Quantum geometry and flat band Bose-Einstein condensation

TL;DR

This paper explores how quantum geometry influences Bose-Einstein condensates in flat band systems, revealing that quantum geometric properties determine condensate stability, sound velocity, and enable strong correlations with weak interactions.

Contribution

It uncovers the fundamental role of quantum geometry in flat band BECs, linking geometric properties to condensate stability and correlation regimes.

Findings

Quantum geometry dictates sound speed and depletion in flat band BECs.

Finite quantum distance ensures BEC stability.

Quantum geometry enables strong correlations with weak interactions.

Abstract

We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using multiband Bogoliubov theory, and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.