The effects of the N atom collective Lamb shift on single photon superradiance

The problem of single photon collective spontaneous emission, a.k.a. superradiance, from N atoms prepared by a single photon pulse of wave vector k(0) has been the subject of recent interest. It has been shown that a single photon absorbed uniformly by the N atoms will be followed by spontaneous emission in the same direction [M. Scully, E. Fry, C.H.R. Ooi, K. Wodkiewicz, Phys. Rev. Lett. 96 (2006) 010501; M. Scully, Laser Phys. 17 (2007) 635]; and in extensions of this work we have found a new kind of cavity QED in which the atomic cloud acts as a cavity containing the photon [A.A. Svidzinsky, J.T. Chang, M.O. Scully, Phys. Rev. Lett. 100 (2008) 160504]. In most of our studies, we have neglected virtual photon ("Lamb shift") contributions. However, in a recent interesting paper, Friedberg and Mannassah [R. Friedberg, J.T Manassah, Phys. Lett. A 372 (2008) 2514] study the effect of virtual photons investigating ways in which such effects can modify the time dependence and angular distributions of collective single photon emission. In the present Letter, we show that such virtual transitions play no essential role in our problem. The conclusions of [M. Scully, E. Fry, C.H.R. Ooi, K. Wodkiewicz, Phys. Rev. Lett. 96 (2006) 010501; M. Scully, Laser Phys. 17 (2007) 635; A.A. Svidzinsky, J.T. Chang, M.O. Scully, Phys. Rev. Lett. 100 (2008) 160504] stand as published. However, the N atom lamb shift is an interesting problem in its own right and we here extend previous work both analytically and numerically. (C) 2009 Elsevier B.V. All rights reserved.