Physics Letters A 372 (2008) 5732–5733 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla Comment Comment on: “Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory” [Phys. Lett. A 372 (2008) 2514] Anatoly Svidzinsky ∗ , Jun-Tao Chang Institute for Quantum Studies and Department of Physics, Texas A&M University, College Station, TX 77843, USA article info abstract Article history: Received 9 May 2008 Received in revised form 2 June 2008 Accepted 23 June 2008 Available online 11 July 2008 Communicated by P.R. Holland In a recent Letter [R. Friedberg, J.T. Manassah, Phys. Lett. A 372 (2008) 2514] Friedberg and Manassah argue that effect of virtual photons has serious consequences for large atomic samples. Here we show that such effect is negligible for evolution of a uniformly excited atomic state prepared by absorption of a single photon.  2008 Elsevier B.V. All rights reserved. The many-body problem of single photon superradiant emission by an extended uniformly excited cloud of N atoms, see Eq. (1), is the subject of current interest and debate [1–5]. The atomic decay is typically treated by Weisskopf–Wigner theory. In particular, the Lamb shift (virtual field quanta) contribution is neglected in the case of radiation emitted by a large (atomic cloud radius R is much larger then the radiation wavelength λ) sample. In a recent pa- per Friedberg and Manassah [6] challenge this analysis. They say: “effect of virtual field quanta has serious consequences for large samples” [6]. Hence, they claim that, e.g., the results of Ref. [1] which studies the evolution of state (1) for R ≫ λ omitting virtual quanta are incorrect. In a previous publication we considered correlated spontaneous emission of N atoms properly taking into account the effect of virtual photons [7]. We found that for R ≫ λ the virtual quanta practically do not change the evolution of the state (1) and, hence, the results obtained in Ref. [1] are valid. In Fig. 1 we plot the ra- diation pattern for a large sample ( R = 5.125λ) and show that we get the same answer with and without including virtual photons. This clearly supports the validity of previous calculations. In the next few paragraphs we further elaborate on the issue and show analytically that the time evolution of the uniformly excited state |+〉 = 1 √ N N  j=1 exp(i k 0 · r j )|b 1 ... a j ... b N 〉 (1) for R ≫ λ is accurately described omitting virtual photons. DOI of original article: 10.1016/j.physleta.2007.11.064. * Corresponding author. E-mail address: asvid@jewel.tamu.edu (A. Svidzinsky). Fig. 1. Radiation pattern at frequency ω for R/λ = 5.125 produced by decay of the state (1) calculated taking into account virtual photons (solid line) and omitting them (dots). In plot we use logarithmic scale. For a system of N two level (a and b) atoms located at r j , ini- tially one of the atoms is in the excited state a and E a − E b = ℏω, the state vector can be written as Ψ = N  j=1 β j (t )|b 1 ... a j ... b N 〉|0〉+  k γ k (t )|b 1 ... b N 〉|1 k 〉. (2) States in the first sum correspond to zero number of photons, while in the second sum the photon occupation number is equal to one and all atoms are in the ground state b. Eigenstates and eigenvalues of the system determine evolution of an arbitrary ini- tial state. If atoms are distributed continuously inside a sphere of radius R ≫ λ some eigenvalues and the corresponding eigenfunc- tions are given by (k 0 R ≫ n) λ n ≈ 3N 2(k 0 R ) 2 , (3) β nm (r) ≈  j n (k 0 r ) − i k 0 r cos  k 0 r − nπ 2  Y nm (ˆ r ), (4) where k 0 = ω/c, j n (z) are the spherical Bessel functions, Y nm are spherical harmonics and ˆ r is a unit vector in the direction of r. De- cay rate of an eigenstate n is Γ n = Re(λ n )γ , where γ is the single 0375-9601/$ – see front matter  2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2008.06.089