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Journal of Statistical Mechanics Theory and Experiment

Effects of quantum dot characteristics on electronic spin–subband state entanglement

Rosa Safaiee, Neda Foroozani, Mohammad Mehdi Golshan

Published Feb 16, 2009• 4 citations
Publisher

Abstract

The entanglement dynamics of spin–subband states for an electron in a 2D isotropic Rashba quantum dot, with an applied magnetic field of arbitrary strength, is studied. We explicitly include the confining (gate) effects as a two-dimensional isotropic harmonic oscillator. The von Neumann entropy, as a measure of entanglement, is calculated as a function of time, by going to the Fock–Darwin representation. Our results indicate that the period and amplitude of the collapse–revival behavior of the entanglement between the spin states and the structural subbands strongly depend upon the size of the quantum dot (confining length) and choice of heterostructural materials. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these factors.

DOI
10.1088/1742-5468/2009/02/p02038

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The entanglement dynamics of spin–subband states for an electron in a 2D isotropic Rashba quantum dot, with an applied magnetic field of arbitrary strength, is studied. We explicitly include the confining (gate) effects as a two-dimensional isotropic harmonic oscillator. The von Neumann entropy, as a measure of entanglement, is calculated as a function of time, by going to the Fock–Darwin representation. Our results indicate that the period and amplitude of the collapse–revival behavior of the entanglement between the spin states and the structural subbands strongly depend upon the size of the quantum dot (confining length) and choice of heterostructural materials. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these factors.
In this paper we study the entanglement dynamics of spin–subband states for an electron in a quasi-one-dimensional Rashba quantum loop, in a strong perpendicular magnetic field, explicitly including the confining potential and the Rashba spin–orbit coupling into the entropy, which is a measure of entanglement, as a function of time. Our results indicate that the entanglement between the spin states and the structural subbands undergoes periodic oscillations. Furthermore, it is shown that the period of oscillations strongly depends upon the Rashba coupling, while the amplitudes may be optimized by making proper choices of the external magnetic field. It is also shown that the maxima of entanglement, in the long run, oscillate under periodic envelopes, whose characteristics depend upon the magnetic field. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these agents.
In this paper, the mechanism of entanglement between electronic spin states and their spatial degrees of freedom in graphene is reported. From a calculation of the time evolution of von Neumann entropy, as a measure of entanglement, we show that the general behavior is oscillatory with characteristics depending on the external magnetic field, the Rashba spin–orbit coupling and the Landau states. The effect of these agents on the degree of entanglement is also discussed. It is shown that an increase in the magnetic field decreases the degree of entanglement, while an increase in Rashba spin–orbit coupling enhances the entanglement. Furthermore, for higher Landau levels the electronic states become more entangled. The material presented in this paper offers new means of controlling the entanglement of electronic states.
Exact-diagonalization calculations for N=3N=3N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of interelectron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection Sz=1∕2{S}_{z}=1∕2Sz​=1∕2 are similar to the representative class of strongly entangled states referred to as the WWW states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zigzag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.
We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulating the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting in two regimes: one of low entanglement and the other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities and, therefore, the degree of entanglement.
We study the decay of entanglement of quantum-dot electron-spin qubits under hyperfine-interaction-mediated decoherence. We show that two-qubit entanglement of a single entangled initial state may exhibit decay characteristic of two disentanglement regimes in a single sample, when the external magnetic field is changed. The transition is manifested by the suppression of time-dependent entanglement oscillations which are superimposed on the slowly varying entanglement decay related to phase decoherence which results in oscillatory behavior of entanglement sudden death time as a function of the magnetic field. This unique behavior allows us to propose the double-quantum-dot two-electron spin Bell state as a promising candidate for precise measurements of the magnetic field.
We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulating the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting in two regimes: one of low entanglement and the other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities and, therefore, the degree of entanglement.