Ivakhnenko O. Dynamics of nonadiabatic transitions in quantum and classical two-level systems

The dissertation is devoted to the study of fundamental dynamical phenomena which emerge due to the driving of the quantum and classical two-level systems in microscopic and mesoscopic structures. In the introduction the relevance is briefly justified of the dissertation topic, defined 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 are described. Also, this chapter has discussed the information about the publications, personal applicant's contribution, 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 on the topic of this thesis. The main phenomena of two-level system (TLS) driving are briefly described. Variety different systems can be considered as two-level systems. In particular, the Landau-Ziner-Stükelberg-Majorana (LZSM) transition is introduced. Chapter 2 is devoted to a detailed analysis of the one-time transition of the LZSM and its properties, such as dynamics for a different speed of transition and different initial conditions, as well as time of the transition in different bases. In this chapter, the method of transition matrices and the transition with preservation of population are also introduced for the first time. Chapter 3 is devoted to describing of various approaches to the multiple transitions of LZSM under the action of a harmonic excitation signal. More accurate formula for the average time occupancy of levels in the diabatic basis is obtained for the first time within the approach of the adiabatic-impulse model (AIM). The influence of excitation frequency on interferograms within the rotating wave approximation (RWA) is investigated. The effect of decoherence relaxation and temperature on the dynamics of the two-level system is investigated. The relative complexity of interferogram calculations by different methods is presented for the first time as the time required to construct the same interferogram by different methods and approximations. Chapter 4 is devoted to the description and demonstration of the usage of multiple non-adiabatic LZSM transitions as a basis for quantum logic operations. LZSM transitions have several advantages over Rabi oscillations, which are commonly used for quantum logic operations, such as faster operation speed with higher accuracy. That allows us to apply more operations before the influence of the dissipative environment becomes significant. Chapter 5 is devoted to the theoretical description of the interaction of a transmon qubit with a semi-limited transmission line, the study of the reflection coefficient of such a system. For the first time, a theory to simulate the behavior of such a system, is developed. It is shown that the probability of excitation is proportional to the decrease in the reflection coefficient of such a system, and the similarities and differences between theoretical and experimental interferograms are demonstrated. It is proposed to introduce a nonlinear correction to the excitation amplitude for a better agreement between theory and experiment. One of the advantages of this system is the ability to manipulate the absorption of a two-level system, which provides a new way to manipulate quantum states. Chapter 6 is devoted to the study of similarities and differences between the qubit and classical systems of two coupled oscillators. With only two approximations, we can move from Newton's equation to the Schrödinger equation. The solution of the Schrödinger equation with classical analogs of the parameters is described. For the first time, the result of interferometry like quantum interferometry for a classical system under the action of a rectangular noise excitation signal is calculated. This analogy can be used to simulate interference phenomena on a classical system, which usually does not require extremely low temperatures to operate and can operate at room temperature, which makes them more accessible. Chapter 7 is devoted to the study of dynamics of the laterally compressed buckled membrane, which has two stable states for its use as one of the plates of a memcapacitor (a capacitor with a memory effect). It is shown for the first time that there are two types of membrane switching: symmetric and asymmetric, asymmetric jumping requires a lower threshold force, and that it is sufficient to consider only two eigenfunctions to calculate the minimum threshold force for membrane switching. The results of calculations for the threshold force required for switching are compared with other theoretical and numerical calculations.