Criticality and hidden criticality in multi-species Bose-Einstein condensates

TL;DR

This paper introduces a general analytical approach to multi-species Bose-Einstein condensates, revealing phase transitions and critical phenomena linked to matrix singularities in the coupled Gross-Pitaevskii equations.

Contribution

It provides a novel analytical framework for understanding phase transitions and criticality in multi-species BECs, including the concepts of hidden criticality.

Findings

Identification of full-state and partial-state phase transitions.

Discovery of criticality originating from matrix singularities.

Extension of hidden criticality concept from superconductivity to BECs.

Abstract

A general approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) for K-species Bose-Einstein condensates (BEC). Analytical solutions have been obtained under the Thomas-Fermi approximation. We aim at finding out the common features of the K-species BEC. In particular, two types of phase-transitions, full-state-transition and partial-state transition, are found. In the former all species are involved in the transition, while in the latter only a few specified species are essentially involved. This leads to the criticality and the hidden criticality (previously found in multi-band superconductivity). We further found that the former originates from the singularity of the whole matrix of the CGP, while the latter originates from the singularity of a specified sub-matrix (which is contributed by only a few specified species). It is emphasized that the singularity is not a by-product of the TFA, but is inherent in the CGP.