Supefluidity of flat band Bose-Einstein condensates revisited

TL;DR

This paper revisits the superfluid properties of flat band Bose-Einstein condensates, revealing new contributions to superfluid weight and connecting physical observables to quantum geometry, with improved theoretical formulas and numerical validation.

Contribution

It introduces a corrected calculation of superfluid weight considering condensate density and chemical potential changes, and links sound speed and excitation fraction to generalized quantum metrics.

Findings

Superfluid weight includes a previously neglected contribution from condensate density and chemical potential changes.

Speed of sound and excitation fraction relate to orbital-position-independent quantum metrics.

Second order perturbation theory aligns well with numerical results for sound speed dependence.

Abstract

We consider the superfluid weight, speed of sound and excitation fraction of a flat band Bose-Einstein condensate (BEC) within multiband Bogoliubov theory. The superfluid weight is calculated by introducing a phase winding and minimizing the free energy with respect to it. We find that the superfluid weight has a contribution arising from the change of the condensate density and chemical potential upon the phase twist that has been neglected in the previous literature. We also point out that the speed of sound and the excitation fraction are proportional to orbital-position-independent generalizations of the quantum metric and the quantum distance, and reduce to the usual quantum metric (Fubini-Study metric) and the Hilbert-Schmidt quantum distance only in special cases. We derive a second order perturbation correction to the dependence of the speed of sound on the generalized quantum metric, and show that it compares well with numerical calculations. Our results provide a consistent connection between flat band BEC and quantum geometry, with physical observables being independent of the orbital positions as they should, and complete formulas for the evaluation of the superfluid weight within the Bogoliubov theory. We discuss the limitations of the Bogoliubov theory in evaluating the superfluid weight.