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arXiv:quant-ph/0308126 · Physics Letters A

Entanglement and nonlocality versus spontaneous emission in two-atom systems

Lech Jakóbczyk, Anna Jamróz

Published Oct 11, 2003• 43 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2003.09.044

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The behavior of the system of radiators at short and long time intervals in comparison with the retardation between them is studied. The entanglement behavior of atomic states in the process of spontaneous emission is determined. The theory that describes the spontaneous emission of two hydrogen-like atoms within a short time period in comparison with the inverse value of photon emission frequency is proposed. It is demonstrated that at a short time interval the rate of spontaneous emission in an oscillatory manner tends to the exponential law of spontaneous emission. The simple kinetic equation, which describes this stage of system evolution, is obtained.
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 formulae 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 r 12 and interact with each other via the dipole–dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic 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.
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.