The Emission Spectrum Of Trapped Atom And The Evolution Of Quantum Entanglement

Trapped atoms(ions) have wide applications in the fields of quantum computation and communication.Much attention has been paid on the system of the trapped atom(ion) interacting with the radiation field. Quantum entanglement is a fundmental resource for the manipulation, storage and transfer of quantum information. So generation of entanglement state, measurement and transfer of entanglement have attracted a lot of attention in quantum optics and quantum information science.We investigate the emission spectrum and the dynamical behaviors of a harmonically trapped two-level atom in an ideal cavity. We also studied the evolution of the entanglements between two atoms and between two modes in a system consisting two different atoms interacting with two cavity modes where one atom only interact with one cavity mode.First, We have investigated the emission spectrum and the dynamical behaviors of a harmonically trapped two-level atom driven by a single mode runing-wave field, the effective Hamiltonian of the system is given with different detuning parameter. The generalized expression of the emission spectrum and the state vector of the system are deduced. We have shown that the harmonically trapped two-level atomic emission spectrum and the dynamical behaviors of the system are closely dependent on the initial state of the system, the detuning parameter and Lamb-Dicke parameter. In given conditions, the GHZ states of the atomic internal degree of freedom, the vibrational mode and the light field could be created, the Bell-type states of the atomic internal degree of freedom and the light field (the vibrational mode) could be generated.Second, the emission spectrum of a harmonically trapped two-level atom driven by a one mode standing-wave field with small Lamb-Dicke parameter is investigated, we discuss the effects of the atomic c.m. motion on the emission spectrum. We show that the atomic c.m motion don't affect the atomic spectrum phase sensitivity when there is no correlation between atomic c.m. motion and the field. With the increase of the average energy for atomic c.m. motion, the peaks of the emission spectrum move towards each other, their heights change according to the state of the field and atomic motion. While there is correlation between atomic c.m. motion and the field, the atomic spectrum becomes insensitive to the relative phase between the field and the atomic dipole. In some certain conditions, there are fewer peaks that become higher and narrow.By means of negativity and concurrence, we investigate the time evolution of the entanglement of the two atoms and the entanglement between the two modes in the system of two atoms interacting with two-mode fields. We find the two entanglements can swap with each other, and even they have a very good coincidence relation under certain condition. Comparing negativity and concurrence, we show that they can keep identical with each other on the standard of the existence of entanglement, but on the standard of the degree of entanglement they may not always keep pace with each other.In the end, we studied the effects of the dipole-dipole(dd) interaction between atoms on transferring entanglement between atoms and cavity modes. We find that for the weak dd interaction, the entanglement between the atoms can be induced by it and the entanglement transfer between the atoms and the modes is almost not influenced by it. For the strong dd interaction, although it can still produce the atomic entanglement and maintain the initial atomic entanglement, it is difficult to transfer the entanglement from the atoms to the modes.