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arXiv:0811.2647 · Physical Review A

Photon exchange and correlation transfer in atom-atom entanglement dynamics

Juan León, Carlos Sabín

Published Jan 6, 2009• 29 citations
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Abstract

We analyze the entanglement dynamics of a system composed by a pair of neutral two-level atoms that are initially entangled, and the electromagnetic field, initially in the vacuum state, within the formalism of perturbative quantum field theory up to the second order. We show that entanglement sudden death and revival can occur while the atoms remain spacelike separated and therefore cannot be related with photon exchange between the atoms. We interpret these phenomena as the consequence of a transfer of atom-atom entanglement to atom-field entanglement and vice versa. We also consider the different bipartitions of the system, finding similar relationships between their entanglement evolutions.

DOI
10.1103/physreva.79.012301

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We analyze the entanglement dynamics of a system composed by a pair of neutral two-level atoms that are initially entangled, and the electromagnetic field, initially in the vacuum state, within the formalism of perturbative quantum field theory up to the second order. We show that entanglement sudden death and revival can occur while the atoms remain spacelike separated and therefore cannot be related with photon exchange between the atoms. We interpret these phenomena as the consequence of a transfer of atom-atom entanglement to atom-field entanglement and vice versa. We also consider the different bipartitions of the system, finding similar relationships between their entanglement evolutions.
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states. We study two different coupling schemes motivated by the forms that can arise due to atomic separation. We observe a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our quantitative analysis shows that these cases with different couplings and initial states differ significantly in these qualitative features. The multifarious behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.
We analyze entanglement generation between a pair of neutral two level atoms that are initially excited in a common electromagnetic vacuum. The nonlocal correlations that appear due to the interaction with the field can become entanglement when the field state is known. We distinguish two different situations: in the first, the field remains in the vacuum state, and second two photons are present in the final state. In both cases we study the dependence of the entanglement with time and interatomic distance, at ranges related with locality issues.
Investigates the property of entanglement between a pair of two-level atoms placed in two apart squeezed reservoirs correlated by two-mode squeezed light.Studies the relation of the property to the qubits initial state.The result shows that the sudden death and revival of entanglement of the qubits always occurs between the apart squeezed reservoirs with the time evolution.Never-theless,each the entanglements of various initial state eventually maintains at a same stationry level,has no relationship with the initial state of atom.
An investigation is reported of the collective effects and the dynamics of atom–atom entanglement in a system of two distant two-level atoms which are coupled via an optical element. In the system under consideration, the two atoms, which are trapped in the foci of a lens, are coupled to a common environment being in the vacuum state and they emit photons spontaneously. A fraction of the emitted photons from each atom is thus focused on the position of the other atom. The presence of optical element between two distant atoms leads to the occurrence of delayed collective effects, such as delayed dipole–dipole interaction and delayed collective spontaneous emission, which play the crucial role in the dynamical behaviour of the entanglement. We discuss the phenomena of entanglement sudden birth, entanglement sudden death, and revival of entanglement for both cases of initial one-photon and initial two-photon unentangled atomic states. We show that the evolution of the entanglement is sensitive not only to the interatomic distance but also to the initial state of the system as well as to the properties of the optical element.
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states and interatomic separations. We study two specific atomic separations which give rise to symmetric atom-field couplings. For general atomic distances we consider a subset of initial states analytically, and then treat the more general situation numerically. We examine a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our analysis shows a stark contrast in features of entanglement between the two special coupling schemes often considered; further, these features are uncharacteristic of those arising for general distances, due to the high degree of symmetry present in the special cases. The variety of behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.
By using the negativity method,we study the entanglement dynamics of two entangled atoms,which are in two levels,that go through the high Q fields in the Fock state one by one.The results shows that the initial state of the two-atom and the field in the Fock state are influenced by the entanglement dynamics of two atoms,and we also make the significant comparison of the two-atom entanglement evolutions in the condition that the two atoms are laid in the QED at the same time.We find that: when the cavity field is in the vacuum state,the two-atom entanglements under these two models evolve periodicity;when we choose the cavity field in a Fock state,the entanglement between the two atoms can appear tobe the phenomenon of entanglement sudden death.Furthermore,we investigate the entanglement transfer problem and the relationship among entanglement sudden death,the initial state,and the number of the Fock state.