Quantum Properties Of The Atom-field System In Strong Coupling Regime

The strong interaction between a qubit and a quantum harmonic oscillator is now realized experimentally in different kinds of systems such as Josephson charge qubit, semiconducting dots and circuit QED, etc.. The dynamics of such strong coupling systems can be modeled by the Rabi model. However, the qubit is coupled to the oscillator so strongly that the well-known rotating wave approximation(RWA) is broken, and the counter-rotating wave terms must be considered. In such strong coupling regime, the qubit-oscillator interacting strength is com-parable to the oscillator frequency or the natural transition frequency of the qubit。Theoretical and experimental investigations have found novel phenomena, such as the asymmetry of vac-uum Rabi-splitting, photon blockade, nonclassical states generation, superradiance transition, and collapse and revival dynamics. Only when the effects of counter-rotating wave terms in the Rabi model are considered, these new phenomena can be satisfactorily explained in the strong coupling regime. Therefore, the researches of the effect of counter-rotating wave terms in the Rabi model have become one of the most hot points of quantum information, quantum optics and condensed matter physics.Based on these, some quantum actions of Rabi model in strong coupling regime are inves-tigated in this dissertation. The main contents are as follows:Firstly, the dynamic of the quantum trace distance for the states of the qubit strongly in-teracting with a bosonic field is studied. In order to gain physical insight into the effect of the counter-rotating wave terms on the dynamic of the qubit, two specific initial states which are the eigenstates of the qubit and field coupling system with the resonant interaction under the standard RWA are chosen. The reduced density matrices of the qubit in these two initial states are the same. Starting from these two initial states, we find that the time-evolution of the trace distance for the qubit states is only related to the difference between the populations in the qubit excited state but independent of the coherence of the qubit. If the RWA is applied under the resonant interaction, the dynamic of the trace distance for the qubit states remains zero. But the effect of the counter-rotating wave terms brings the deviation of the qubit states starting from the two initial states, which are exhibited by the time-dependence trace distance. The stronger the coupling between the qubit and the field is, the more obvious the deviation is.Secondly, we present a simple and straightforward analytical method to investigate the physical emission spectrum of the Rabi model without the RWA. we generalize the definition of the physical emission spectrum valid with the RWA in order to meet without the RWA with some modifications due to the physical consideration in the strong coupling regime. The multi-peak Rabi splitting, even the qubit initially in its ground state and the bosonic field initially in vacuum, are obviously observed in the strong coupling regime. These new features of physical emission spectrum originate from the effect of counter-rotating wave terms. Moreover, the intercrossing of energy level can also be observed in the strong coupling regime.Finally, we present a simple and straightforward analytical method based on two unitary transformations to investigate the Berry phase of the Rabi model without the RWA. To compare the validity of our analysis explicitly, we have given the high-accuracy numerical results of the Berry phase. It is found that our results agree well with the high-accuracy numerical results near the resonance situations. The Berry phase of ground state is relevant to the second-order terms of the coupling strength, and the Berry phases of the first excited and second excited state are mainly relevant to the first-, second-, and third-order terms of the coupling strength when the effect of the CRTs is taken into account.