Improving the understanding of the dynamics of open quantum systems

TL;DR

This thesis investigates the impact of initial system-environment correlations on open quantum system dynamics, deriving a master equation that accounts for these correlations and demonstrating their significance in quantum parameter estimation.

Contribution

It introduces a master equation incorporating initial correlations and analyzes their effects, challenging the common assumption of uncorrelated initial states in open quantum systems.

Findings

Initial correlations significantly affect system dynamics even at weak coupling.

The derived master equation captures the influence of initial correlations.

Using two two-level systems enhances environment parameter estimation.

Abstract

This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for the practical implementation of modern quantum technologies. In studies of open quantum systems performed to date, a very common assumption is that the system and the environment are in separated initial states to begin with. One primary objective of this thesis is to critically analyse this assumption. We follow two different approaches to investigate the dynamics. First, we solve an exactly solvable spin-spin model where a central spin system interacts with a collection of quantum spins. We analyse exactly the central spin dynamics, starting from both initially correlated and uncorrelated SE states, and look at the dynamical differences due to the different starting states. Second, we consider an arbitrary system interacting with an arbitrary environment and derive a master equation that describes the system dynamics and incorporates the effect of the initial SE correlations. This effect of initial correlations is captured by an extra term appearing in the master equation. The master equation is subsequently applied to the paradigmatic SE models such as the spin-boson model and the spin-spin model. We demonstrate that the role played by initial correlations can be noticeable even if the SE coupling strength is kept smaller. The next part of the thesis deals with estimating the parameters characterizing the environment of a quantum system where we show that the use of two two-level systems can greatly enhance the estimation of the environment parameters.