Momentum-space Landau levels in driven-dissipative cavity arrays

TL;DR

This paper explores how momentum-space Landau levels emerge in a driven-dissipative cavity array system, proposing experimental methods to observe their properties through spectroscopic measurements.

Contribution

It introduces a theoretical framework linking momentum-space Landau levels to driven-dissipative cavity arrays and proposes a realistic optical experiment to observe these effects.

Findings

Eigenstates resemble momentum-space Landau levels in certain limits

Steady-state responses can reveal Berry curvature effects

Proposed spectroscopic methods to probe geometric properties

Abstract

We theoretically study the driven-dissipative Harper-Hofstadter model on a 2D square lattice in the presence of a weak harmonic trap. Without pumping and loss, the eigenstates of this system can be understood, in certain limits, as momentum-space toroidal Landau levels, where the Berry curvature, a geometrical property of an energy band, acts like a momentum-space magnetic field. We show that key features of these eigenstates can be observed in the steady-state of the driven-dissipative system under a monochromatic coherent drive, and present a realistic proposal for an optical experiment using state-of-the-art coupled cavity arrays. We discuss how such spectroscopic measurements may be used to probe effects associated both with the off-diagonal elements of the matrix-valued Berry connection and with the synthetic magnetic gauge.