2104.14257Apr 29, 2021This document includes a letter "Quantum geometry and flat band Bose-Einstein condensation" and a longer article "Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band". The former presents the main, and the latter the details of the calculations, considers physical quantities not studied in the letter, and provides a substantially extended discussion of the subject

Quantum geometry and flat band Bose-Einstein condensation

Aleksi Julku, Georg M. Bruun, Päivi Törmä

Quantum Gases

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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.

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