We study the spatial decoherence dynamics for the relative position of two atoms interacting with a single-mode cavity which are assumed initially in three different states.It is assumed that the atomic relative position is in the state of a superposition of two Gaussian wave packets and that the cavity field is initially in thermal state,Fock state and squeezed state respectively.Based on the reduced density matrix for the atomic relative position,we study the influence of the atom-field interaction on the quantum coherence of atomic relative position.We find that for different initial states of the cavity field,the quantum decoherence dynamics of the atomic relative position is different.When the cavity field is initially in a thermal state or Fock state,the spatial coherence oscillates with decay and revival periodically,while when the cavity field is initially in a squeezed state,the spatial coherence of the two-atom relative position is partially destroyed,and the decay degree is connected with the value of the atomic relative position in a cosine law.
A spatially varying field mode is included in calculating the squeezing effect for a system of two-level atoms in the good-cavity limit. Two examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are used to demonstrate the quite general method. In qualitative terms, the squeezing predicted for plane waves is preserved. However, for a given value of atomic cooperativity parameter C, there is a degradation in squeezing because of the spatially varying field structure.
We present a way to engineer an effective anti-Jaynes-Cumming and a Jaynes-Cumming interaction between an atomic system and a single cavity mode and show how to employ it in reservoir engineering processes. To construct the effective Hamiltonian, we analyze the interaction of an atomic system in a $\ensuremath{\Lambda}$ configuration, driven by classical fields, with a single cavity mode. With this interaction, we first show how to generate a decoherence-free displaced squeezed state for the cavity field. In our scheme, an atomic beam works as a reservoir for the radiation field trapped inside the cavity, as employed recently by S. Pielawa et al. [Phys. Rev. Lett. 98, 240401 (2007)] to generate an Einstein-Podolsky-Rosen entangled radiation state in high-
Q resonators. In our scheme, all the atoms have to be prepared in the ground state and, as in the cited article, neither atomic detection nor precise interaction times between the atoms and the cavity mode are required. From this same interaction, we can also generate an ideal squeezed reservoir for atomic systems. For this purpose we have to assume, in addition to the engineered atom-field interaction, a strong decay of the cavity field (i.e., the cavity decay must be much stronger than the effective atom-field coupling). With this scheme, some interesting effects in the dynamics of an atom in a squeezed reservoir could be tested.