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Communications in Theoretical Physics

Entanglement Properties Between Two Spatially Separated Atoms with Cascade Configuration in Free Space

Yang Guo-Hui, Junfeng Zhang, Miao Xiang-Yang, Zhou Ling

Published Mar 1, 2010• 0 citations
Publisher

Abstract

We investigate the entanglement properties between two identical atoms with cascade configuration through the retarded dipole-dipole interaction in free space when their spatial separation is on the order of radiation wavelength or less. We analyze the function of Hamiltonian induced by dipole-dipole interaction. By solving master equation, we show that the spontaneous emission induce entanglement and destroy entanglement too. We also show the long life time of entanglement within cascade configuration.

DOI
10.1088/0253-6102/53/3/29

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We investigate the entanglement properties between two identical atoms with cascade configuration through the retarded dipole-dipole interaction in free space when their spatial separation is on the order of radiation wavelength or less. We analyze the function of Hamiltonian induced by dipole-dipole interaction. By solving master equation, we show that the spontaneous emission induce entanglement and destroy entanglement too. We also show the long life time of entanglement within cascade configuration.
We report on the generation of entanglement between two spatially separated identical atoms in free space. We show that the evolution of the entanglement occurs due to the radiative coupling between the two atoms via the retarded dipole-dipole interaction. The magnitude of the entanglement is found to be strongly dependent on the initial states and the distance between the two atoms. We also study the different effects on the entanglement of the dipole-dipole collective parameters in the master equation. By introducing incoherent pumping, a steady entanglement can be acquired, and the condition for generating steady entanglement is also obtained.
We report possibility of generating entanglement between two atoms in free space when their spatial separation is on the order of wavelength or less. We show that these two atoms get coupled by photon exchange due to spontaneous decay, which in turn generates the atomic entanglement. By introducing the incoherent pumping, one can obtain the steady entanglement, and the incoherent pumping can overcome the decay of the atoms. Moreover, one can obtain the larger value of steady entanglement via proper tuning the incoherent pumping.
The time evolution of short linear chains consisting of dipole coupled two-level systems (atoms) is investigated under the influence of oscillator modes, which represent the environment. The dynamics of the system is calculated using the super-radiant master equation. The focus is on phenomena related to the environment induced decoherence and entanglement degradation. For large atomic distances the initially present pair entanglement is destroyed independently from the spatial position of the two atoms, while when the distance between the atoms becomes comparable to the resonant wavelength the rate of entanglement degradation corresponds to the strength of the pair interaction. Below one resonant wavelength of atomic separation, formation of pair entanglement is also possible in the initial stage of the time evolution. In this case it is found that pair entanglement is formed and destroyed periodically, and the strengths of the consecutive ‘entanglement revivals’ are damped depending on the initial state. The subradiant states, for which decoherence is slow, also preserve pair entanglements for an exceptionally long time.
The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.
Abstract. We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small inter-atomic separations, in contrast to the small sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
This paper studies quantum entanglement between two spatially separated atoms driven by a coherent laser field in the dissipative process of spontaneous emission. It is shown that the entanglement strongly depends on the detuning of the laser frequency from atomic transition frequency, the interatomic separation and the Rabi frequency of the coherent laser field. A considerable amount of steady state entanglement can be obtained near Δ = —α (i.e., the dipole-dipole interaction and the detuning cancel out mutually) for small atomic separation and large Rabi frequency of the coherent laser field.