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Physical Review A

Single-mode superfluorescence theory compared with experiment

Richard M. Friedberg, Brian J. Coffey

Published Apr 1, 1976• 8 citations
Publisher

Abstract

We compare the experimental curves of Skribanowitz et al., showing superradiance from pumped HF gas, with the "single-mode" time-evolution formula of Bonifacio and Lugiato. All parameters are varied freely except the length $L$ of the sample. It is found impossible to obtain even rough agreement. When ${\ensuremath{\tau}}_{c}$ is taken longer than $\frac{L}{c}$, no ringing is predicted; when shorter, the predicted ringing is many times faster than that observed.

DOI
10.1103/physreva.13.1645

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Physical Review Letters•Oct 8, 1979•4 citations
We compare the experimental curves of Skribanowitz et al., showing superradiance from pumped HF gas, with the "single-mode" time-evolution formula of Bonifacio and Lugiato. All parameters are varied freely except the length LLL of the sample. It is found impossible to obtain even rough agreement. When \ensuremathτc{\ensuremath{\tau}}_{c}\ensuremathτc​ is taken longer than Lc\frac{L}{c}cL​, no ringing is predicted; when shorter, the predicted ringing is many times faster than that observed.
We have found that room-temperature HF gas at millitorr pressures, optically pumped to produce a total inversion at a rotational transition in the v=1v=1v=1 vibrational state, emits a superradiant pulse with ringing after a considerable delay (\ensuremath{\sim} microseconds). A semiclassical analysis shows that for a high-gain system the pulse evolution is determined by a single parameter ${\ensuremath{\tau}}_{R}$, and that inhomogeneous broadening is unimportant. Close agreement between theory and experiment is obtained.
This paper shows how the Bonifacio-Lugiato mean-field model of atomic superfluorescence, which is particularly attractive because it deals with a crystalline array of emitters, can be extended to the nuclear case. However, limits exist on the validity of certain approximations used in the development of the model. In particular, a numerical instability that increases without bound is shown to exist in the non-Markovian case, placing in doubt the application of the semiclassical theory derived for the non-Markovian case.
Superfluorescence is treated in the Markovian master-equation approach. We show that we have to consider the complex coupling between any pair of atoms in order to reproduce superfluorescence signals with ringings as exhibited by experiments. We compare numerical results of our model with those obtained by a semiclassical approach of superfluorescence. The quantum treatment is found to be in agreement with the semiclassical approach only if the semiclassical tipping angle is taken equal to the square root of the number of radiating particles.
Single crystals of KCl containing $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ centers (8\ifmmode\times\else\texttimes\fi{}1016{10}^{16}1016-7\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 ${\mathrm{cm}}^{\ensuremath{-}3}$) were excited at low temperatures (T<30T<30T<30 K) using frequency-quadrupled single pulses of a mode-locked Nd-doped yttrium aluminum garnet laser. At excitation intensities above 20 GW/cm2{\mathrm{cm}}^{2}cm2 a spontaneous emission of coherent light was observed which could be identified as Dicke superfluorescence. This superfluorescence was observed on two of the zero-phonon lines in the vibrational progression of the $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ fluorescence spectrum (0-10 and 0-11 at 592.8 and 629.1 nm, respectively). We have studied the time dependence, the statistics of the delay times, and the intensities. The observed delay times vary between 0.5 and 10 ns, the observed pulse widths between 0.5 and 6 ns, and the coherence time was found to be longer than 100 ps. The observed linewidths of the superfluorescence ($0.016\mathrm{nm}\ensuremath{\cong}14\mathrm{GHz}$) is a factor of 2.5 smaller than that of the spontaneous fluorescence (0.042 nm at 4.2 K). The superfluorescence is observed only below a critical temperature which depends on the $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ concentration (8 to 28 K for concentrations between 8\ifmmode\times\else\texttimes\fi{}1016{10}^{16}1016 and 7\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 ${\mathrm{cm}}^{\ensuremath{-}3}$).