Entangling two atoms via spontaneous emission

Abstract

We discuss the creation of entanglement between two two-level atoms in the\ndissipative process of spontaneous emission. It is shown that spontaneous\nemission can lead to a transient entanglement between the atoms even if the\natoms were prepared initially in an unentangled state. The amount of\nentanglement created in the system is quantified by using two different\nmeasures: concurrence and negativity. We find analytical formulas for the\nevolution of concurrence and negativity in the system. We also find the\nanalytical relation between the two measures of entanglement. The system\nconsists of two two-level atoms which are separated by an arbitrary distance\n$r_{12}$ and interact with each other via the dipole-dipole interaction, and\nthe antisymmetric state of the system is included throughout, even for small\ninter-atomic separations, in contrast to the small sample model. It is shown\nthat for sufficiently large values of the dipole-dipole interaction initially\nthe entanglement exhibits oscillatory behaviour with considerable entanglement\nin the peaks. For longer times the amount of entanglement is directly related\nto the population of the slowly decaying antisymmetric state.\n