Quantum Dynamics in Various Noise Scenarios

Abstract

We provide an alternative derivation of a master equation formalism for open quantum systems and apply it to illustrative examples. Using this formalism, we show that generally there can be interference between non-interacting baths on a system's reduced dynamics, confirming results in Phys. Rev. A 89, 042117 (2014). However, we also find that, up to second order, such interference vanishes as long as the baths are initially statistically independent, thereby identifying a satisfiable condition for non-interference. We use a two-dimensional series expansion method to develop a master equation formalism that deals with the effects of both system-environment interaction and classical noise on a system's dynamics in a unified manner. We apply this formalism to the example of a Zeeman-splitted atom in a stochastic B-field interacting with an optical cavity and find that the atom's total decoherence rate is, up to second order, a simple sum of the decoherence rate due to the atom-cavity interaction alone and that due to the stochastic B-field alone. We also develop a formalism for the dynamics of the (marginal) probability density of open classical systems in a similar fashion as the master equation formalism for open quantum systems.