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Physical review. B, Condensed matter

Statistical properties of speckle distributions in resonant secondary emission

Erich Runge, R. Zimmermann

Published Feb 15, 2000• 10 citations
Publisher

Abstract

Quantitative analysis of speckle distributions, i.e., intensity fluctuations, in resonant secondary emission is a powerful tool to study quantum coherence in a wide range of optically excited systems. Finite directional or temporal resolution and any instability in the setup will necessarily reduce the fluctuations which would be misinterpreted as loss of coherence. We discuss the consequences of this averaging and show how the amount of averaging can be extracted from histograms of the speckle intensity and how it can be corrected for. Using functional integration methods, analytic expressions for the intensity distribution in experiments with finite directional or temporal resolution are derived. These should help to make the quantitative speckle analysis a widely used technique for measuring quantum coherence optically.

DOI
10.1103/physrevb.61.4786

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Quantitative analysis of speckle distributions, i.e., intensity fluctuations, in resonant secondary emission is a powerful tool to study quantum coherence in a wide range of optically excited systems. Finite directional or temporal resolution and any instability in the setup will necessarily reduce the fluctuations which would be misinterpreted as loss of coherence. We discuss the consequences of this averaging and show how the amount of averaging can be extracted from histograms of the speckle intensity and how it can be corrected for. Using functional integration methods, analytic expressions for the intensity distribution in experiments with finite directional or temporal resolution are derived. These should help to make the quantitative speckle analysis a widely used technique for measuring quantum coherence optically.
A new method to measure the coherence of inhomogeneously broadened optical excitations in semiconductor nanostructures is presented. The secondary emission of excitons in semiconductor quantum wells is investigated. The spectrally-resolved coherence degree of resonantly-excited light emission is deduced from the intensity fluctuations over the emission directions (speckles). The spectral correlations of the speckles give direct access to the homogeneous line width as function of spectral position within the inhomogeneously broadened ensemble. The combination of static disorder and phonon scattering leads to a partially coherent emission. The temperature dependence of the homogeneous line width is well explained by phonon scattering.
A linear optical method to measure coherence and dephasing of excitations in solids is presented. The spectrally resolved degree of coherence of resonantly scattered light is deduced from the intensity fluctuations over its emission directions (speckles). The spectral intensity correlation gives a direct measure of the dephasing rate within the inhomogeneously broadened ensemble. For localized excitons in semiconductor quantum wells, the combination of static disorder, phonon scattering, and radiative decay leads to a spectral dependence of the emission coherence and the dephasing rate, which is well described by model calculations.
The technique of the speckle analysis of resonant secondary emission is reviewed. It is a novel, linear optical technique to measure the microscopic intensity and polarization dynamics in inhomogeneously broadened ensembles, that represents an alternative for established non-linear optical techniques such as photon-echo or spectral hole burning. Both time-resolved and spectrally resolved variants of the speckle analysis are discussed. Experimental results obtained on semiconductor quantum wells using both techniques are presented.
A new method to measure the time-dependent coherence of both homogeneously and inhomogeneously broadened optical excitations in solids is presented. The coherence degree of resonantly excited light emission is deduced from the intensity fluctuations over the emission directions (speckles). This method determines the decays of intensity and coherence separately, thus distinguishing lifetime from pure dephasing. The secondary emission of excitons in semiconductor quantum wells is investigated. Here the combination of static disorder and inelastic scattering leads to a partially coherent emission. The temperature dependence is well explained by phonon scattering.
Summary form only given. The question of the coherence properties of the radiation from two-dimensional electron-hole-pair states in systems of reduced dimensionality has recently gained new interest both in theory and experiment. In these experiments the light emission from a short-pulse excited semiconductor QW in a direction different from the excitation or reflection directions (secondary emission, SE) was studied either by spectral interferometry or speckle analysis. As origin of the SE either disorder or Coulomb interaction is under discussion. We report in our contribution a careful study of both the specular and non-specular resonant-emission from GaAs quantum well exciton states applying interferometric controlled spectral interferometry with an accuracy of about 50 attosetonds.
We have performed spectral interferometry with Rayleigh scattered light coming from a single speckle and emitted after resonant creation of excitons in GaAs quantum wells. The experiment confirms the coherence of the secondary emission at early times, regardless of sample parameters, but underlines the stochastic nature of a single speckle. The scattered electric field is calculated, correctly accounting for the center-of-mass quantization in the disordered potential. We find that the amplitudes of the electric fields emitted by different excitons are uncorrelated, so that the well-known Poisson distribution for speckle intensities applies.