Retardation in two-atom systems

John Konrady

L. V. Chebotarev

Qurrat-ul-Ain Gulfam, Z. Ficek, Jörg Evers

The role of retardation in the entanglement dynamics of two distant atoms interacting with a multimode field of a ring cavity is discussed. The retardation is associated with a finite time required for light to travel between the atoms located at a finite distance and between the atoms and the cavity boundaries. We explore features in the concurrence indicative of retardation and show how these features evolve depending on the initial state of the system, distance between the atoms, and the number of modes to which the atoms are coupled. In particular, we consider the short-time and the long-time dynamics for both the multi- and subwavelength distances between the atoms. It is found that the retardation effects can qualitatively modify the entanglement dynamics of the atoms not only at multi- but also at subwavelength distances. We follow the temporal evolution of the concurrence and find that at short times of the evolution the retardation induces periodic sudden changes of entanglement. To analyze where the entanglement lies in the space spanned by the state vectors of the system, we introduce the collective Dicke states of the atomic system that explicitly account for the sudden changes as a periodic excitation of the atomic system to the maximally entangled symmetric state. At long times, the retardation gives rise to periodic beats in the concurrence that resemble the phenomenon of collapses and revivals in the Jaynes-Cummings model. In addition, we identify parameter values and initial conditions at which the atoms remain separable or are entangled without retardation during the entire evolution time, but exhibit the phenomena of sudden birth and sudden death of entanglement when the retardation is included.

G. A. Gallup

Ming-Keh Chen, Kwong T. Chung

The retardation long-range potentials between two 1${\mathrm{}}^{1}$S (or 2${\mathrm{}}^{3}$S) helium atoms are calculated. The complex dynamic multipole polarizabilities of 1${\mathrm{}}^{1}$S and 2${\mathrm{}}^{3}$S states of helium are obtained through a variation-perturbation approach with B-spline and Slater-type basis functions in a configuration-interaction scheme. They are used to calculate the retardation long-range potentials. The retardation coefficients are examined. Their relative magnitudes are different for different systems. The possibility of an excited state of helium dimer from the 1${\mathrm{}}^{1}$S--2${\mathrm{}}^{3}$S ${\mathrm{He}}_{2}$ state is estimated. \textcopyright{} 1996 The American Physical Society.

Ho Trung Dung, Kikuo Ujihara

The spontaneous emission of a pair of two identical and fixed two-level atoms, sharing initially a single excitation, is considered. It is shown that the solution which involves all the retardation times obtained by Milonni and Knight [Phys. Rev. A 10, 1096 (1974)] is also valid for interatomic distances less than half of a transition wavelength. The effects of the interatomic distance on the time evolution of the atomic state populations are examined.