The Entanglement Transfer Between Two Atoms And Two-mode Field

Quantum entanglement is a fundamental resource for the manipulation, storage and transfer of quantum information. Since atoms are usually used to store information and photons are utilized as a reliable information carrier to transfer and process information, storing entanglement into atoms and transferring entanglement between atoms and photons have been widely concerned.We investigate a system consisting two different atoms interacting with two cavity modes where one atom only interact with its own local cavity mode. The dynamical behaviors of the entanglements between two atoms and between two modes as well as the transfer between them are studied. It is found they are affected by the atom-field couplings, the dipole-dipole (dd) interaction between two atoms and the initial state of the system.First, the discussions are given when the interaction between each atom and the corresponding cavity mode is described by the linear Jaynes-Cummings model (JCM).When the two atom-field subsystems are separated, (i) if the two cavity modes are initially in vacuum, it is found that it is possible for the entanglement to be perfectly transferred between the atoms and the modes if the two atom-mode couplings are equal to each other, otherwise the efficiency of the entanglement transfer declines. The relation between negativity and concurrence is also discussed. It is shown that for the two-qubit quantum system, the ranges of the two criteria are the same as well as their abilities in measuring the existence of entanglement in the system. However, when the system is in a mixed state, they are not always equal to each other during the time evolution. (ii) If the two cavity modes are initially in squeezed vacuum, it is found that the entanglements of the atomic subsystem and the two-mode subsystem are well periodical only when the initial squeezing of the fields is small, meanwhile, the entanglement transfer between the two subsystems is approximately perfect. When r≈0.86, the efficiency of the transfer reaches the highest value as well as the maximum achievable entanglement between the atoms.When there exists dd interaction between the atoms and the two cavity modes are initially in vacuum, 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.Second, we discuss the situation when the interaction between the atom and its local cavity mode is an intensity-dependent one. We assume the cavity modes are driven by a two-mode squeezed vacuum field, it is shown that the entanglements of the two subsystems is exactly periodical and the periodicity doesn't depend on the initial state of the system; for any given squeezing parameter r, the period of the entanglement transfer between two subsystems isπ. In addition, the maximum achievable entanglement between the atoms is a monotonous increasing function of r, and if the initial squeezing is large enough, it is possible for the atoms to be entangled into a Bell state at the half period points.