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AIP conference proceedings

Characterizing electron entanglement in multi-mode mesoscopic conductors

Fabio Taddei, Vittorio Giovannetti, Diego Frustaglia, Rosario Fazio, Massimo Macucci, Giovanni Basso

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We show that current correlations at the exit ports of a beam splitter can be used to detect electronic entanglement for a fairly general input state. First, we demonstrate that multi‐mode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero‐frequency current correlations in an electronic Hong‐Ou‐Mandel interferometer. By this means, one can further establish a lower bound to the entanglement of formation of two‐electron input states. Second, we include the situation where electron pairs can enter the beam splitter from the same port or be separated due to backscattering. The proposed scheme allows to discriminate between particle‐number and mode entanglement.

DOI
10.1063/1.3140503

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We show that current correlations at the exit ports of a beam splitter can be used to detect electronic entanglement for a fairly general input state. First, we demonstrate that multi‐mode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero‐frequency current correlations in an electronic Hong‐Ou‐Mandel interferometer. By this means, one can further establish a lower bound to the entanglement of formation of two‐electron input states. Second, we include the situation where electron pairs can enter the beam splitter from the same port or be separated due to backscattering. The proposed scheme allows to discriminate between particle‐number and mode entanglement.
We show that multimode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero-frequency current correlations in an electronic Hong-Ou-Mandel interferometer. By this means, one can further establish a lower bound to the entanglement of formation of two-electron input states. Our results extend the work of Burkard and Loss [Phys. Rev. Lett. 91, 087903 (2003)] to many channels and provide a way to test the existence of entangled states involving both orbital and spin degrees of freedom.
We determine a lower bound for the entanglement of formation of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross correlators) after transmission through an electronic beam splitter and can be used to gain information about the entanglement from experiment. Spin relaxation (T1 processes) and decoherence (T2) during the ballistic coherent transmission of carriers are taken into account within Bloch theory. A variable inhomogeneous magnetic field gives rise to a useful lower bound for the entanglement of arbitrary states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and T(1,2) can be determined from current correlators.
We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.
We propose a scheme for a complete reconstruction of one- and two-particle orbital quantum states in mesoscopic conductors. The conductor in the transport state continuously emits orbital quantum states. The orbital states are manipulated by electronic beam splitters and detected by measurements of average currents and zero frequency current shot-noise correlators. We show how, by a suitable complete set of measurements, the elements of the density matrices of the one- and two-particle states can be directly expressed in terms of the currents and current correlators.
We propose a scheme for dynamically creating orbitally entangled electron-hole pairs through a time-dependent variation of the electrical potential in a mesoscopic conductor. The time-dependent potential generates a superposition of electron-hole pairs in two different orbital regions of the conductor, a two-particle interferometer in the quantum Hall regime. The orbital entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current noise. Adiabatic cycling of the potential, in both the weak and strong amplitude limits, is considered.