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arXiv:cond-mat/0009193 · The European Physical Journal B

Electronic entanglement in the vicinity of a superconductor

Gordey B. Lesovik, Thierry Martin, G. Blatter

Published Dec 1, 2001• 321 citations
arXivHTMLPDF
DOI
10.1007/s10051-001-8675-4

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Superconductor coupled to two Luttinger liquids as an entangler for electron spins

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We consider an s-wave superconductor (SC) which is tunnel coupled to two spatially separated Luttinger-liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e., it creates spin singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin-density fluctuations produced by the injected spin-entangled electrons.

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Superconductors, Quantum Dots, and Spin Entanglement

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A single-electron trap built with two superconductor-insulator-normal metal tunnel junctions and coupled to a readout SINIS-type single-electron transistor A (SET A) was studied in a photon detection regime. As a source of photon irradiation, we used an operating second SINIS-type SET B positioned in the vicinity of the trap. In the experiment, the average hold time of the trap was found to be critically dependent on the voltage across SET B. Starting in a certain voltage range, a photon-assisted electron escape was observed at a rate roughly proportional to the emission rate of the photons with energies exceeding the superconducting gap of S-electrodes in the trap. The discussed mechanism of photon emission and detection is of interest for low-temperature noise spectrometry, and it can be of relevance for the ampere standard based on hybrid SINIS turnstiles.
Abstract Superconductivity and exciton condensation are fundamental phenomena in condensed matter physics, associated with the condensation of electron–electron and electron–hole pairs, respectively, into coherent quantum states. In this study, we present evidence of a superconductor to exciton condensate transition within the context of the three-band Hubbard model of copper-oxide-like materials. As the electron–electron repulsion increases, the superconducting phase is superseded by exciton condensation. In support of theoretical predictions—not yet realized experimentally—we observe the coexistence of the two condensates in the vicinity of the transition where the quantum states become a superposition of electron–electron and electron–hole condensates. Coexistence is rigorously computed from large eigenvalues and their eigenvectors in both the two-electron reduced density matrix (2-RDM) and the particle-hole RDM, which we obtain from a direct variational ground-state energy minimization with respect to the 2-RDM by semidefinite programming. We further discern that adjacent d orbitals and intervening p orbitals facilitate electron–electron pairing between copper orbitals, thereby supporting the superexchange mechanism for superconductivity. These observations suggest the feasibility of witnessing a superconductor to exciton condensate transition in copper-oxide analogs, bearing significant implications for identifying materials conducive to efficient transport processes.
We consider an s-wave superconductor (SC) which is tunnel coupled to two spatially separated Luttinger-liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e., it creates spin singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin-density fluctuations produced by the injected spin-entangled electrons.