Lasing, quantum geometry and coherence in non-Hermitian flat bands

TL;DR

This paper explores how the geometrical properties of Bloch states can stabilize lasing in flat band lattices with flat dispersion, revealing novel quantum geometric effects on collective excitations and phase dynamics.

Contribution

It introduces a general projection method to analyze lasing in flat bands and uncovers the role of quantum geometry in collective excitations and phase behavior.

Findings

Collective excitations exhibit diffusive behavior governed by quantum geometry.

Phase dynamics show a cancellation of Kardar-Parisi-Zhang nonlinearity.

Numerical simulations confirm analytical predictions in the diamond chain.

Abstract

We show that lasing in flat band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the single-particle dispersion is flat in both its real and imaginary parts. We illustrate a general projection method and compute the collective excitations, which are shown to display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions. Then, we analytically show that the phase dynamics display a surprising cancellation of the Kardar-Parisi-Zhang nonlinearity at the leading order. Because of the relevance of Kardar-Parisi-Zhang universality in one-dimensional geometries, we focus our study on the diamond chain and provide confirmation of these results through full numerical simulations.