# Quantum Simulation of Competing Orders with Fermions in Quantum Optical Lattices

## TL;DR

This paper proposes a quantum simulation scheme using ultracold Fermi atoms in optical cavities to explore competing orders like superfluidity and magnetism, emulating strongly correlated electronic systems.

## Contribution

It introduces a method to control and study multiple quantum phases in a cavity QED setup by tuning external parameters, enabling simulation of complex electronic behaviors.

## Key findings

- Access to coexistence of superfluid and magnetic phases via cavity back-action
- Control of quantum phases through pump beam polarization and doping
- Simulation of strongly correlated electronic systems in optical cavity setups

## Abstract

Ultracold Fermi atoms confined in optical lattices coupled to quantized modes of an optical cavity are an ideal scenario to engineer quantum simulators in the strongly interacting regime. The system has both short range and cavity induced long range interactions. We propose such a scheme to investigate the coexistence of superfluid pairing, density order and quantum domains having an- tiferromagnetic or density order in the Hubbard model in a high finesse optical cavity at T = 0. We demonstrate that those phases can be accessed by properly tuning the linear polarizer of an external pump beam via the cavity back-action effect, while modulating the system doping. This allows emulate the typical scenarios of analog strongly correlated electronic systems.