Open Access

Ralf Blattmann

• In this thesis, we investigate several aspects of driven open quantum systems relevant for experiments with artificial solid-state based systems. First, we propose how to measure the work performed by a time-dependent force and, thus, the work fluctuation relations in a quantum system. Generally, the experimental investigation of these relations in the quantum regime is hindered by the fact that it requires many projective energy measurements. As alternative that circumvents this problem, we investigate the implementation of a recent interferometric method in a circuit QED setup. We highlight that this method could be employed to obtain the work statistics of closed as well as open driven system, even in the strongly dissipative regime. Our simulations demonstrate the experimental feasibility. In the second part, we explore the possibility to entangle an excitonic two-level system in a semiconductor quantum dot with a cavity defined on a photonic crystal by sweeping the cavityIn this thesis, we investigate several aspects of driven open quantum systems relevant for experiments with artificial solid-state based systems. First, we propose how to measure the work performed by a time-dependent force and, thus, the work fluctuation relations in a quantum system. Generally, the experimental investigation of these relations in the quantum regime is hindered by the fact that it requires many projective energy measurements. As alternative that circumvents this problem, we investigate the implementation of a recent interferometric method in a circuit QED setup. We highlight that this method could be employed to obtain the work statistics of closed as well as open driven system, even in the strongly dissipative regime. Our simulations demonstrate the experimental feasibility. In the second part, we explore the possibility to entangle an excitonic two-level system in a semiconductor quantum dot with a cavity defined on a photonic crystal by sweeping the cavity frequency across its resonance with the exciton transition. The dynamic cavity detuning is established by a radio-frequency surface acoustic wave (SAW). It induces Landau-Zener transitions between the excitonic and the photonic degrees of freedom and, thereby, entangles the subsystems. We perform a theoretical study with a master equation approach and optimize the scheme by using tailored Fourier-synthesized SAW pulses. Assuming experimentally demonstrated system parameters, we show that the composed pulses increase both the maximum entanglement and its persistence. The latter is only limited by the dominant dephasing mechanism, i.e., the photon loss from the cavity. Sweeping periodically through an avoided crossing leads to a series of transitions and results in Landau-Zener-Stuckelberg-Majorana (LZSM) interference patterns which we investigate in the third part of this thesis. We derive the structure of these patterns for a qubit that experiences quantum dissipation for time-periodic, but otherwise general driving. A spin-boson Hamiltonian serves as model which we treat with a Bloch-Redfield master equation in Floquet basis. It predicts a peak structure that depends sensitively on the operator through which the qubit couples to the bath. The Fourier transforms of the LZSM patterns exhibit arc structures which reflect the shape of the driving. These features are captured by an effective time-independent Bloch equation which provides an analytical solution.…