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 $% \hat{\varrho}_{c_{1}c_{2}}$ coupled to a two-mode vacuum reservoir. The mode $c_{1}$($c_{2}$) is emitted during the first(second) transition of a nondegenerate three-level cascade laser. By means of the master equation of the state $\hat{\varrho}_{c_{1}c_{2}}$, we derive analytical expression of the steady-state covariance matrix of the modes $c_{1}$ and $c_{2}$. Using realistic experimental parameters, we show that the state $\hat{\varrho}% _{c_{1}c_{2}}$ can exhibit asymmetric steering. Furthermore, by an appropriate choice of the physical parameters of the state $\hat{\varrho}% _{c_{1}c_{2}}$, we show that one-way steering can be achieved. Essentially, we demonstrate that one-way steering can, in general, occur only from $% c_{1}\rightarrow c_{2}$. Besides, we perform a comparative study between the steering of the two laser modes and their Gaussian R\'{e}nyi-2 entanglement. As results, 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 $\hat{\varrho}_{c_{1}c_{2}}$% . In particular, we found that the steering remains always less than the Gaussian R\'{e}nyi-2 entanglement.