First-order photon condensation in magnetic cavities: A two-leg ladder model

TL;DR

This paper investigates a first-order phase transition to a photon condensed state in a fermionic ladder system coupled to a magnetic cavity mode, revealing the importance of light-matter entanglement and finite-size effects.

Contribution

It introduces a model of fermions in a ladder geometry coupled to a magnetic cavity, demonstrating a first-order photon condensation transition and analyzing the role of entanglement and finite-size corrections.

Findings

First-order phase transition with a sudden change in fermionic band structure.

Photon mode remains Gaussian in the thermodynamic limit.

Light-matter entanglement is crucial for accurate finite-size descriptions.

Abstract

We consider a model of free fermions in a ladder geometry coupled to a nonuniform cavity mode via Peierls substitution. Since the cavity mode generates a magnetic field, no-go theorems on spontaneous photon condensation do not apply, and we indeed observe a phase transition to a photon condensed phase characterized by finite circulating currents, alternatively referred to as the equilibrium superradiant phase. We consider both square and triangular ladder geometries, and characterize the transition by studying the energy structure of the system, light-matter entanglement, the properties of the photon mode, and chiral currents. The transition is of first order and corresponds to a sudden change in the fermionic band structure as well as the number of its Fermi points. Thanks to the quasi-one dimensional geometry we scrutinize the accuracy of (mean field) cavity-matter decoupling against large scale density-matrix renormalization group simulations. We find that light-matter entanglement is essential for capturing corrections to matter properties at finite sizes and for the description of the correct photon state. The latter remains Gaussian in the the thermodynamic limit both in the normal and photon condensed phases.