle imbalance through mean-field and many-body methods.

Contribution

It introduces a detailed phase diagram analysis incorporating trap and particle number imbalance, and compares mean-field predictions with correlated many-body results.

Findings

Mean-field predicts a simple rule for phase boundary.

Critical coupling strength for phase transition estimated.

Significant deviations between mean-field and many-body results at certain trap ratios.

Abstract

We explore a few-body mixture of two bosonic species confined in quasi-one-dimensional parabolic traps of different length scales. The ground state phase diagrams in the three-dimensional parameter space spanned by the harmonic length scale ratio, inter-species coupling strength and particle number ratio are investigated. As a first case study we use the mean-field ansatz (MF) to perform a detailed analysis of the separation mechanism. It allows us to derive a simple and intuitive rule predicting which of the immiscible phases is energetically more favorable at the miscible-immiscible phase boundary. We estimate the critical coupling strength for the miscible-immiscible transition and perform a comparison to correlated many-body results obtained by means of the Multi-Layer Multi-Configuration Time Dependent Hartree method for bosonic mixtures (ML-X). At a critical ratio of the trap frequencies, determined solely by the particle number ratio, the deviations between MF and ML-X are very pronounced and can be attributed to a high degree of entanglement between the components. As a result, we evidence the breakdown of the effective one-body picture. Additionally, when many-body correlations play a substantial role, the one-body density is in general not sufficient for deciding upon the phase at hand which we demonstrate exemplarily.