Liul M. Dynamic processes in multi-level mesoscopic systems

The dissertation is devoted to a detailed study and analysis of dynamic processes that occur during the interaction of mesoscopic two-level (qubits) and multi-level (qudites) systems with an exciting signal. The introduction briefly substantiates the relevance of choosing the topic of the dissertation work, defines the purpose and main tasks of the research, and also describes the object, subject and research methods. The scientific novelty and practical significance of the obtained results are formulated. Information about publications, personal contribution of the recipient and approval of the results of the dissertation is provided. Information about the structure and scope of the presented dissertation work is also indicated. Chapter 1 is devoted to the review and analysis of the literature on the topic of the dissertation. It examines theoretical and experimental aspects of the dissertation work. Experiments were analyzed, the description of which is devoted to further calculations. In particular, a solid-state artificial atom in the two-level approximation was considered - a direct current qubit, a double quantum dot based on silicon, a solid-state artificial atom in a four-level approximation. The rate-equation, the Lindblad equation, and the theoretical aspects of superconducting qubits are considered. A detailed study of the theoretical aspects of superconducting qubits, the self-contained Josephson contact, a superconducting ring with a Josephson contact (SQUID) is described.. In chapter 2 the rate-equation is applied to describe two quantum systems: a persistent-current qubit and a solid-state artificial atom. The rate-equation for a two-level system — a persistent-current qubit is written. The interferogram: the probability of the population of the |1> state of the system as a function of the excitation field amplitude and energy detuning is obtained. The dynamics of the persistent-current qubit is studied. For this purpose, the Lindblad equation was written down and solved. On the other hand, the rate-equation was written and solved for this system. After that, these two approaches were compared with each other. A solid-state artificial atom is theoretically studied in the four-level approximation, in particular, the Hamiltonian of the system is presented and the rate equations describing it are written. Chapter 3 is devoted to the application of the rate-equation to describe the double quantum dot. Special attention is paid in the chapter to the study of possible areas of double quantum dots application and their position in modern physics. An expression for the energy levels of a double quantum dot is derived. An expression for the energy levels of a double quantum dot is derived. A system of balance equations for the studied double quantum dot is obtained. Solving the obtained equations made it possible to construct an experimentally measured quantity — the phase response of the resonator as a function of the amplitude of the excitation signal and energy tuning. Based on the comparative analysis of theoretical and experimental results, it was concluded that the obtained interferogram shows the same patterns as the experimental one. In addition, the dependence of the occupancy probabilities of a certain level on time for different regimes was constructed. In one of sections, the system is considered in the energy basis and it is assumed that the upper energy level does not affect the behavior of the system and therefore it can be neglected. For such a case, the rate-equations are written and possible boundary cases are discussed. Chapter 4 is devoted to the theoretical and experimental study of the transmon-type qubit connected to a semi-infinite transmission line behavior. The introduction to the chapter describes the relevance and expediency of studying this kind of systems, as well as briefly describes the methods of theoretical research. The experimental aspects of studying the dynamics of a transmon-type qubit connected to a semi-infinite transmission line are considered. During the experiment, probing and excitation (pump) signals act on the qubit. By varying the parameters of these signals and then analyzing the probing signal, it is possible to study the system dynamics. Theoretical description of a transmon-type qubit connected to a semi-infinite transmission line are given. One of the main results is the obtained interferograms: the dependence of the reflection coefficient r on the pump power and probing signal frequency at a fixed pump frequency and probing signal power. The dynamic behavior of a transmon-type qubit coupled to a semi-infinite transmission line is studied in detail depending on the values of the pump frequency and the pump power of the signal. The case of the absence of an exciting (pump) signal is also considered.