Abstract:
The entropy correlation and the entanglement of a moving atom interacting with k-photon Jaynes-Cummings model are investigated. Entropy exchange between atomic and field subsystems, which is a form of anti-correlated behavior, is explored. Analytical results show that atomic motion, transition number k of field and field-mode structure can influence the entropy exchange between atom and light field. Moreover, the relationship between entropy correlations and entanglement is also discussed.

Abstract:
Considering a moving two-level atom interacting with a single-mode thermal field through multi-photon process, in this paper we study the entropy exchange between the atom and the field by using quantum partial entropy and entanglement measured by using Concurrence, and investigate the effects of the initial atomic state, the atomic motion, the mean photon number and the transition photon number on entropy and entanglement. The results show that the entropy exchange and the entanglement exhibit the periodic evolution due to atomic motion, and entropy exchange occurs. The entanglement between the atom and the field is strengthened as the transition photon number increases. When the partial entropy exchange between atom and field is zero, the entanglement is also zero.

Abstract:
A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulas describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon correlations and nonzero collective decay. It is shown that nonidentical atoms are a better source of stationary entanglement than identical atoms. We discuss the optimal physical conditions for creating entanglement in the system, in particular, it is shown that there is an optimal and rather small value of the mean photon number required for creating entanglement.

Abstract:
We report the observation of entanglement between a single trapped atom and a single photon at a wavelength suitable for low-loss communication over large distances, thereby achieving a crucial step towards long range quantum networks. To verify the entanglement we introduce a single atom state analysis. This technique is used for full state tomography of the atom-photon qubit-pair. The detection efficiency and the entanglement fidelity are high enough to allow in a next step the generation of entangled atoms at large distances, ready for a final loophole-free Bell experiment.

Abstract:
We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second order coherence degree, von Neumann entropy, spin squeezing for multi-particle entanglement, as well as genuine two and three-mode entanglement parameters for steady state and non-equilibrium situations. Coherent transfer of population between the radiation modes and quantum state mapping between the two-level atom and the optical modes are discussed. A potential experimental realization of the theoretical results in a superconducting coplanar waveguide resonator containing diamond crystals with Nitrogen-Vacancy color centers and a superconducting artificial two-level atom is discussed.

Abstract:
We report the observation of entanglement between a single trapped atom and a single photon at remote locations. The degree of coherence of the entangled atom-photon pair is verified via appropriate local correlation measurements, after communicating the photon via an optical fiber link of 300 m length. In addition we measured the temporal evolution of the atomic density matrix after projecting the atom via a state measurement of the photon onto several well defined spin states. We find that the state of the single atom dephases on a timescale of 150 $\mu$s, which represents an important step toward long-distance quantum networking with individual neutral atoms.

Abstract:
With the quantum interference between two transition pathways, we demonstrate a novel scheme to coherently control the momentum entanglement between a single atom and a single photon. The unavoidable disentanglement is also studied from the first principle, which indicates that the stably entangled atom--photon system with superhigh degree of entanglement may be realized with this scheme under certain conditions.

Abstract:
We have investigated the evolution of the atomic quantum entropy and the entanglement of atom--photon in the system with competing k-photon and l-photon transitions by means of fully quantum theory, and examined the effects of competing photon numbers (k and l), the relative coupling strength between the atom and the two-mode field (\lambda/g), and the initial photon number of the field on the atomic quantum entropy and the entanglement of atom--photon. The results show that the multiphoton competing transitions or the large relative coupling strength can lead to the strong entanglement between atoms and photons. The maximal atom--photon entanglement can be prepared via the appropriate selection of system parameters and interaction time.

Abstract:
Stationary photon-atom entanglement is discussed by applying the method of flow equation to the Jaynes-Cummings model. A nonlocal continuous unitary transformation is explicitly constructed and the associated positive operator-valued measures for the photons and atom are obtained. Then, flow of the entanglement entropy is analyzed. A comment is also made on implementing the unitary operation in the method of flow equation. This method may offer a new strategy for quantum-state engineering.

Abstract:
With quantum interference of two-path spontaneous emissions, we propose a novel scheme to coherently control the atom--photon momentum entanglement through atomic internal coherence. A novel phenomenon called ``momentum phase entanglement'' is reported, and we found, under certain conditions, that more controllable entangled state can be produced with super--high degree of entanglement.