Stability of Symmetry Breaking States in Finite-size Dicke Model with Photon Leakage

Abstract: We investigate the finite-size Dicke model with photon leakage. It is shown that the symmetry breaking states, which are characterized by non-vanishing $\langle \hat{a} \rangle \neq 0$ and correspond to the ground states in the superradiant phase in the thermodynamic limit, are stable, while the eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity symmetry. We introduce and analyze an effective master equation that describes the dynamics of a pair of the symmetry breaking states that are the degenerate lowest energy eigenstates in the superradiant region with photon leakage. It becomes clear that photon leakage is essential to stabilize the symmetry breaking states and to realize the superradiant phase without the thermodynamic limit. Our theoretical analysis provides an alternative interpretation using the finite-size model to explain results from cold atomic experiments showing superradiance with the symmetry breaking in an optical cavity.