Decoherence and relaxation of a pair of interacting spins coupled to independent environments

Abstract

In this thesis, a scheme for calculating the dynamics of two coupled dissipative spins is developed, where each of the spins is coupled to its own boson bath. We derive analytic path sum results both in the Markov-regime and in the one-boson exchange regime. The analysis is also performed with the Bloch-Redfield method. It is shown that the two different approaches lead to identical results for the dynamics. This is not obvious a priori because both methods are based on different procedures.

The path sum method gives detailed insight into the internal dynamics of two coupled spins because we consider every path sequence that contributes to the time evolution.

While most studies of coupled spins are restricted to one type of coupling, e.g., Ising type, we will generalize here to linear combinations of possible couplings. Especially interesting is the occurrence of a frustration of decoherence, if the spins are interacting via a linear combination of longitudinal and transverse coupling and, when in addition, some of the eigenfrequencies become degenerate. Our analysis shows that degenerate but mutual exclusive ground states lead to increased coherence times. Maximization of coherence is one of the crucial goals of quantum state engineering.

Another topic of interest is the impact of non-linear quantum environments, formed by surrounding dissipative spins. A distribution of bistable background charges is known to be responsible for $1/f$ noise in solid state devices, like the superconducting quantum interference devices. Since $1/f$ noise is seemingly the dominating source of decoherence at very low temperature, there is a profound theoretical interest in modeling it. Therefore, we analyze two interacting spins, where one of them is coupled to a boson bath and thereby represents a resonant non-linear quantum environment. We study the crossover from a non-linear to a linear bath and study the corresponding time scale for the relevant bath correlations. Interestingly, for large and increasing temperature we find a decreasing decoherence for the central spin.

In dieser Arbeit wird ein Verfahren zur Berechnung der Dynamik zweier gekoppelter Spins entwickelt, welche jeweils an ein bosonisches Wärmebad gekoppelt sind. Zuerst berechnen wir analytische Pfadsummenergebnisse sowohl im Markov-Regime, wie auch im Ein-Boson Austausch-Regime. Die Untersuchung wird anschließend auch mit der Bloch-Redfield-Methode durchgeführt. Es wird gezeigt, dass die beiden unterschiedlichen Methoden zu identischen Ergebnissen führen. Dies ist nicht von vornherein offensichtlich, da die Methoden auf unterschiedlichen Vorgehensweisen basieren.