The evolution from BCS to Bose pairing in two-band superfluids: Quantum phase transitions and crossovers by tuning band offset and interactions

We show that in two-band s-wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband s-wave interactions, in sharp contrast to single-band s-wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: I) BCS pairing in both bands (BCS-BCS), II) BCS pairing in one band and BEC pairing in the other (BCS-BEC), and III) Bose pairing in both bands (BEC-BEC). Furthermore, we show that by fine tuning the interband interactions to zero one can induce QPTs in the ground state between three distinct superfluid phases. There are two phases where only one band is superfluid (S ₁ or S ₂), and one phase where both bands are superfluid , a situation which is absent in one-band s-wave systems. Lastly, we suggest that these crossovers and QPTs may be observed in multi-component systems such as ⁶Li, ⁴⁰K, ⁸⁷Sr, and ¹⁷³Yb.