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arXiv:cond-mat/0109224 · Physical Review Letters

Statistics of Dynamics of Localized Waves

A. A. Chabanov, Azriel Z. Genack

Published Nov 16, 2001• 44 citations
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Abstract

The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity. The distribution of the delay time weighted by the intensity is found to be a double-sided stretched exponential to the 1/3 power centered at zero. The correlation between dwell time and intensity provides a dynamical test of photon localization.

DOI
10.1103/physrevlett.87.233903

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The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity. The distribution of the delay time weighted by the intensity is found to be a double-sided stretched exponential to the 1/3 power centered at zero. The correlation between dwell time and intensity provides a dynamical test of photon localization.
We discuss the delay-time statistics of superfluorescent pulses by introducing the concept of a passage time at which the field intensity reaches a specified value. Such passage times can be estimated accurately from the early-stage linear dynamics of the radiating system. The distribution function for the passage times, we show, can be expressed as a functional integral over the random zero point fluctuations of the atomic polarization. The functional integral can be evaluated exactly and reduced to an elementary closed form. Our theory applies both to the sharp and the broadened atomic line. The results we obtain agree with experimental data and numerical calculations already in existence for the unbroadened line. For the broadened line we predict substantial changes of the mean value and the variance of the passage time as the width of the atomic line increases. We also investigate the influence of the shape of the spectral distribution of atomic frequencies and show that the delay statistics depend significantly on the way in which the spectral density decreases in the wings of the atomic line.
The probability distribution p(n)p(n)p(n) for the detection of nnn photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density p(I)\mathcal{p}(I)p(I) and the moments of the light intensity III, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. p(I)\mathcal{p}(I)p(I) is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.
Statistical properties of the output fluctuations of a photon detector measuring the intensity of radiation at a given frequency emitted by a dispersive blackbody are investigated using Langevin's technique. The variance-to-mean ratio of the accumulated counts, and the power spectral density of the count rate are obtained in terms of properties of the emitting medium. The possibility and limitations of obtaining information about the emitter by measuring these quantities are discussed. It is found in particular that the temperature of the emitting medium can be determined in principle by observing the intensity fluctuations of the radiation at a single frequency. The photon fluctuations in a microwave cavity are also discussed in the framework of the present formalism and compared to previous work.