Two-band superfluidity from the BCS to the BEC limit

TL;DR

This paper explores the evolution of two-band superfluidity across the BCS-BEC crossover, revealing phase transitions, collective excitations, and deriving effective equations in different regimes.

Contribution

It provides a comprehensive analysis of two-band superfluidity, including phase transitions, collective modes, and derivation of coupled Ginzburg-Landau and Gross-Pitaevskii equations.

Findings

Quantum phase transition from 0-phase to π-phase occurs with interband interaction tuning.

Identification of two low-energy collective excitations: in-phase and out-of-phase modes.

Derivation of coupled Ginzburg-Landau equations reducing to Gross-Pitaevskii equations in the BEC limit.

Abstract

We analyze the evolution of two-band superfluidity from the weak coupling Bardeen-Cooper-Schrieffer (BCS) to the strong coupling Bose-Einstein condensation (BEC) limit. When the interband interaction is tuned from negative to positive values, a quantum phase transition occurs from a 0-phase to a $\pi$-phase state, depending on the relative phase of two order parameters. Furthermore, population imbalances between the two bands can be created by tuning the intraband or interband interactions. We also find two undamped low energy collective excitations corresponding to in-phase and out-of-phase modes. Lastly, we derive the coupled Ginzburg-Landau equations, and show that they reduce to coupled Gross-Pitaevskii equations for two types of bosons in the BEC limit.