RAGE QUIT BOSON X GENERATOR
We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.
The new approach is applied to the spin-boson model with different sets of parameters, to investigate the convergence of the high order expansions of the TCL generator. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. The key quantity in the TCL master equation is the so-called kernel or generator, which describes effects of the bath degrees of freedom. The time-convolutionless (TCL) quantum master equation provides a powerful tool to simulate reduced dynamics of a quantum system coupled to a bath. It is shown that by collective exchange of bosons via a thermal one-dimensional environment effects similar to superradiance and subradiance are possible even for rather large qubit distances and at high temperatures. We investigate how spatial noise correlations influence the relaxation of entangled solid-state qubits. Finally, using the causal master equation approach the decoherence of two spatially separated qubits subject to bit-flip noise is studied. Compared to general non-Markovian master equations, the causal master equation has the advantage of being more intuitive and of allowing for algebraic methods, e.g. We reveal why this approach fails and derive a non-Markovian causal master equation that captures the main effects of the spatial separation. In a second part it is shown that a direct application of the Bloch-Redfield theory to a spatially extended system of qubits leads to a violation of causality and predicts spurious decoherence-free subspaces. A main focus is put on (i) the short-time dynamics of a single qubit which in the standard description with exponential decay rates shows up as a reduced initial amplitude of coherent qubit oscillations, and (ii) the consequences of a spatial qubit separation of several qubits for bipartite qubit entanglement and the register fidelity. For this problem the reduced qubit dynamics possesses an exact solution which is presented in explicit form. One part of the work concentrates on the case where the bath fluctuations induce pure dephasing of the qubit states. A natural realization of this model is the coupling of quantum dot spin and charge qubits to phonons of the underlying substrate. The non-local qubit-field coupling explicitly takes effects from a finite propagation time of field distortions between separated qubits into account.
The environment that causes decoherence of the qubit states is modeled as a bosonic field. This work investigates the decoherence of a qubit register caused by spatially correlated quantum noise and develops theoretical tools to describe the associated reduced qubit dynamics.
Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi’s golden rule is investigated. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases.
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