Quantum Decoherence in System-Bath Interferometry

In this paper, we study a quantum harmonic oscillator in a Mach-Zehnder-type interferometer which interacts with an environment, including electromagnetic oscillators. By solving the Lindblad master equation, we calculate the resulted interference pattern of the system. Interestingly, we show that even if one considers the decoherence effect, the system will keep some of its quantum properties. Indeed, the thermalization process does not completely leave the system in a classical state and the system keeps some of its coherency. Such an effect can be detected, when the frequency of the central system is high and the temperature is low, even with zero phase angle. This observation makes the quantum-to-classical transition remain as a vague notion in decoherence theory. By introducing an entropy measure, we express the influence of the bath as a maximization of system's entropy instead of classicalization of the state.