Ryzhov A. Application of Landau-Zener-Stückelberg-Majorana interferometry for the control of the dynamics of quantum systems

Dissertation for a Doctor of Philosophy degree in speciality 104 - «Physics and Astronomy» (10 - Natural Sciences). - B. Verkin Institute for Low Temperature Physics and Engineering, NAS of Ukraine, Kharkiv 2024. The dissertation is devoted to the study of the dynamics of quantum two-level and multilevel systems and the development of new approaches to its description and control using the Lindblad equation, Landau-Zener-Stückelberg-Majorana interferometry, adiabatic-impulse model and rate equation approach. In the introduction I briefly justify the relevance of the dissertation topic, define purpose and main tasks of the research, objects, subject, and research methods. The scientific novelty is formulated and the practical value of the obtained results is described. Also, this chapter includes the information about the publications, personal applicant's contributions, and approbation of the dissertation results. The information about the structure and volume of the dissertation is also given. The chapter 1 is devoted to the review and analysis of the literature related to the topic of the dissertation. A transition of the occupation probability between energy levels of a quantum system during the passage of an avoided crossing of the levels is known as a Landau-Zener-Stückelberg-Majorana (LZSM) transition. When a quantum system with an avoided-level crossing is subject to periodic strong driving with sufficiently large amplitude, a sequence of LZSM transitions occurs. The physical observables of the system, like the occupation probabilities of the energy levels, exhibit periodic dependence on the parameters of the external driving, known as LZSM interferometry. The chapter 2 is devoted to the study of an alternative paradigm for implementing quantum logic gates based on non-resonant driving with LZSM transitions. We further develop this paradigm, explore the dynamics of a multi-level quantum system under LZSM drive and optimize the parameters for increasing the quantum logic gates speed. We define the parameters of the external driving required for implementing a specific quantum logic gate, demonstrate the implementations of X, Y, Hadamard, and phase gates implementations using both Rabi oscillations and LZSM transitions, and compare the speed and fidelities achieved with both paradigms. We generalize the considered paradigm to realize quantum logic gates for multi-level quantum systems, and describe the realizations of two-qubit iSWAP and CNOT gates. We also provide some details for implementing other two-qubit gates: SWAP, CZ, CS. The chapter 3 is devoted to the study of the spectroscopy for a silicon double quantum dot (DQD). A periodically driven quantum system with avoided level crossing experiences both non-adiabatic transitions and wave-function phase changes. For qubits with repelling energy levels, the LZSM interference displays arc-shaped resonance lines. In the case of a multi-level system with an avoided level crossing of the two lower levels, the shape of the resonances can change from convex arcs to concave heart-shaped and harp-shaped resonance lines. We consider this for silicon quantum dots. We consider a four-state Hamiltonian and discuss how to prepare the DQD states for low-frequency LZSM spectroscopy by dressing them with a resonant signal. The dressing allows to adopt the formulas of the LZSM interferometry for the two-level quantum systems. We discuss the interference fringes obtained, and analyze the shape of the resonant lines. The chapter 4 is devoted to the description of the quantum multi-level systems with the Lindblad master equation, the adiabatic-impulse model, and the rate equation approach. We study a strongly driven dissipative four-level DQD. We obtain its Hamiltonian and solve the Lindblad master equation. There are four different LZSM regimes: multi-passage, single-passage, double-passage, and incoherent one. We calculated occupation probabilities of each system's state as functions of time for all operation regimes. We also describe how to use the adiabatic-impulse model and the rate equation approach for description of quantum multilevel systems. By combination of the adiabatic-impulse model and the rate equation approach it is possible in some cases to describe the dynamics of multilevel quantum systems with energy relaxation and LZSM crossings. We calculate the dynamics of the detector of microwave photons, based on the flux qubit for the reset stage of the detector.