The generation of an entangled state for a pair fof two-level atoms embedded in a bad cavity injected with a squeezed vacuum is investigated. The degree of entanglement between the two atoms strongly depends on the mean photon number and the strength of two-photon correlations of the squeezedvacuum, the cavity-induced decay rate of atoms, and the atomic separation.

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.

We have studied the time evolutiort of the phase operators of the radiation field in the system contain-ing a V-type three-level atom interaeting with the bimodal field by means of the phase formalism given by Pegg and Borneo [J. Me.d. Opt. 36, 7 (1998); Phys: Rev. A 39, 1665 (1989)]. That the atomic coherent trapping will happen in an appropriate initial state of the system has also been verified.

The dynamical behavior of entanglement ofr excitons in two quatum dots placed in two separately singlemode optical cavities driven by an external boradband two-mode squeezed vacuum is studied in the low exciton density regime. It is found that if the field in the two separated cavitied is initially prepared in a pure two-mode squeezed vacuum state, the excitons in the two quantum dots cna evolve into a pure entangled state only when the dissipation of the cavitied and excition modes is negligible. When the efect of the dissipation is included, the excitions will be in a two-mode Gaussian entangled mixed state whose properties are decided by the externally driven fiedld and the initial field. The dependence of the entanglement property of the excitons in the two quantum dots on the squeezing properties of the fields in the two cavities is also discussed.

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.