Quantum correlations in dissipative gain–loss systems across exceptional points

We investigate the behavior of correlations dynamics in a dissipative gain–loss system. First, we consider a setup made of two coupled lossy oscillators, with one of them subject to a local gain. This provides a more realistic platform to implement parity–time (PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{P}\mathcal{T}$$\end{document}) symmetry circumventing the implementation of a pure gain. We show how the qualitative dynamics of correlations resembles that for a pure gain–loss setup. The major quantitative effect is that quantum correlations are reduced, while total ones are enhanced. Second, we study the behavior of these correlations across an exceptional point (EP) outside of the PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{P}\mathcal{T}$$\end{document}-symmetric regime of parameters, observing how different behaviors across the EP occur only in the transient dynamics. This shows how PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{P}\mathcal{T}$$\end{document} symmetry plays a relevant role at large times.