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arXiv:cond-mat/9906071 · Physical review. B, Condensed matter

Noise of entangled electrons: Bunching and antibunching

Guido Burkard, Daniel Loss, Eugene V. Sukhorukov

Published Jun 15, 2000• 251 citations
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Abstract

Addressing the feasibility of quantum communication with entangled electrons in an interacting many-body environment, we propose an interference experiment using a scattering setup with an entangler and a beam splitter. It is shown that, due to electron-electron interaction, the spin correlation of the entangled singlet and triplet states is reduced by ${z}_{F}^{2}$ in a conductor described by Fermi liquid theory. We calculate the quasiparticle weight factor ${z}_{F}$ for a two-dimensional electron system. The current noise for electronic singlet states turns out to be enhanced (bunching behavior), while it is reduced for triplet states (antibunching). Within standard scattering theory, we find that the Fano factor (noise-to-current ratio) for singlets is twice as large as for independent classical particles and is reduced to zero for triplets.

DOI
10.1103/physrevb.61.r16303

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If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing and quantum communication, will be possible. We review our proposed spin-quantum dot architecture for a quantum computer and review some recent results on a deterministic source of entanglement generated by coupling quantum dots. Addressing the feasibility of quantum communication with entangled electrons we consider a scattering set-up with an entangler and beam splitter where the current noise exhibits bunching behavior for electronic singlet states and antibunching behavior for triplet states. We show that spin currents can produce noise even in the absence of any charge currents.
We extend our previous work on shot noise for entangled and spin polarized electrons in a beam-splitter geometry with spin-orbit (SO) interaction in one of the incoming leads (lead 1). In addition to accounting for both the Dresselhaus and the Rashba spin-orbit terms, we present general formulas for the shot noise of singlet and triplets states derived within the scattering approach. We determine the full scattering matrix of the system for the case of leads with two orbital channels coupled via weak SO interactions inducing channel anticrossings. We show that this interband coupling coherently transfers electrons between the channels and gives rise to an additional modulation angle---dependent on both the Rashba and Dresselhaus interaction strengths---which allows for further independent coherent control of the electrons traversing the incoming leads. We derive explicit shot noise formulas for a variety of correlated pairs (e.g., Bell states) and lead spin polarizations. Interestingly, the singlet and each of the triplets defined along the quantization axis perpendicular to lead 1 (with the local SO interaction) and in the plane of the beam splitter display distinctive shot noise for injection energies near the channel anticrossings; hence, one can tell apart all the triplets, in addition to the singlet, through noise measurements. We also find that spin-orbit induced backscattering within lead 1 reduces the visibility of the noise oscillations, due to the additional partition noise in this lead. Finally, we consider injection of two-particle wavepackets into leads with multiple discrete states and find that two-particle entanglement can still be observed via noise bunching and antibunching.
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We investigate the spin entanglement in the superconductor-quantum dot system proposed by Recher, Sukhorukov, and Loss, coupling it to an electronic beamsplitter. The superconductor-quantum dot entangler and the beamsplitter are treated within a unified framework and the entanglement is detected via current correlations. The state emitted by the entangler is found to be a linear superposition of nonlocal spin singlets at different energies, a spin-entangled two-particle wave packet. Colliding the two electrons in the beamsplitter, the singlet spin state gives rise to a bunching behavior, detectable via the current correlators. The amount of bunching depends on the relative positions of the single particle levels in the quantum dots and the scattering amplitudes of the beamsplitter. It is found that the bunching-dependent part of the current correlations is of the same magnitude as the part insensitive to bunching, making an experimental detection of the entanglement feasible. The spin entanglement is insensitive to orbital dephasing but suppressed by spin dephasing. A lower bound for the concurrence, conveniently expressed in terms of the Fano factors, is derived. A detailed comparison between the current correlations of the nonlocal spin-singlet state and other states, possibly emitted by the entangler, is performed. This provides conditions for an unambiguous identification of the nonlocal singlet spin entanglement.
Entanglement acts as a fundamental resource for many applications in quantum communication. We propose and theoretically analyze methods for preparing and detecting entanglement between the spins of electrons in a mesoscopic environment. The entanglement production mechanism which we present is based on two quantum dots coupled to a superconductor from which paired electrons are injected via Andreev tunneling. The spin-correlated electrons can then hop from the quantum dots into normal leads. For detection we propose to measure the shot noise which is produced by the entangled electrons after they have passed a beam splitter. The enhancement of the noise by a factor of two turns out to be a unique signature for the spin singlet, a maximally entangled state. In a different setting, the entangled ground state in two tunnel-coupled quantum dots is detected via the Aharonov–Bohm oscillations in the co-tunneling current.
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