Two types of phase diagrams for two-species Bose-Einstein condensates

TL;DR

This paper derives analytical solutions for two-species Bose-Einstein condensates under the Thomas-Fermi approximation, classifies phase diagrams into symmetric and asymmetric phases, and explores parameter effects on phase transitions and collapse.

Contribution

It introduces a simplified analytical framework for phase diagrams of two-species BECs and proposes an experimental method to determine particle number ratios.

Findings

Identified three critical values governing phase transitions.

Mapped phase diagrams for different inter-species interactions.

Proposed an experimental approach to measure particle number ratios.

Abstract

Under the Thomas-Fermi approximation, a relatively much simpler analytical solutions of the coupled Gross-Pitaevskii equations for the two-species BEC have been derived. Additionally, a model for the asymmetric states has been proposed, and the competition between the symmetric and asymmetric states has been evaluated. The whole parameter-space is divided into zones, each supports a specific phase, namely, the symmetric miscible phase, the symmetric immiscible phase, or the asymmetric phase. Based on the division the phase-diagrams against any set of parameters can be plotted. Thereby, the effects of these parameters can be visualized. There are three critical values in the inter-species interaction $% V_{AB} $ and one in the ratio of particle numbers $N_{A}/N_{B}$. They govern the transitions between the phases. Two cases, (i) the repulsive $V_{AB}$ matches the repulsive $% V_{A}+V_{B}$, and (ii) the attractive $V_{AB}$ nearly cancels the effect of the repulsive $V_{A}+V_{B}$ have been particularly taken into account. The former leads to a complete separation of the two kinds of atoms , while the latter lead to a collapse. Finally, based on an equation derived in the paper, a convenient experimental approach is proposed to determine the ratio of particle numbers .