Fractional Quantum Hall States in the Optical Phase Space

In recent years, there has been growing interest in creating topological phases of matter in photonic systems, both in classical and quantum regimes of light. One main class of such topological states are chiral topological photonic states that mimic quantum Hall effects on photonic platforms which have been experimentally observed in different settings. In this work, we propose a new approach for generating topologically ordered photonic states within the phase space of coherent quantum optical states. Specifically, we present a many-body photonic Hamiltonian that supports such states, demonstrating that its eigenstates show significant overlap with well-known quantum Hall states. Additionally, we outline a protocol for preparing the required initial states and discuss possible experimental methods to realize the proposed Hamiltonian.