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Laser Physics

The Eikonal-SVEAS analytic closed forms for single-photon superradiance

Richard M. Friedberg, Jamal T. Manassah

Published Dec 7, 2009• 15 citations
Publisher

Abstract

Using the Slowly Varying Envelope Approximation in Space and the Eikonal Approximation, we obtain closed-form analytic expressions for the single-photon superradiance from a spherical cloud of two-level atoms in the scalar photon theory. The value 0.171, calculated in this approximation for the value of the maximum probability of secondary excited states, agrees with those obtained from the eigenmode analysis method and from the Debye-refined method.

DOI
10.1134/s1054660x10010056

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Using the Slowly Varying Envelope Approximation in Space and the Eikonal Approximation, we obtain closed-form analytic expressions for the single-photon superradiance from a spherical cloud of two-level atoms in the scalar photon theory. The value 0.171, calculated in this approximation for the value of the maximum probability of secondary excited states, agrees with those obtained from the eigenmode analysis method and from the Debye-refined method.
Using the eigenmode analysis of the scalar photon theory, I compute the probability of the atoms remaining excited and the probability for the atoms remaining in the initial quantum state of a system of two-level atoms cloud in a sphere initially prepared to radiate in the forward direction, i.e., the single photon superradiance problem. The convergence in the results obtained for increasingly larger radii for the sphere suggests that the asymptotic limits for these quantities are obtained for a sphere with a radius equal to six times the resonant wavelength. I predict the maximal value of the probability of secondary excited states from large spheres at 17.1%.
We calculate the field eigenmodes of the superradiant emission from an ensemble of NNN two-level atoms and confirm the results of other authors that Dicke superradiant emission is restricted to a small number of modes, with more than 90% of the photons emitted in a single dominant mode. While numerical techniques are effective due to the symmetry of the problem, we develop also an analytical method to approximate the modes in the limit of a large number of emitters.
Using the eigenmodes of the scalar-photon kernel of interacting NNN two-level atoms in a cylindrical configuration, I obtain the time dependence of the superradiant emission for this geometry in two cases of interest. In particular, I consider first the case when one or two eigenmodes dominate the system's dynamics for an inverted system which has been initially prepared in an isotropic state and show that for certain values of the radius of the cylinder ($r=m\ensuremath{\lambda},m \mathrm{integer}$) one obtains temporal modulation in the state function. In the second case of interest, I show that the angular distribution of the state function of a system initially prepared in a phased state appears to be chaotic; however, I show that this behavior is due to the high multiplicity of modes having close values for their amplification coefficients.
Abstract Single photon emission from a collection of resonantly excited two-level atoms is an expanding field. Recent work has shown single photon superradiance from an extended ensemble yields enhanced directional spontaneous emission. This paper presents an operator which commutes with the observables and breaks their degeneracy for the single photon states. Its eigenvectors are a unimodular basis for the single photon states. A simple scheme is given for writing out these states directly without iterative construction and without requiring recourse to Gram–Schmidt orthogonalization. A relatively simple scheme is proposed for experimental realization. In the final part of the paper the mathematical method is extended to generate cooperative states with smaller cooperativity number R .