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Physical Review Letters

Coherent Ringing in Superfluorescence

Daniel J. Heinzen, J. E. Thomas, Michael S. Feld

Published Feb 18, 1985• 44 citations
Publisher

Abstract

Superfluorescence emitted from small regions of the output face of an initially inverted medium is found to exhibit ringing; this confirms that coherent ringing is an intrinsic property of superfluorescence. The system studied is a pure two-level Rb transition at $\ensuremath{\lambda}=2.73$ \ensuremath{\mu}m, prepared in a cell by means of cw single-mode radiation. The Fresnel number of the sample is 1.7.

DOI
10.1103/physrevlett.54.677

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Superfluorescence emitted from small regions of the output face of an initially inverted medium is found to exhibit ringing; this confirms that coherent ringing is an intrinsic property of superfluorescence. The system studied is a pure two-level Rb transition at \ensuremathλ=2.73\ensuremath{\lambda}=2.73\ensuremathλ=2.73 \ensuremath{\mu}m, prepared in a cell by means of cw single-mode radiation. The Fresnel number of the sample is 1.7.
A generalized master equation previously proposed to describe oscillatory superfluorescence is numerically solved in the case of strong ringing. When the atomic system is fully excited, anomalous fluctuations and large atom-field correlations make the time evolution of the mean quantities (e.g., number of photons, total population inversion) quantitatively different from those found in the semiclassical treatment. In particular, because of fluctuations, the minima of the radiation output are notably larger than zero. On the contrary, when the atomic system exhibits a sizable initial macroscopic polarization (superradiance), we find a remarkable non-Markoffian effect consisting of a sizable delay in the radiation emission. However, in such conditions all quantum effects disappear, as in the case of pure superradiance.
We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ensuremath{\ge} 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.
A dense sample of atomic Rb vapor excited by a 4 ps laser pulse two-photon resonant with the $5S\ensuremath{-}5D$ transition in a large Fresnel number geometry emits a delayed coherent omnidirectional ir pulse on the $5D\ensuremath{-}6P$ transition. This superfluorescence emission involves a coherent population transfer to the 6P6P6P level and results in simultaneous directional uv emission and coherent population transfer back to the ground 5S5S5S state. This uv emission is a manifestation of parametric time-delayed four-wave mixing. For a composite noncollinear, $|{\stackrel{\ensuremath{\rightarrow}}{k}}_{1}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}|{\stackrel{\ensuremath{\rightarrow}}{k}}_{2}|$, excitation, the uv radiation pattern is conical and the cone angle depends on the angle between the excitation pulses.
Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.