Gaussian quantum steering in a nondegenerate three-level laser

Abstract

Steering is a type of nonseparable quantum correlation, where its inherent asymmetric feature makes it distinct from Bell nonlocality and entanglement. In this paper, we investigate quantum steering in a two-mode Gaussian state [Formula: see text] coupled to a two-mode vacuum reservoir. The mode [Formula: see text] ([Formula: see text]) is emitted during the first (second) transition of a nondegenerate three-level cascade laser. By means of the master equation of the state [Formula: see text], we derive the analytical expression of the steady-state covariance matrix of the modes [Formula: see text] and [Formula: see text]. Using realistic experimental parameters, we show that the state [Formula: see text] can exhibit asymmetric steering. Furthermore, by an appropriate choice of the physical parameters of the state [Formula: see text], we show that one-way steering can be achieved. Essentially, we demonstrate that one-way steering can, in general, occur only from [Formula: see text]. Besides, we perform a comparative study between the steering of the two laser modes and their Gaussian Rényi-2 entanglement. As a result, we found that the entanglement and steering behave similarly in the same circumstances, i.e. both of them decay under dissipation effect; moreover, they can be well enhanced by inducing more and more quantum coherence in the state [Formula: see text]. In particular, we found that the steering remains always less than the Gaussian Rényi-2 entanglement.