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Journal of Electronic Materials

Effect of Electron–Electron Interaction on Nonlinear Near-Resonance Electromagnetic Response of Quantum Dot Systems

V. P. Bondarenko, Miroslaw Zaluzny, Yang Zhao

Published Sep 19, 2007• 2 citations
Publisher
DOI
10.1007/s11664-007-0217-2

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In this paper, by applying generalized density-matrix equations, we explore the ultrafast dynamics of photo-generated electron–hole pairs in the system composed of electromagnetically coupled GaAs/AlGaAs quantum dots and reveal the physics mechanism behind laser-controlled nonlinear-optical response of electron–hole pairs. For the single-dot system, we present numerical results to show the transient dependence of carrier occupations and induced quantum coherence of electron–hole pairs in the presence of either a single or double laser pulses, as well as for a step turning-on of the laser field. For a dipole-radiation coupled double-dot system, we study numerically the time dependence of both intradot and interdot self-consistent depolarization fields within and between two dots, respectively. Meanwhile, we further demonstrate the significance of phase matching between induced depolarization fields and incident-laser pulse in order to maximize the stimulated transitions of electron–hole pairs and ensure non-quenched Rabi oscillations in each quantum dot. The employed theoretical model and the associated numerical analysis method are expected to facilitate designing and developing artificial quantum molecules composed of arbitrarily dielectric-embedded quantum dots with non-local quantum interactions and entanglement, as well as optically manipulating electron states of artificial quantum molecules.
The effects of local fields, due to electron–hole dipole–dipole interactions, on the excitonic population dynamics of a quantum dot system are studied. The system interacts resonantly with a continuous wave electromagnetic field. We present analytical solutions of the nonlinear optical Bloch equations for any initial condition. We also thoroughly investigate the dynamics of population inversion of the system and show that effects such as extended Rabi oscillations, self-trapping in the initial state and symmetry-breaking can occur.
I recent years, significant attention has been given to nonlinear optical phenomena, such as nonlinear optical absorption and dispersion, derived from a driven quantum transition of semiconductor nanostructures, such as semiconductor quantum wells, quantum disks and mainly quantum dots. An important issue that is widely studied is the effect of probe electromagnetic field intensity on the total (nonlinear) absorption coefficient and on the total (nonlinear) index of refraction. Some of the phenomena that are commonly found for large electromagnetic field intensities are the creation of a strong dip in the absorption spectrum near or at resonance (the so-called bleaching effect), negative absorption near or at resonance that leads to optical gain and the change of the slope of the total index of refraction near or at resonance from negative to positive that changes the behavior of the system from fast to slow light. Unfortunately, these phenomena do not exist and are artifacts of a common abuse of the theoretical methodology for the study of the total absorption coefficient and the total index of refraction. The main error is that the total absorption coefficient and the total index of refraction was initially derived from density matrix equations using perturbation theory and includes first-order (linear) as well as third-order (nonlinear) terms. This method gives correct results for small electromagnetic field intensities and it leads to saturation of absorption and dispersion in this regime. However, for larger intensities it gives the misleading results mentioned above due to either failure of the order of perturbation theory considered in the derivation of the total absorption coefficient and the total index of refraction or even failure of perturbation theory at all in the treatment of the problem. In this work, we revisit the problem of the total absorption coefficient and the total index of refraction in a symmetric semiconductor quantum dot structure (we choose the example of a core-shell quantum dot) under a strong probe field excitation. We use the two-level model, solve the relevant density matrix equations under the rotating wave approximation and under steady state conditions, and obtain the correct form of the nonlinear optical susceptibility that is then used for the derivation of the formulae of the total absorption coefficient and the total index of refraction under the interaction with a strong probe field. Actually, the commonly used perturbation theory formulae can be obtained by our formulae using a series expansion and keeping terms up to second order in electric field amplitude. We also derive the electronic structure of the quantum dot system by solving numerically the time-independent Schrodinger equation, under the effective mass approximation, using the potential morphing method and obtain the energy difference and the electric dipole matrix element for the relevant transitions of the quantum dot system. Then, for the specific quantum dot system we compare the results of the total absorption coefficient and the total index of refraction for the two methodologies (the perturbation result and our result) for different electromagnetic field intensities.