Quantum Fluctuations and Transverse Effects in Superfluorescence
Superfluorescence (SF) emission profiles are computed using one-way coupled Maxwell-Bloch equations. Transverse effects are included in the full three-spatial-dimension case as well as in the cylindrical-symmetry case. Initiating quantum fluctuations[3–5] are approximated by a random polarization source with a completely random phase and root-mean-square tipping angle of 2/ N, where N is the number of atoms in each volume element. These fluctuations reduce the tail of the output obtained with transverse effects alone. In fact, the fluctuations in output pulse shapes encompass the Cs data of Gibbs, Vrehen and Hikspoors; see Fig. 1. The standard deviation for the delay time is found to be (12.5±4)% for Fresnel number of 0.8 compared with the value (10±2)% recently measured by Vrehen and der Weduwe, also for Cs. The Fresnel-number dependence of the standard deviation is shown in Fig. 2; Drummond and Eberly have more extensive results for Fresnel numbers from 1 to 16. Excluded from Fig. 2 were phase-wave fluctuations in which the second peak exceeded the first. Figure 3 shows that the transverse profiles retain little of the on-axis ringing found without fluctuations. Ringing can also be removed by inhomogeneous broadening, but the 32-ns T2* of the Cs experiment has little effect; T2* < 1 ns is needed to eliminate plane-wave ringing.
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- 1.Reviews of SF: M.S. Feld and J.C. MacGillivray, in Coherent Nonlinear Optics, ed. by M. S. Feld and V. S. Letokhov (Springer, Berlin, 1980); M. F. H. Schuurmans, Q. H. F. Vrehen, D. Polder, and H. M. Gibbs, in Advances in Atomic and Molecular Physics, ed. by D. R. Bates and B. Bederson ( Academic, New York, 1981 ) p. 168.Google Scholar
- 3.R. Glauber and F. Haake, Phys. Lett. 68A, 29 (1978).Google Scholar
- 6.For more details see present authors, Phys. Rev. A, to be published (March 1983); F. P. Mattar, ARO Workshop on Coupled Nonlinear Oscillators, Los Alamos National Laboratory, Los Alamos, New Mexico and Los Alamos Nonlinear Optics Conference Proc., ( SPIE, April 1981 ).Google Scholar
- 10.F. A. Hopf, Phys. Rev. A 20, 2064 (1979).Google Scholar