Femtosecond Spectral Interferometry of Resonant Secondary Emission from Quantum Wells: Resonance Rayleigh Scattering in the Nonergodic Regime

Abstract

We report the first investigation of resonant secondary emission from quantum well excitons using ultrafast spectral interferometry. Observation of high-contrast spectral fringes demonstrates a significant phase correlation of the spectral components of the Rayleigh scattered light and allows us to determine the temporal dynamics of the coherent emission. The results contradict the present theories for resonant Rayleigh scattering based on ensemble averaging, and show the nonergodic nature of resonance Rayleigh scattering from semiconductor quantum wells. [S0031-9007(98)07109-9] PACS numbers: 78.35. + c, 78.47. + p, 78.66. -w The nature of scattered light has been a topic of interest for almost a century. Rayleigh scattering has been a wellestablished concept since the pioneering work of Lord Rayleigh on the scattering of sunlight by atmospheric index fluctuations on a subwavelength scale [1]. A central issue in the theoretical treatment of scattered light has been the problem of how to describe scattering from a large number of scatterers. One usually resorts to statistical methods, where ensemble averaging is often the only way to get meaningful experimental predictions [2]. Interference between fields from different scatterers is ignored in the ensemble averaging process and only the incoherent sum of intensities from each scatterer is considered. All effects of spatial coherence-the ability of the ensemble of scatterers to form speckles-are thus lost [3]. Theories based on ensemble averaging postulate therefore a zero expectation value for the scattered field amplitude in order to calculate a well-defined expectation value for the scattered intensity. The motivation for using ensemble averages lies in the "ergodic hypothesis," which states that a time average for a single realization of the ensemble is identical to an ensemble average. Whether the ergodic theorem can be used depends on the specific experimental situation. In particular, the typical fluctuations of the field must be faster than the time resolution of the actual experiment [4,5].The properties of secondary emission (i.e., emission in nonspecular directions) from quantum well excitons following ultrafast resonant excitation have recently been the focus of an intense scientific debate [6][7][8][9]. It is now commonly accepted that the emission is composed of exciton luminescence and resonance Rayleigh scattering (RRS). The origin of the RRS is the spatially fluctuating exciton resonance frequency causing the inhomogeneous broadening of the absorption line [10]. The experimental distinction between luminescence and RRS is difficult due to their spectral similarities. However, it was inferred that the rise of the secondary emission is dominated by RRS at low exciton densities by comparing experimental data with a theoretical model based on ensemble averaging [7,9].Whether models based on ensemble averages can provide meaningful experimental predictions for the femtosecond dynamics of RRS is not clear. An understanding of the dynamics of RRS is o...

Comment on “Quantum Theory of Secondary Emission in Optically Excited Semiconductor Quantum Wells”

“…For the scattered directions only the correlation functions ͗b y q z ,q k h 2k e k1q k ͘ are nonzero. The calculated SE is therefore mainly incoherent as it does not carry a phase that could produce strong enough interferences, which would be quantitatively in agreement with the experiments [5,8].…”

“…For the scattered directions only the correlation functions ͗b y q z ,q k h 2k e k1q k ͘ are nonzero. The calculated SE is therefore mainly incoherent as it does not carry a phase that could produce strong enough interferences, which would be quantitatively in agreement with the experiments [5,8].Another important property of the coherent SE is the linear dependence on the excitation density, which has been explicitly reported [5,6,10]. The early SE calculated by Kira et al shows a nonlinear dependence of the peak intensity and density-dependent rise time (see Fig.…”

“…." In this Comment we show that the SE calculated by Kira et al is incoherent and nonlinear, and therefore inadequate for SE experiments performed under low-excitation conditions [2][3][4][5][6][7][8]. Such experiments are in agreement with an explanation in terms of disorder-induced resonant Rayleigh scattering (RRS) and have indeed given clear evidence for the following: (i) The temporal coherence of the SE at early times.…”

“…Another important property of the coherent SE is the linear dependence on the excitation density, which has been explicitly reported [5,6,10]. The early SE calculated by Kira et al shows a nonlinear dependence of the peak intensity and density-dependent rise time (see Fig.…”

“…The coherent part of SE produces interferences with a replica of the exciting laser pulse [5,8] and present speckles [7]; because the quantum average of the electric field operator in the SE direction is nonzero, ͗E q ͘ ϵ ͗b q 1 b y q ͘ fi 0. Experiments show that this average electric field makes up 25% [5] or up to 50% [8] of the total intensity of the SE. Fluctuations of the electric field operator are much too weak to explain these experimental findings.…”