Non-equilibrium steady states in an open tricritical Dicke model

The Lindblad formalism has been successfully employed to determine the non-equilibrium steady states (NESS) of Dicke-like models under a semiclassical description, predicting non-equilibrium superradiant phase transitions occurring in the thermodynamic limit. High tunability and control in AMO experimental setups allow us to construct more complex light-matter interacting Hamiltonians with richer properties, however, the conventional semiclassical approximations might not be suitable for these systems, and a more general method is required to determine if these exotic features survive in an open description. In this work, we explore the implementation of the density matrix form of the Lindblad equation in order to describe the steady-state behavior of more intricate light-matter interacting quantum open systems. Here we describe the effect of photon losses in the critical properties on a recently proposed generalization of the Dicke Hamiltonian that exhibits a quantum tricritical point.