The Study On The Dynamics Of The Atom-cavity System In Strong Coupling Regime

The strong coupling of atoms and cavity is very attractive, as photons emitted by atoms inside the cavity can be reabsorbed and reemitted, etc. leading to Rabi oscillations. In the strong coupling regime, the eigenstates of the atom-cavity system are composed of dressed states with double lad-der shape. Because of the dressed states, on the one hand, excitation of the atom-cavity system by a first photon blocks the transmission of a sec-ond photon, thereby converting an incident poissonian stream of photons into a subpoissonian, anti-bunched stream. On the other hand, when the atoms and cavity are tuned, the spectrum of the first pair of dressed states splits into two new resonances, named normal-mode or vacuum-Rabi splitting. It has been observed in many atom experiments. In fact, obser-vation of the normal-mode splitting is a benchmark signature that a system has reached the strong-coupling regime of cavity QED. Furthermore, for coupled atom-cavity arrays, the quantum phase transition occurs, which relies on the strong coupling of atoms and cavities, accompanying with the transferring of the excitations from polaritonic to photonic.In the present work, we first analyze the effects of the dipolc-dipole interaction on the spectrum of the atom-cavity system. By a unitary trans-formation, the two dipole-coupled atoms can be transformed into an effec-tive atom, and then we can get the dressed states of the systems. In low excitation limit, the atomic saturation is neglected, and the spectrum shows two resonances. We find the effects of the dipole-dipole interaction resembles that of the positive detuning, which influence the position and height of the two resonances. For higher excitation, the atom-cavity detun-ing can reduce the atomic saturation, making the original closed structure separate. While the effects of the dipole-dipole interaction on the atomic saturation is not obvious, and with the increase of it the spectrum only deforms a little. However, the strong dipole-dipole interaction can result in the decoupling of the atoms and cavity, which leads to the spectrum showing a singlet.For two coupled cavities, the exact numerical solutions can be easily found and can reflect the basic characteristics of the coupled atom-cavity arrays essentially. So we study the dipole-dipole interaction on the quan-tum phase transition of two coupled atom-cavity systems. We first analyze the nature of the ground state for some particular values of atom-cavity detunings and dipole-dipole interaction strengthes. Then by choosing three different order parameters, we study the phase diagram for a wide range of dipole-dipole interacting intensity and atom-cavity detuning. We find that the ground state of the system represents richer behaviors than the Bose-Hubbard model. The phase space is divided into four regions. They are the atomic insulator state, the polaritonic insulator state, the polari-tonic superfluid state, and the photonic superfluid state. In the scope of parameter values we have taken in this paper, the insulator or superfluid phases is determined by the sum value of atom-cavity detuning and dipole-dipole interaction. For small negative values of it, the ground state shows polaritonic insulator states; while for small positive values of it. the ground state shows polaritonic superfluid state. The larger the negative value of it,the more obvious the atomic insulator nature appears, and oppositely it shows photonie superfluid nature.A summary about our present work and a outlook about our future work are shown in the end of the paper.