Interplay between nonclassicality and $\mathcal{PT}$ symmetry in an effective two level system with open system effects

A three level atom in $\Lambda$ configuration is reduced to an effective two level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system when subjected to a beam-splitter type of interaction, it provides the scope of directly (indirectly) probing the nonclassical properties of the output (input) state. Here, we study nonclassical properties of the output state by using some well known measures of nonclassical correlations like the measurement induced disturbance, concurrence and negativity. The nonclassical features are found to enhance in the $\mathcal{PT}$ symmetric (PTS) phase compared to the $\mathcal{PT}$ symmetry broken (PTSB) phase. Further, the output ports of the beam-splitter are subjected to different quantum noise channels, both non-Markovian, e.g., random telegraph noise as well as Markovian, e.g., phase damping, and amplitude damping noise. The application of noise channels is found to decrease the degree of nonclassicality, though continuing to exhibit distinct behavior in PTS and PTSB phases, with the dominant behavior appearing in the former case.