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Optics and Spectroscopy

Model of a quantum dot coherently interacting with an ultrashort pulse of electromagnetic radiation

Andrei I. Maimistov, S. O. Elyutin

Published Aug 1, 2002• 2 citations
Publisher

Abstract

Based on a model of strong coupling for two electrons that are localized inside a quantum dot characterized by only two levels of size quantization, a set of equations is derived, which allows one to describe coherent transient processes in an ensemble of isolated dots. This set of equations is a generalization of the Bloch equations, which are used in studying the processes occurring under the action of ultrashort pulses of electromagnetic interaction. The model obtained is reduced to the model of two-level atoms only if radiation is circularly polarized.

DOI
10.1134/1.1503756

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Based on a model of strong coupling for two electrons that are localized inside a quantum dot characterized by only two levels of size quantization, a set of equations is derived, which allows one to describe coherent transient processes in an ensemble of isolated dots. This set of equations is a generalization of the Bloch equations, which are used in studying the processes occurring under the action of ultrashort pulses of electromagnetic interaction. The model obtained is reduced to the model of two-level atoms only if radiation is circularly polarized.
Based on a model of strong coupling for two electrons that are localized inside a quantum dot characterized by only two levels of size quantization, a set of equations is derived, which allows one to describe coherent transient processes in an ensemble of isolated dots. Here one considered the case of ultrashort durations of electromagnetic field pulses, when the processes of polarization and population relaxation can be neglected. The resulting set of equations is a generalization of the Maxwell-Bloch equations, which are used in studying the processes occurring under the action of ultrashort electromagnetic pulses. The model obtained is reduced to the model of two-level atoms only if radiation is circularly polarized.
We consider the model of quantum dots interacting with coherent radiation when the relaxation processes may be neglected. The system under investigation consists of two discrete energy levels of the quantum dots in the presence of strong electron-electron Coulomb interaction and the transitions between these levels in response to electromagnetic radiation. By using the suitable generalisation of the Hubbard model the system of equations describing the evolution of the state of quantum dot was derived.
A system of equations is formulated describing the evolution of a slowly varying envelope of an arbitrarily polarized ultrashort pulse of electromagnetic radiation in a medium with its resonant properties determined by an ensemble of isolated quantum dots. It is assumed that the concentration of quantum dots is small and that the whole system is equivalent to a gas of resonant four-level atoms. Particular solutions are found that correspond to the propagation of a stationary optical pulse. It is shown by numerical solution of the generalized truncated Maxwell-Bloch equations that steady-state propagation is possible only for circularly polarized light pulses, whereas the pulses of arbitrary polarization either decay and experience the dispersion-related broadening or are converted into circularly polarized solitary waves.
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.