We study quantum dynamic phenomena in mesoscopic systems, which include superconducting circuits, low-dimensional semiconductor-based structures, nanomechanical resonators. We make use and develop the toolbox of modern condensed matter theory in order to sharpen our understanding of quantum phenomena, which are nowadays available for probing and controlling. Not only we study theoretically fundamental phenomena, such as Rabi oscillations and Landau-Zener-Stuckelberg-Majorana transitions, but we tightly relate our research to the experimental works. Recent results are outlined below, while complete list of the publications can be found in the Publications as well as at Scholar.
Qubit-Based Memcapacitors and Meminductors
There is growing interest in electronic circuit elements that have memory; namely, memristive, memcapacitive, and meminductive circuit elements, generalizing the well-known resistors, capacitors, and inductors. We proposed and studied quantum realizations of memory circuit elements based on solid-state qubits. The quantum properties of qubit-based systems make their response unique, thus introducing a new functionality to the toolbox of memory devices.
A transmission-line resonator at low temperatures behaves as quantum oscillator; its impact on coupled qubit can be described by the procedure known as dressing the qubit’s states. We developed the theory for the case of doubly-driven resonator and described the series of effects observed by the experimentalists from IPHT, Jena. It was demonstrated that such qubit-resonator system can be used for amplification or attenuation of weak signals.
Quantum Inductance and Capacitance
If a quantum system is included in a circuitry, it should be described in terms of the probabilities of energy level occupations. The system is then characterized by respective parametric inductances, capacitances, and resistances. Due to their dependencies on probabilities, they are also attributed the adjective “quantum”. We exploited such theory for the description of artificial few-level systems.
It was known since long ago that not only non-adiabatic LZSM transitions appear between discrete energy levels, but also the phase acquired during evolution matters. This phase, known as Stuckelberg phase, may result in constructive or destructive interference. We have generalized the theory to describe recently observed interference fringes in different microscopic and mesoscopic systems. This subject remains the hot topic, of which one evidence is that our review article has recently passed the milestone of 300 citations.
Delayed-Response Quantum Back Action
The semiclassical theory was developed for the description of the system composed of a classical resonator coupled to a quantum subsystem. Particularly, we considered the impact of the relaxation in the latter on oscillations in the former. This resulted in significantly increasing or decreasing the resonator quality factor. We believe that our theoretical approach is useful for the description of the experiments, such as this one: .
When multiple driving frequency matches the energy gap in the quantum system, this can be excited by means of the multi-photon transitions. We studied such excitations for different layouts, including single- and double-qubit systems with direct and ladder-type transitions. Even though the realistic systems are quite sophisticated – beside a quantum subsystem they include driving and controlling electronics – we succeeded in quantitative description of different driven dissipative qubit-based systems. This research resulted in the review article, the monograph, and several original papers.