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Journal of Statistical Mechanics Theory and Experiment

Temporal behavior of entanglement between electronic spin and subband states in a Rashba nanoloop

Rosa Safaiee, Mohammad Mehdi Golshan, Neda Foroozani

Published Nov 27, 2009• 12 citations
Publisher

Abstract

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.

DOI
10.1088/1742-5468/2009/11/p11014

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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.
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, 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.
Free entanglement—the milestone of any quantum information processing scheme—among the π -electronic spin and its spatial states in graphene, as a function of temperature, is the main concern of the present report. It is assumed that a perpendicular magnetic field generates the Landau levels so that a coupling with the pseudo-spin (sublattice) states is enacted. Moreover, the pseudo-Rashba spin–orbit interaction (SOI), responsible for the coupling of spin and sublattice states, is also taken into account. From the structure of the total Hamiltonian, we introduce a Casimir operator which, in due turn, assists the development of a simple but efficient algorithm for our numerical computation. We then proceed by constructing the thermal density operator, its partially transposed one and, thereby, compute the negativity, the proper measure of free hybrid entanglement, at any temperature. Our results show that the negativity is nonvanishing at absolute zero temperature due to the fact that the ground state is an entangled one. Moreover, our results indicate that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement (free) is maximal strongly depend on the magnetic field and pseudo-Rashba spin–orbit strength; decreasing the magnetic field and/or increasing the pseudo-Rashba parameter (PRP) enhances the maximal entanglement monotonically. As the temperature increases, however, it is shown that the negativity decreases asymptotically to zero. As a result, there exists distillable entanglement amid the π -electronic spin and its spatial states in graphene at any finite temperature .
We present a theoretical examination of the fractional dynamics of information entropy within a semiconductor nanowire system influenced by Rashba spin–orbit interaction and external magnetic fields. Moreover, we determine the fractional nanowire state through the analytical solution of the fractional Schrödinger equation, considering various initial states of the nanowire system. Our research emphasizes the impact of the fractional order and the interaction parameters on the behavior of information entropy. Our findings reveal that the temporal behavior of information entropy is highly sensitive to any variations in the magnetic field length, the Rashba spin–orbit interaction, and the fractional order parameter. The results demonstrate that these parameters are pivotal in determining the coherence and correlation properties of the nanowire system. Therefore, precise control of these factors paves the way for enhancing entanglement performance and facilitating information transfer in spintronic and quantum communication applications.
Abstract We investigate the spin–orbit (SO) coupling effect on phase coherence of spin states for electrons confined to one-dimensional nanowires (NWs). It has been shown that SO interactions destroy coherent superpositios of spin states leading to states with nonzero entropy. Relationships between the von Neumann entropy and experimental characteristics of the spin are investigated for a single- and two electron systems. The dependence of a degree of decoherence on the Rashba coupling constant is determined analytically. New aspects of transport properties of a quasi-one-dimensional NW have been also studied.
We study the dynamics of entanglement for a one-dimensional spin system, where spins are coupled through nearest-neighbor exchange interaction and subject to different external magnetic fields. First we examine the system size effect on the entanglement with three different external magnetic fields changing with time ttt: an exponential function ${e}^{[\ensuremath{-}Kt]}$ and two periodic sin[Kt]\mathrm{sin}[Kt]sin[Kt] and cos[Kt]\mathrm{cos}[Kt]cos[Kt] functions, where KKK is a control parameter. We have found that the entanglement fluctuates shortly after a disturbance by an external magnetic field when the system size is small. For larger system size, the entanglement reaches a stable state for a long time before it fluctuates. However, this fluctuation of entanglement disappears when the system size goes to infinity. We also show that in a periodic external magnetic field, the nearest-neighbor entanglement displays a periodic structure with a period related to that of the magnetic field. Moreover, changing the direction of the magnetic field will destroy the concurrence in the system.