Quantum Zeno effect and nonclassicality in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric system of coupled cavities

Abstract

The interplay between the nonclassical features and the parity-time ($\mathcal{PT}$) symmetry (or its breaking) is studied here by considering a $\mathcal{PT}$-symmetric system consisting of two cavities with gain and loss. The conditions for $\mathcal{PT}$ invariance are obtained for this system. The behavior of the average photon number corresponding to the gain and loss modes for different initial states (e.g., vacuum, NOON, coherent, and thermal states) has also been obtained. With the help of the number operators, quantum Zeno and anti-Zeno effects are studied, and the observed behavior is compared in $\mathcal{PT}$-symmetric (PTS) and $\mathcal{PT}$-symmetry-broken (PTSB) regimes. It has been observed that the relative phase of the input coherent fields plays a key role in the occurrence of these effects. Further, some nonclassicality features are witnessed using criteria based on the number operator(s). Specifically, intermodal antibunching, sum, and difference squeezing are investigated for specific input states. It is found that the various nonclassical features, including the observed quantum Zeno and anti-Zeno effects, are suppressed when one goes from the PTS to PTSB regime. In other words, the dominance of the loss or gain rate in the field modes over the coupling strength between them diminishes the nonclassical features of the system.