چكيده لاتين
In this thesis, through the theoretical study of the quantum Rabi model, we will discuss non-classical effects in various regimes of the fundamental atom-radiation field interaction. These regimes involve the interaction between a two-level atom and a single mode of the radiation field within a cavity whose dimensions are much smaller than the wavelength of the radiation field. The primary motivation for this study is rooted in the competition between the atom-field coupling strength and other characteristic frequencies of the system such as the dissipation rate of the system and the bare frequency of its subsystems, which result in distinct interaction regimes and influence the quantum behavior of the system. When the coupling strength is smaller than the dissipation rates of the subsystems, like the spontaneous emission of the two-level atom and the rate of photon escape from the cavity, the interaction system experiences damping prior to the effective exchange of energy between the atom and the radiation field. This signifies the weak coupling regime. In the strong coupling regime, the atom’s interaction with the radiation field dominates over the dissipative processes, leading to the creation of mixed excitation quanta involving both atomic and photon modes known as polariton quasi-particles. However, this interaction still operates within the perturbation theory framework due to the smallness of the coupling constant in comparison to the subsystems’ bare frequencies. Through increasing the atom-field coupling strength, we introduce the concepts of ultrastrong and deep strong coupling regimes, which are separated from each other by a criterion different from the weak and strong coupling regimes, so that if the coupling constant is significantly fraction of one of the bare frequencies of the subsystems, the system is in the ultrastrong coupling regime, while deep strong coupling regime indicates a situation where the strength of coupling is greater than the bare frequencies. Initially, by examining the mathematical structure of the quantum Rabi Hamiltonian, we demonstrate that in the ultrastrong and deep strong regimes, the validity of the rotating wave approximation breaks down. This breakdown results in counter rotating terms, interpreted as virtual photon transitions. These transitions, along with the presence of virtual excitations with dual atomic-photon nature in the ground state, induce quantum correlations and strong entanglement between atomic and photonic modes. This, in turn, leads to nonlinearities in the form of anharmonicity in the energy level structure. This anharmonicity is the most conspicuous effect in the ultrastrong coupling regime, so that the quantum excitation of the interaction system appears as distinguishable quasi-particles, polaritons. Due to the inherent limitations on increasing the atom-field coupling strength, it’s not feasible to achieve the ultrastrong and deep strong coupling regimes in the optical frequency range in cavity quantum electrodynamics setups. Thus, we focus on the physical modeling of circuit quantum electrodynamics settings within the quantum Rabi model framework. We illustrate that microwave photons trapped in superconducting transmission lines can coherently interact with artificial atoms or superconducting quantum bits located inside resonators. The low loss and remarkable flexibility in engineering superconducting qubit and resonator’s features contribute to making these setups crucial platforms for realizing ultrastrong and deep strong coupling regimes. Another aspect we address is the time evolution in different atom-field
