Dephasing and Decoherence in Open Quantum Systems: A Dyson's Equation Approach

by Cardamone, David Michael.

In this work, the Dyson’s equation formalism is outlined and applied to several open quantum systems. These systems are composed of a core, quantum-mechanical set of discrete states and several continua, representing macroscopic systems. The macroscopic systems introduce decoherence, as well as allowing the total particle number in the system to change. Dyson’s equation, an expansion in terms of proper self-energy terms, is derived. The hybridization of two quantum levels is reproduced in this formalism, and it is shown that decoherence follows naturally when one of the levels is replaced by a continuum. The work considers three physical systems in detail. The first, quantum dots coupled in series with two leads, is presented in a realistic two-level model. Dyson’s equation is used to account for the leads exactly to all orders in perturbation theory, and the time dynamics of a single electron in the dots is calculated. It is shown that decoherence from the leads damps the coherent Rabi oscillations of the electron. Several regimes of physical interest are considered, and it is shown that the difference in couplings of the two leads plays a central role in the decoherence processes. The second system relates to the decay-out of superdeformed nuclei. In this case, decoherence is provided by coupling to the electromagnetic field. Two, three, and infinite-level models are considered within the discrete system. It is shown that the two-level model is usually sufficient to describe decay-out for the classic regions of nuclear superdeformation. Furthermore, a statistical model for the normal-deformed states allows extraction of parameters of interest to nuclear structure from the two-level model. An explanation for the universality of decay profiles is also given in that model. The final system is a proposed small molecular transistor. The Quantum Interference Effect Transistor is based on a single monocyclic aromatic annulene molecule, with two leads arranged in the meta configuration. This device is shown to be completely opaque to charge carriers, due to destructive interference. This coherence effect can be tunably broken by introducing new paths with a real or imaginary self-energy, and an excellent molecular transistor is the result. 14