Pairing Mechanism at Finite Temperatures in Bosonic Systems

Abstract

The pure Bose–Hubbard model, a staple of optical lattice-related research that describes bosonic condensation, is examined at finite temperatures. Advanced analytical methods are used, most importantly path integrals and quantum rotors. A first-order trace approximation is commonly applied while integrating over bosonic fields to obtain a phase-only model. Here, a second-order trace approximation is considered instead. This extension leads to an effective phase model with two types of superfluid, i.e., standard Bose–Einstein condensation and additional temperature-driven bosonic pair condensation. This effective model is further treated with a self-consistent harmonic approximation in order to compare the two superfluids. This analysis shows that the pairing mechanism strengthens the condensate phase at finite temperatures.