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Journal of Physics Conference Series

Spin evolution of two valence electrons in two separated ions

Biplab Goswamit, A. V. Volotka, S. Fritzsche

Published Jul 1, 2017• 1 citation
Publisher

Abstract

The spin evolution of two spin-1/2 valence electrons, located at two separated ions, is investigated with the help of Breit equation. This evolution that arise solely depends on their dipole-dipole magnetic interaction. Special attention is paid to the effects beyond the leading order of the dipole-dipole magnetic interaction. In contrast to just including the leading order, it is found that the spin-spin interactions flips the spin of both electrons together, while the spin-orbit interactions typically changes the spin of just single electron. As a consequence, different behaviour is observed in the time evolution of two different entangled Bell states.

DOI
10.1088/1742-6596/875/6/052007

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•Jan 1, 2011•0 citations
The spin evolution of two spin-1/2 valence electrons, located at two separated ions, is investigated with the help of Breit equation. This evolution that arise solely depends on their dipole-dipole magnetic interaction. Special attention is paid to the effects beyond the leading order of the dipole-dipole magnetic interaction. In contrast to just including the leading order, it is found that the spin-spin interactions flips the spin of both electrons together, while the spin-orbit interactions typically changes the spin of just single electron. As a consequence, different behaviour is observed in the time evolution of two different entangled Bell states.
For a hvo electron hopping system we work the spin parts within the framework of quantum mechanics by taking the spin-flip operators as a part of the Hamiltonian. The system of two electrons hopping in a magnetic field with the dipole-dipole interaction each other and with a spin-flip perturbation is modelled. For the positive dipole-dipole interactions, we have derived a formula to determine the magnitude of the spin-flip operators. For free spin systems without the dipole-dipole interactions, we find also the solutions for the systems obeying the nowadays Pauli exclusion principle as recalled in this paper. When the spin-flips are tuned off mathematically, the system is not able to return back to usual no spin-flip case by possibly leaving with some residual effects or results in the wave function descriptions of the system. We find that these effects are even not satisfied by the so-called extended symmetrization principle as defined and proposed in this paper. This is a new consequence.
We study the influence of an additional uncontrolled (stray) magnetic field upon the measurement of long-range spin-spin interaction strength of two spin-1/2 valence electrons bound in two separate ions at well-defined distances from each other. This stray field, which is neither perpendicular nor parallel to the line connecting two ions, could appear due to the Earth magnetic field, or, due to the slight angular misalignment between the applied magnetic field and the line connecting two ions. It is found that the presence of the stray magnetic field plays an important role in the dynamics of the spin-states of two electrons. If neglected in the analysis, moreover, such a stray field may affect the measurement of the spin-spin interaction strength, especially at smaller inter-spin distances.
We consider a semi-classical model to describe the origin of the spin–orbit interaction in a simple system such as the hydrogen atom. The interaction energy is calculated in the rest-frame of the nucleus, around which an electron, having linear velocity and magnetic dipole-moment travels in a circular orbit. The interaction energy is due to the coupling of the induced electric dipole with the electric field of the nucleus. Assuming the radius of the electron's orbit remains constant during a spin-flip transition, our model predicts that the energy of the system changes by the factor emerging naturally as a consequence of equilibrium and the change of the kinetic energy of the electron. The correct factor for the spin–orbit coupling energy is thus derived without the need to invoke the well-known Thomas precession in the rest-frame of the electron.
We investigate the time evolution of the local spin in a molecular magnet interacting with injected electrons. By solving the time-dependent Schrödinger equations, we find that the variation in the magnetization of the molecular magnet and the electron spin crucially depends on the strength of the exchange interaction. We calculate the time evolution of the entanglement between the injected electron and the molecular magnet. It is found that the entanglement oscillates in time and the oscillations are closely related to the changes in the spins. The study provides an estimation of the feasibility of the encoding and read-out by using the polarization of the molecular magnets and the injected electrons.
We consider a semi-classical model to describe the origin of the spin-orbit interaction in a simple system such as the hydrogen atom. The interaction energy U is calculated in the rest-frame of the nucleus, around which an electron, having linear velocity v and magnetic dipole-moment μ, travels in a circular orbit. The interaction energy U is due to the coupling of the induced electric dipole p=(v/c)×μ with the electric field En of the nucleus. According to quantum mechanics, the radius of the electron’s orbit remains constant during a spin-flip transition. Under such circumstances, our model predicts that the energy of the system changes by ΔE=1/2U, the factor 1/2 emerging naturally as a consequence of equilibrium and the change of the kinetic energy of the electron. The correct 1/2 factor for the spin-orbit coupling energy is thus derived without the need to introduce the well-known Thomas precession in the rest-frame of the electron.
In the last years, the electron spin in quantum dots has become a most promising candidate for the realization of qubits, the basic element for quantum computation. In quantum dot spin qubits the exchange interaction implements a fundamental two qubit gate, which originates in the Coulomb interaction and the Pauli principle. Compared to single qubit gates, the exchange based gates are much faster and easier to control locally, motivating the solely exchange energy based quantum computation. The control is based on the exponential sensitivity of the exchange energy on the interparticle distance. Manipulation then can proceed, for example, shifting the single particle states electrically or compressing them magnetically. The practical manipulation schemes require quantitative knowledge of the exchange energy. The spin-orbit interaction plays an important role in this nano-system. Indeed the usual exchange interaction changes its magnitude, while a new term, called anisotropic exchange, appears. In this thesis we propose an accurate effective spin Hamiltonian for modeling spin-orbit-induced spin dynamics in the presence of the magnetic field. We have also performed numerically exact calculations of the isotropic and anisotropic exchange coupling in realistic two-electron GaAs coupled quantum dots in the presence of both Dresselhaus and Bychkov-Rashba spin-orbit interactions. The numerics allow us to establish the goodness of our model and to see the limits of previous statements. Furthermore we find that in zero magnetic field the second-order spin-orbit effects are absent at all interdot couplings.