The time-dependent characteristic function for the vibratlonal quanta of two ions separately trapped in two caacaded optical eavities is obtained analytieally beyond the bad cavity linit, in which tfie motional mode of the ion in the first cavfiy is coupled to lhe cavity, field via an effective parametrc interacion and that of the ion in the second cavity" via a liaear-mixing interaction as proposed by Peng and Parkias Pfiys. Rev. A 65, 062323 (2002l]. It is fond, that the two ions develop in a two-mode mixed Gaussian entangle state if there exists a unidirecfional coupling from the first cavitv to the seecond one.

We investigate the spontaneous-emission properties of a two-level atom embedded in a three-dimensinal anaisotropic photonic crystal. In addition to the modified density of states, the atom is driven by a coherent intense lowfrequency field (LFF), which creates additional multihoton decay channels with the exchange of two low-frequency photons and one spontaneous photon during an atomic transition, Due to the ow frequency of the appliced field, the various transition pathways may interfere with each other and thus give rise to a modifeed system dynamics. We find that even if all the atomic(bare and induced) transition frequencies are in the conducting band of the photonic crystal, there still mya exist a photon-atom bound state in coexistence with propagating modes. the system also allows us to generate narrow linesin the spontaneous-emission spectrum. This spectrum is a funcion of the distance of the observer form the atom due to the band gap in the photonic crystal. The system properties depend on three characteristic frequencies, which are influenced by quantum interfernce effects. Thus these results can b attributed to a combination of interference and band-gap effects.

The interactions between a two-level atom and a coherent field with a time-varying frequency have been investigated. The two typical cases-the frequency of the field varying with time in the forms of sine and rectangle-have been considered. It is found that the collapse-revival phenomenta of the atomic population inveersion are defomed as th frequencychangfing with tiem in sine form and the rectangular frequency modulation can lead to some new collapses and new revivals in the evolution of the atomic population inversion.

By means of adiabatically eliminationg the upper level or levels of a A-configuration atom coupling to a two-mode quantized field, we have studied the influencesofac Stark shifts on the atomic coherent population trapping in two important atom-field coupling systems via nondegenerated Raman two-photon processes.The states of the field that trap the atom in its two nondegenerate lower levels are obtained, and the important roles of ac Stark shifts and properties of the atomic upper level or levels in the states of the trapping field in two Raman-coupling systems are also analyzed.

In this paper, we have investigated the influence of the cvunler-rotating terms on the squeezing of light in the two photon layaes-Cummings mcodel by means of the nonrelativistic QED. We verified that the effect af the virtual-photon field increases the squeezing. The relations between the degree of squeezing and the frequency of field, the mean photon number, and the atom-field coupling constant have alsp been analyzed.