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.

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.

Spontaneous emission of an atom with two close upper levels arid one lower level in a multilayer dielectric medium, and quantum interference between transitions form the upper leves to the lower one, are considered. Since the medium is inhomogeneous along the direction normal to tbe interfaces of the dielectric layers, the vancuum had an anisotropic spatial structure, and quantum interference between the two decay channels can appear even if the two dipole matrix elemeats are ortbogonal to each other. If the atom is pLaced in a three-layer dielectric plate cavity, a strong quantum interference interference similar to that for an atom with two nearly parallel dipole moments in free space arises due to the influence of anisotropic of anisotropic vacuum. Putting the atom in a three-layer dielectric waveguide and a one-dimensional photonic crystal, there appears a strong quantum interference similar to that for an atom with nearly antiparallel dipole moments.

The decay and radiation of an atom in a photonic crystal with an incomplete gap was investigated. If the transtition frequency is close to a band edge, the Weisskopf-Wigner approximation is not applicable and the decay is nonexponential. The decay could be greatly enhanced or decreased by the self-emitted field.

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.