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arXiv:cond-mat/0607603 · Physical Review B

Two-spin entanglement induced by electron scattering in nanostructures

Gian Luca Giorgi, FERDINANDO DE PASQUALE

Published Oct 20, 2006• 19 citations
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Abstract

We present a model where two magnetic impurities in a discrete tight-binding ring become entangled because of scattering processes associated to the injection of a conduction electron. We introduce a weak-coupling approximation that allows us to solve the problem in an analytical way and compare the theory with the exact numerical results. We obtain the generation of entanglement both in a deterministic way and in a probabilistic one. The first case is intrinsically related to the structure of the two-impurity reduced density matrix, while the second one occurs when a projection on the electron state is performed.

DOI
10.1103/physrevb.74.153308

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We present a model where two magnetic impurities in a discrete tight-binding ring become entangled because of scattering processes associated to the injection of a conduction electron. We introduce a weak-coupling approximation that allows us to solve the problem in an analytical way and compare the theory with the exact numerical results. We obtain the generation of entanglement both in a deterministic way and in a probabilistic one. The first case is intrinsically related to the structure of the two-impurity reduced density matrix, while the second one occurs when a projection on the electron state is performed.
We investigate the Aharonov-Bohm (AB) interference pattern in the electron transmission through a mesoscopic ring in which two identical noninteracting magnetic impurities are embedded. Adopting a quantum waveguide theory, we derive the exact transmission probability amplitudes and study the influence of maximally entangled states of the impurity spins on the electron transmittivity interference pattern. For suitable electron wave vectors, we show that the amplitude of AB oscillations in the absence of impurities is, in fact, not reduced within a wide range of the electron-impurity coupling constant when the maximally entangled singlet state is prepared. Such state is thus able to inhibit the usual electron decoherence due to scattering by magnetic impurities. We also show how this maximally entangled state of the impurity spins can be generated via electron scattering.
We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively largely inhibit the electron transport or make the wire completely transparent for any electron spin state. In the latter case, a resonance condition can always be found, representing an anomalous behaviour compared to typical decoherence induced by magnetic impurities. We provide an explanation for these phenomena in terms of the Hamiltonian symmetries. Finally, a scheme to generate maximally entangled spin states of the two impurities via electron scattering is proposed.
Based on Yosida's ground state of the single-impurity Kondo Hamiltonian, we study three kinds of entanglement between an impurity and conduction electron spins. First, it is shown that the impurity spin is maximally entangled with all the conduction electrons. Second, a two-spin density matrix of the impurity spin and one conduction electron spin is given by a Werner state. We find that the impurity spin is not entangled with one conduction electron spin even within the Kondo screening length ${\ensuremath{\xi}}_{K}$, although there is the spin-spin correlation between them. Third, we show the density matrix of two conduction electron spins is nearly the same as that of a free electron gas. The single impurity does not change the entanglement structure of the conduction electrons in contrast to the dramatic change in electrical resistance.
The possibility of generating entanglement between two solid-state electron spin-qubits by spin-dependent scattering of a third, propagating electron is attractive. A process of this kind could work well beyond the range of the direct interaction between the two spins. In this study, the binding of electrons in one-dimensional structures is theoretically modeled using a real-space analog of the Anderson model. The respective binding sites are arranged in two different geometries. The first is a straightforward series arrangement, and the second a parallel arrangement in which the binding sites are embedded in either arm of an Aharonov-Bohm style ring. For the series arrangement, the entanglement between the bound electrons is calculated and is shown to be low (concurrence <0.2<0.2<0.2) in all regions of significant transmission. In contrast, the parallel arrangement allows full entanglement to be generated from a ${S}_{z}=1(\ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\uparrow}⟩)$ or ${S}_{z}=0(\ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\downarrow}⟩)$ starting configuration with an overall probability of success up to 0.5.
We theoretically study how a scattered electron can entangle molecular spin qubits (MSQs). This requires solving the inelastic transport of a single electron through a scattering region described by a tight-binding interacting Hamiltonian. We accomplish this using a Green's-function solution. We can model realistic physical implementations of MSQs by parametrizing the tight-binding Hamiltonian with first-principles descriptions of magnetic anisotropy and exchange interactions. We find that, for two-MSQ systems with inversion symmetry, projective measurement of the spin degree of freedom of the scattered electron offers probabilistic control of the degree of entanglement between the MSQs.
We show how entanglement between two conduction electrons is generated in the presence of a localized magnetic impurity embedded in an otherwise ballistic conductor of special geometry. This process is a generalization of beam-splitter mediated entanglement generation schemes with a localized spin placed at the site of the beam splitter. Our entangling scheme is unconditional and robust to randomness of the initial state of the impurity. The entangled state generated manifests itself in noise reduction of spin-dependent currents.