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arXiv:cond-mat/0509010 · Europhysics Letters (EPL)

Entanglement between static and flying qubits in quantum wires

J. H. Jefferson, A. Ramšak, Tomaž Rejec

Published Apr 25, 2006• 30 citations
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Abstract

A weakly bound electron in a semiconductor quantum wire is shown to become entangled with an itinerant electron via the Coulomb interaction. The degree of entanglement and its variation with energy of the injected electron, may be tuned by choice of spin and initial momentum. Full entanglement is achieved close to energies where there are spin-dependent resonances. Possible realisations of related device structures are discussed.

DOI
10.1209/epl/i2005-10584-1

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A weakly bound electron in a semiconductor quantum wire is shown to become entangled with an itinerant electron via the Coulomb interaction. The degree of entanglement and its variation with energy of the injected electron, may be tuned by choice of spin and initial momentum. Full entanglement is achieved close to energies where there are spin-dependent resonances. Possible realisations of related device structures are discussed.
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We propose a scheme to produce spin entangled states for two interacting electrons. One electron is bound in a well in a semiconductor quantum wire and the second electron is transported along the wire, trapped in a surface acoustic wave (SAW) potential minimum. We investigate the conditions for which the Coulomb interaction between the two electrons induces entanglement. Detailed numerical investigation reveals that the two electrons can be fully spin entangled depending on the confinement characteristics of the well and the SAW potential amplitude.
Several recent experiments have demonstrated the viability of a passive device that can generate spin-entangled currents in two separate leads. However, manipulation and measurement of individual flying qubits in a solid state system has yet to be achieved. This is particularly difficult when a macroscopic number of these indistinguishable qubits are present. In order to access such an entangled current resource, we therefore show how to use it to generate distributed, static entanglement. The spatial separation between the entangled static pair can be much higher than that achieved by only exploiting the tunnelling effects between quantum dots. Our device is completely passive, and requires only weak Coulomb interactions between static and flying spins. We show that the entanglement generated is robust to decoherence for large enough currents.
The entanglement of flying qubits with static qubits in the solid state is important in the development of quantum computing. It has recently been shown theoretically that the spin-dependent scattering of a propagating electron from a bound electron is sufficient to give full entanglement between the qubits embodied in their respective spins [J. H. Jefferson et al., Europhys. Lett. 74, 764 (2006); D. Gunlycke et al., J. Phys.: Condens. Matter 18, S851 (2006)]. In this paper a generalized, real-space Anderson model is introduced for a quasi-one-dimensional structure consisting of a binding site coupled to ideal leads. Degeneracy of both the binding site and the leads is incorporated to represent, for example, conduction band degeneracy in carbon nanotubes. The model is used to calculate the spin-dependent scattering behavior and resultant static-flying qubit entanglement created by the scattering process. Degeneracy (and more generally, multiplicity) in the binding site gives rise to inelastic scattering processes. In the elastic scattering regime, a degenerate binding site gives rise to antiresonant structures in the transmission spectrum. Additional degeneracy in the leads restricts this effect to the second set of leads, raising the possibility of spin filtration, though this is eliminated in the inelastic scattering regime. Degeneracy in the binding site also gives rise to multiple resonances in transmission that will improve the probability of obtaining entangled pairs relative to the nondegenerate case. This effect is maximized when the components of the degenerate binding site are symmetrically coupled to the leads.
A GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs based two-qubit quantum device that allows the controlled generation and straightforward detection of entanglement by measuring a stationary current-voltage characteristics is proposed. We have developed a two-particle Green's function method of open systems and calculate the properties of three-dimensional interacting entangled systems nonperturbatively. We present concrete device designs and detailed charge-self-consistent predictions. One of the qubits is an all-electric Mach-Zehnder interferometer that consists of two electrostatically defined quantum wires with coupling windows, whereas the second qubit is an electrostatically defined double quantum dot located in a second two-dimensional electron gas beneath the quantum wires. We find that the entanglement of the device can be controlled externally by tuning the tunneling coupling between the two quantum dots.