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arXiv:quant-ph/0611025 · Journal of Physics A Mathematical and Theoretical

Electron Fabry–Perot interferometer with two entangled magnetic impurities

Francesco Ciccarello, G. Massimo Palma, Michelangelo Zarcone, Yasser Omar, Vitor Rocha Vieira

Published Jun 27, 2007• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1751-8113/40/28/s09

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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.
In a recent paper—F. Ciccarello et al., New J. Phys. 8 , 214 (2006)—we have demonstrated that the electron transmission properties of a one-dimensional (1D) wire with two identical embedded spin-1/2 impurities can be significantly affected by entanglement between the spins of the scattering centers. Such an effect is of particular interest in the control of the transmission of quantum information in nanostructures and can be used as a detection scheme of maximally entangled states of two localized spins. In this letter, we relax the constraint that the two magnetic impurities are equal and investigate how the main results presented in the above paper are affected by a static disorder in the exchange coupling constants of the impurities. Good robustness against deviation from impurity symmetry is found for both the entanglement dependent transmission and the maximally entangled states generation scheme.
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 the scattering problem of two-electron transport in one-dimensional channel coupled with an Anderson-type impurity. The treatment includes the backscattering of the electrons. We show that the transport properties are fundamentally different for spin singlet and triplet states, thus the impurity acts as a novel filter that operates based on the total spin angular momentum of the electron pairs, but not individual spins. The filter provides a deterministic generation of electron entanglement in spin, as well as energy and momentum space.
We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. We find conditions for the impurity spins to be maximally entangled with a significant success probability. We then consider a more realistic description which includes both the forward and backscattering amplitudes. In this scenario, we obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling. We find that our scheme allows us to entangle the impurities maximally with a significant probability.
In this paper we study the Aharonov-Bohm oscillations of transmission coefficient for an electron passing through a quantum nanoring with two identical magnetic impurities using quantum waveguide theory. It is shown that the Aharonov-Bohm oscillations are independent of the coupling constant between the electron and magnetic impurities for the singlet spin state of impurities, while for the other spin states of impurities the Aharonov-Bohm oscillations decrease rapidly with an increasing coupling constant. For a triplet spin state of impurities, we can use this system as a quantum NOT gate with an efficiency upper than 50% by adjusting the coupling constant between the electron and magnetic impurities and the magnetic flux passing through the ring.