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Communications in Theoretical Physics

Energy Shift Caused by Non-isotropy of 2-Dimensional Anisotropic Quantum Dot in Presence of Uniform Magnetic Field

Hong-Yi Fan, Xuefen Xu

Published Oct 1, 2005• 1 citation
Publisher

Abstract

Based on the squeezing mechanism in quantum dots in the presence of uniform magnetic field, we derive the energy shift caused by the non-isotropy of 2-dimensional anisotropic quantum dot. We also study sudden squeezing of the size of the quantum dot. The whole discussion is proceeded smoothly by virtue of the entangled state representation.

DOI
10.1088/6102/44/4/615

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Based on the squeezing mechanism in quantum dots in the presence of uniform magnetic field, we derive the energy shift caused by the non-isotropy of 2-dimensional anisotropic quantum dot. We also study sudden squeezing of the size of the quantum dot. The whole discussion is proceeded smoothly by virtue of the entangled state representation.
We have investigated the linear and nonlinear optical properties of a two-dimensional anisotropic quantum dot in a magnetic field. Based on the computed energies and wave functions, the linear, third-order nonlinear and total optical absorption coefficients as well as the refractive index changes have been examined. The results are presented as a function of the incident photon energy for the different cases of anisotropy, dot size and external magnetic field. The results show that the linear and nonlinear optical properties of anisotropic quantum dots are strongly affected by the degree of anisotropy, the dot size, the external magnetic field and the polarized direction of the incident electromagnetic wave. The result also shows that the size effect of anisotropy quantum dots on the optical absorptions is different from that of isotropic quantum dots.
Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individual-particle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, which results in the states with symmetries related to the latter representation only being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number $M\ensuremath{\ge}2$ in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quantum number MMM, with the aid of the magnetic-field dependence of the addition energy is proposed.
In the newly constructed entangled state representation embodying quantum entanglement of Einstein, Podolsky and Rosen, the usual wave function of atomic coherent state ∣τ〉 = exp (μJ+-μ*J-)∣j, -j〉 turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j, where j is the spin value. We then prove that a two-dimensional time-independent anisotropic harmonic oscillator in a uniform magnetic field possesses energy eigenstates which can be classified as the states ∣τ〉 in terms of the spin values j.