Shadow Lattice Stabilization Program for Strongly Correlated States of Light

Recent progress in nanoscale quantum optics and superconducting qubits has made the creation and quantum simulation of strongly correlated, and even topologically ordered, states of photons a real possibility. Many of these states are gapped and exhibit anyon excitations, which could be used for quantum information processing. However, the question of how to stabilize the many-body ground states of photonic quantum simulators against decays remains largely unanswered. We here propose a simple mechanism which achieves this goal. Our construction uses a uniform two-photon drive field to entangle the qubits of the primary lattice with an auxiliary ``shadow" lattice of qubits with a much faster loss rate than the primary qubits. This entanglement raidly refills hole states created by photon losses, and a many-body gap prevents further photons from being added once the strongly correlated ground state is reached. We present a set of general guidelines for designing the shadow lattice and coupling Hamiltonians to stabilize the ground state of a given primary Hamiltonian. We then provide an explicit construction which stabilizes abelian and non-abelian fractional quantum Hall states of light. The device parameters needed for our scheme to work are within reach of current technology.