Robust entanglement and steering in open Dicke models with individual atomic spontaneous emission and dephasing

In this paper, we study steady-state quantum entanglement and steering in an open Dicke model where cavity dissipation and individual atomic decoherence are taken into account. Specifically, we consider that each atom is coupled to independent dephasing and squeezed environments, which makes the widely-adopted Holstein-Primakoff approximation invalid. By discovering the features of quantum phase transition in the presence of the decohering environments, we mainly find that (i) in both normal and superradiant phases, the cavity dissipation and individual atomic decoherence can improve the entanglement and steering between the cavity field and atomic ensemble; (ii) the individual atomic spontaneous emission leads to the appearance of the steering between the cavity field and atomic ensemble but the steering in two directions cannot be simultaneously generated; (iii) the maximal achievable steering in normal phase is stronger than that in superradiant phase; (iv) the entanglement and steering between the cavity output field and the atomic ensemble are much stronger than that with the intracavity, and the steerings in two directions can be achieved even with the same parameters. Our findings reveal unique features of quantum correlations in the open Dicke model in the presence of individual atomic decoherence processes.