# Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

## TL;DR

This paper proposes a frequency-dependent incoherent pump scheme to stabilize strongly correlated photon states in coupled resonator arrays, enabling quantum simulation of zero-temperature many-body physics with robustness against losses.

## Contribution

It introduces a novel non-Markovian reservoir-based pump scheme that stabilizes non-equilibrium steady states mimicking zero-temperature equilibrium states in photon systems.

## Key findings

- Predicted Mott-Insulator-like states with arbitrary densities.
- Observed transition to superfluid-like states at higher tunneling.
- Identified non-equilibrium processes with finite entropy generation.

## Abstract

We introduce a novel frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a non-equilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-Insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or non-integer densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic non-equilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero temperature many-body physics is highlighted.