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arXiv:nlin/0012053

Model of the two level quantum dots ensemble interacting with coherent radiation

Andrey I. Maimistov, Elena V. Kazantseva, S. O. Elyutin

Published Dec 25, 2000• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.nlin/0012053

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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.
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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.
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In this paper, we first derive a Coulomb Hamiltonian for electron–electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix. The coupling with Maxwell equations in case of interaction with an electromagnetic field is also considered from the Cauchy problem point of view. The study is completed by numerical results and a discussion about the advisability of neglecting intra-band coherences, as is done in part of the literature.
In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be represented as an atom with zero kinetic energy, and that all excitonic effects except dipole-dipole interactions may be disregarded. We use Jaynes-Cummings-Paul model with applications to quantum systems based on a time-dependent Hamiltonian and entangled states. We obtain a system of equations describing the interaction and present a method to solve the equations analytically for a single mode field within the Rotating-Wave Approximation. As an example of the applicability of this approach, we solve the system of two two-level quantum dots in a lossless cavity with two modes of electromagnetic field. We furthermore study the evolution of entanglement by defining and computing the concurrency.
The optical resonance of a three-level system of the strongly correlated electrons in the two-level semiconductor quantum dot interacting with the linearly polarized monochromatic electromagnetic radiation is studied. With the application of the Green function method the expressions of the state vectors and the energies of the stationary states of the system in the regime of the optical resonance are derived. The Rabi oscillations of the electron populations at different levels as well as the Rabi splitting of the peaks in the photon emission spectra are investigated. PACS numbers: 71.35.-y, 78.55.-m, 78.67.Hc Keywords: quantum dot, optical resonance, Rabi oscillation, population flopping AJSTD Vol.23(3) pp.161-181 (2006)