Ali Raza Mirza

We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter, a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely, a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

Open quantum systems are a subject of immense interest as their understanding is crucial in the implementation of modern quantum technologies. In the study of their dynamics, the role of the initial system-environment correlations is commonly ignored. In this work, to gain insights into the role of these correlations, we solve an exactly solvable model of a single two-level system interacting with a spin environment, with the initial system state prepared by a suitable unitary operation. By solving the dynamics exactly for arbitrary system-environment coupling strength while taking into account the initial system-environment correlations, we show that the effect of the initial correlations is, in general, very significant and non-trivial. To further highlight the importance of the initial system-environment correlations, we also extend our study to investigate the dynamics of the entanglement between two two-level systems interacting with a common spin environment