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Laser Physics

The metastable states in the cooperative emission from a system of two-level atoms in a sphere

Jamal T. Manassah

Published Apr 27, 2010• 11 citations
Publisher

Abstract

The values of the radii of the sphere enclosing an ensemble of two-level atoms corresponding to metastable states in the cooperative emission are computed. The dynamics of these states and, in particular, the delay in the maximum of the emission intensity are given for the different orders of the critical radii. 1 The article is published in the original.

DOI
10.1134/s1054660x10110150

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The values of the radii of the sphere enclosing an ensemble of two-level atoms corresponding to metastable states in the cooperative emission are computed. The dynamics of these states and, in particular, the delay in the maximum of the emission intensity are given for the different orders of the critical radii. 1 The article is published in the original.
The choice of the wrong kernel for describing the cooperative effects in an ensemble of identical atoms, in most instances, leads to wrong predictions for the system's dynamics whether the system initially was excited weakly or nearly was inverted. In this Brief Report, using previously derived theoretical expressions, I compare the numerical values for the emission amplitude as a function of time for the complex exponential and the sine kernels for different-size spheres. The deviations found in the respective results show that, in general, the two kernels are not, as often claimed, up to a frequency shift in their spectra, interchangeable.
An analysis is made of the deexcitation kinetics of strongly excited extended systems of initially uncorrelated two-level radiators. The possibility of partially cooperative states of the system is predicted when the radiation intensity acquires values intermediate between the spontaneous decay intensity and the Dicke superradiance intensity. The conditions for the onset of cooperative processes are obtained. The threshold for the oscillatory emission conditions is determined and the oscillation frequency is found. Modulation of the emission intensity is predicted with different modulation frequencies before and after the superradiant pulse. The modulation frequencies are determined. Formulas are derived for the superradiant pulse delay times and intensities. The possibility of weakly anisotropic cooperative emission is predicted.
In Dicke superradiance, N identical two-level atoms in a small volume share one collective excitation ladder, and the ensemble discharges in a delayed burst whose peak grows in accordance with N2 rather than N. Real emitters, however, usually have more than two levels. When such an ensemble radiates cooperatively, its multiple decay channels interact rather than simply add up. This mini-review covers recent work that solves this interaction exactly for three-level atoms. We first recall the two-level benchmark: its exact delay statistics, their Gumbel-distributed fluctuation, and the resulting 21.7% deficit of the ensemble-averaged peak below the semi-classical estimate. The master-equation framework developed by Agarwal and Cho, Kurnit and Gilmore, on which the three-level results rest, comes next. The main part surveys three published papers, one for each of the three dipole-allowed three-level configurations. In the cascade, two emission pulses are correlated through an inherited timing. In the shared-source configuration, two channels compete for one atomic reservoir; for equal rates, as shown by Holzinger et al., this competition produces an exactly uniform terminal distribution, as in a Pólya urn. In the shared-sink configuration, two dynamically independent groups of atoms merge exactly into a single collective burst of the combined ensemble. We call this superradiant synthesis.
The collective spontaneous emission of NNN multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The counter-rotating terms are included using a unitary transformation method. We analyze the decay dynamics starting from two initial conditions, the standard Dicke and timed Dicke states. In addition to the dependence on ensemble volume and density, we also study the effect of the ensemble geometry on cooperative emission for spheres, cubes, and quasi-two-dimensional shapes in different orientations. Finally, time-dependent cooperative spontaneous emission rates are introduced and investigated.
Dynamics of spontaneous decay and corresponding emission spectrum areexactly treated for a system of two identical two-level atoms in 1D.Just a one-dimensional case is considered in order to maximally extractan information on mutual influence of spatially remote atoms through theradiation field. As a result, an effect is revealed and considered indetail that there exist stable (metastable) entangled states at definitedistances between the atoms. That state is supported by a(quasi)stationary field bounded between the atoms. Also, acorrespondence is established between the lifetime and emissionspectrum, and possibilities for observing the effect are discussed.