# Simulating frustrated antiferromagnets with quadratically driven QED cavities

## TL;DR

This paper introduces a quantum simulation approach using coupled photonic cavities with two-photon driving to emulate frustrated antiferromagnetic spin systems, revealing spin liquid-like properties in steady states.

## Contribution

It presents a novel method to simulate frustrated antiferromagnets using quadratically driven QED cavities, connecting photonic systems with complex magnetic phases.

## Key findings

- Steady states correspond to degenerate ground states of an antiferromagnetic Ising model.
- Incommensurate cavity geometries produce properties similar to spin liquids.
- Numerical solutions of the quantum master equation demonstrate the feasibility of the approach.

## Abstract

We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate with the antiferromagnetic coupling, the steady state presents properties which bear full analogy with those typical of the spin liquid phases arising in frustrated magnets.