Dynamical Evolution of Quantum Correlations and Decoherence in Coupled Oscillators Interacting with a Thermal Reservoir

Abstract

We investigate the dynamical evolution of quantum discord, entanglement and purity in an open quantum system of two coupled asymmetric harmonic oscillators interacting with a thermal environment. Using the Kossakowski-Lindblad master equation we analyze the time evolution starting with a squeezed vacuum state. In contrast to our previous study on entanglement evolution in asymmetric oscillators, the present work introduces XY-type position-position coupling together with a systematic joint analysis of quantum discord and purity alongside entanglement. We examine the combined effects of the squeezing parameter, asymmetry parameter, coupling constant, dissipation rate and temperature. We find that quantum discord and entanglement exhibit, in general, a non-monotonic decrease over time. Increasing temperature consistently accelerates the degradation of both quantum correlations and purity, whereas increasing dissipation accelerates the degradation of quantum correlations but leads to higher steady-state purity. Increasing the squeezing parameter provides a protective effect by enhancing initial correlations and prolonging entanglement survival time, while increasing the coupling constant leads to higher quantum correlations. The asymmetry parameter exhibits only a weak influence on the correlation evolution. Our analysis reveals that quantum discord demonstrates stronger resilience than entanglement, which can present more complex behaviour including entanglement sudden death and possible temporary revivals and re-suppressions. These findings provide valuable insights for developing robust quantum information protocols and strategies for preserving quantum correlations in realistic open quantum systems, with potential extensions to non-Markovian regimes and multi-mode architectures.

Figures (4)

• Figure 1: Dynamics of quantum discord for different values of (a) temperature with $\varepsilon=0$, $r=1$, $\lambda=0.6$, $\nu=0.8$, $\omega=1$; (b) dissipation coefficient with $\varepsilon=0$, $r=1$, $T=0.2$, $\nu=0.8$, $\omega=1$; (c) squeezing parameter with $\varepsilon=0$, $T=0.2$, $\lambda=0.6$, $\nu=0.8$, $\omega=1$; (d) asymmetric parameter with $T=0.2$, $r=1$, $\lambda=0.6$, $\nu=0.6$, $\omega=1$.
• Figure 2: Dynamics of quantum entanglement for different values of (a) temperature with $\varepsilon=0$, $r=2$, $\lambda=0.6$, $\nu=0.8$, $\omega=1$; (b) dissipation coefficient with $\varepsilon=0$, $r=2$, $T=0.2$, $\nu=0.8$, $\omega=1$; (c) squeezing parameter with $\varepsilon=0$, $T=0.2$, $\lambda=0.6$, $\nu=0.8$, $\omega=1$; (d) asymmetric parameter with $T=0.2$, $r=2$, $\lambda=0.6$, $\nu=0.6$, $\omega=1$.
• Figure 3: Dynamics of purity for different values of (a) temperature with $\varepsilon = 0$, $r = 2$, $\lambda = 0.6$, $\nu = 0.8$, and $\omega = 1$, (b) dissipation coefficient with $T = 0.5$, $r = 2$, $\varepsilon = 0$, $\nu = 0.8$, and $\omega = 1$, (c) squeezing parameter with $\varepsilon = 0$, $T = 0.5$, $\lambda = 0.6$, $\nu = 0.8$, and $\omega = 1$, (d) asymmetric parameter with $\lambda = 0.6$, $r = 2$, $T = 0.5$, $\nu = 0.6$, and $\omega = 1$.
• Figure 4: The evolution (a) entanglement (b) discord (c) purity for different values of coupling constant with $\varepsilon=0.5$, $r=2$, $\lambda=0.6$, $T = 0.2$ and $\omega=1$.