Dissertations, Theses, and Capstone Projects

Date of Degree

6-2020

Document Type

Dissertation

Degree Name

Ph.D.

Program

Physics

Advisor

Roman Ya. Kezerashvili

Advisor

Oleg L. Berman

Committee Members

Godfrey Gumbs

Mark Hillery

Anatoly Kuklov

Muir Kumph

Vladimir I. Tsifrinovich

Subject Categories

Atomic, Molecular and Optical Physics | Quantum Physics

Keywords

quantum vacuum phenomena, lamb shift, superconducting circuits

Abstract

According to quantum field theory, the vacuum is filled with virtual particles which can be turned into real ones under the influence of external perturbations. Phenomena of this kind are commonly referred to as quantum vacuum phenomena. Several quantum vacuum phenomena related to the peculiar nature of the quantum vacuum have been predicted, some of which, such as the Lamb shift and the Casimir effect, have been experimentally found. Other examples of quantum vacuum phenomena include the Unruh effect, the dynamical Casimir effect and the dynamical Lamb effect. The dynamical Lamb effect was first predicted by considering the situation of an atom passing through a cavity at relativistic speed. In this case, the excitation of the atom and the generation of photons is thought to arise because of the sudden change of Lamb shift of the atom. If multiple atoms concurrently experience the dynamical Lamb effect, they can become entangled. A theoretical framework to investigate the time-evolution of a system of N qubits, modeling atoms, coupled to a harmonic oscillator, modeling a cavity, with time-dependent coupling is developed. For the case of a closed system, three different analytical approaches are presented. First, a perturbative approach in the time-domain. This is the standard approach in the solution of Schrödinger equation. Second, a perturbative approach in the Laplace-domain. This can simplify the solution of Schrödinger equation with time-dependent Hamiltonians. However, both approaches require the interaction part of the Hamiltonian to be small compared to the unperturbed Hamiltonian. Third, the framework of Floquet theory is introduced. This can be used in the case of periodic Hamiltonians regardless of the interaction strength. For the case of an open system, the dynamics is investigated by numerically solving the Lindblad master equation. These approaches are then applied to the study of the time-evolution of the quantum entanglement between two and three qubits coupled to a harmonic oscillator. It is demonstrated that different measures of entanglement show a different level of detail of the latter and that time-dependent Greenberger-Horne-Zeilinger states can be created even in the presence of dissipation.The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched “on” and “off”nonadiabatically. We show that by using a superconducting circuit which allows one to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible to observe the dynamical Lamb effect. The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops. Superconducting circuits of this kind are routinely used as quantum information processors. These devices take advantage of quantum properties for mathematical computations, improving their computational capabilities compared to regular computers. We have implemented Shor’s factoring algorithm, in a simplified form, on one such device made available through the cloud by IBM. We study the results of the algorithm on the ibmqx5 superconducting chip, for the particular case of factoring N= 15, 21, and 35. Positive results are obtained for factoring15 and 21, although the device fails to compute the factors of 35 due to the errors introduced by the presence of noise.

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