Dynamics of the Interaction Between Two Coherent States in a Cavity with Finite Temperature Decay

In this study, we present an exact solution to the Lindblad master equation describing the interaction of two quantized electromagnetic fields in a decaying cavity coupled to a thermal reservoir at a finite temperature. The solution is obtained using the superoperator technique, leveraging commutation relations to factorize the exponential of the Lindblad superoperators into a product of exponentials. To demonstrate the applicability of this approach, we analyze the dynamics of the system both analytically and numerically for two initial conditions: nonentangled and entangled coherent states, exploring their temporal evolution. Additionally, we employ entropy and quantum discord analysis to characterize quantum correlations and analyze the behavior of entanglement (or lack thereof) during the evolution. This comprehensive analysis provides valuable insights into the behavior of open quantum systems and their interaction with the environment.