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

Abstract

In a recent Letter, Kira et al. [1] propose a fully quantum mechanical theory for the secondary emission (SE) of a quantum well (QW), assuming that the QW is free of disorder, and that SE originates from the interaction between excitons in the system. The authors ask if "disorder is necessary to explain coherent signatures in the SE." They claim that their "microscopic theory reproduces many of the experimentally observed effects, showing that the SE exhibits intrinsic coherent characteristics . . . ." 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. (ii) A fully linear relation between emission intensity and excitation density over 3 orders of magnitude. (iii) The temporal profile depends only on statistical properties of the disordered potential.On the other hand, the new theoretical formalism by Kira et al. combining semiconductor Bloch equations and field quantization is of largest importance for the dynamics of temporally incoherent resonant QW luminescence [3,9].The term "temporal coherence" of SE has received very lately a clear definition that is experimentally verifiable. 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. The calculations by Kira et al. [1] use explicitly the fact that only in the specular directions is ͗E q ͘ fi 0. 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. 1 in [1]).Nonlinearity is also explicit in their two pulse calculations in which "the two pulse excitation for F 0 leads to an enhancement of the emission intensity by more than an order of magnitude" in comparison to the single-pulse excitation. Experiments on SE excited by two pulses show that the enhancement factor is never larger than 4 [4,10], as predicted by linear theories [11].Finally, the physical origin of the "pulse replica" f...