Temporal and diffraction effects in entanglement creation in an optical cavity

A practical scheme for entanglement creation between distant atoms located inside a single-mode optical cavity is discussed. We show that the degree of entanglement and the time it takes for the entanglement to reach its optimum value is a sensitive function of the initial conditions and the position of the atoms inside the cavity mode. It is found that the entangled properties of the two atoms can readily be extracted from dynamics of a simple two-level system. Effectively, we engineer two coupled qubits whose dynamics are analogous to that of a driven single two-level system. It is found that spatial variations of the coupling constants actually help to create transient entanglement which may appear on the time scale much longer than that predicted for the case of equal coupling constants. When the atoms are initially prepared in an entangled state, they may remain entangled for all times. We also find that the entanglement exhibits an interesting phenomenon of diffraction when the atoms are located between the nodes and antinodes of the cavity mode. The diffraction pattern of the entanglement varies with time and we explain this effect in terms of the quantum property of complementarity, which is manifested as a tradeoff between the knowledge of energy of the exchanged photon versus the evolution time of the system.