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AIP conference proceedings

Orbital Entanglement In Mesoscopic Conductors

Peter Samuelsson, Eugene V. Sukhorukov, Μ. Büttiker

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We present an investigation of orbital entanglement in mesoscopic conductors. Several schemes for generation of orbital entanglement are discussed, such as normal‐superconducting, electron‐hole and dynamic orbital entanglers. The generated, orbitally entangled state is investigated with the focus on the state emitted in an electronic analog of the optical Hanbury Brown Twiss experiment. The one and two particle properties of the emitted state are described in terms of reduced density matrices. Approaches to detect and characterize the entanglement based on zero frequency shot noise are discussed, with the focus on a complete reconstruction of the emitted state via quantum state tomography.

DOI
10.1063/1.2355224

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We present an investigation of orbital entanglement in mesoscopic conductors. Several schemes for generation of orbital entanglement are discussed, such as normal‐superconducting, electron‐hole and dynamic orbital entanglers. The generated, orbitally entangled state is investigated with the focus on the state emitted in an electronic analog of the optical Hanbury Brown Twiss experiment. The one and two particle properties of the emitted state are described in terms of reduced density matrices. Approaches to detect and characterize the entanglement based on zero frequency shot noise are discussed, with the focus on a complete reconstruction of the emitted state via quantum state tomography.
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.
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.
Mesoscopic shot noise is not only probabilistic: it has features which reflect quantum mechanical entanglement. We discuss recent proposals of orbital entanglement generation and detection in mesoscopic coherent conductors. Orbital entanglement avoids the difficulty of detecting spin and leads to simpler structures. Orbital entanglement schemes invoke two two-particle sources. The index of the source plays the role of a pseudo-spin. The rotation of qubits can be implemented with beam-splitters or even just quantum point contacts. Entanglement is detected via violation of a Bell inequality. The necessary correlations can be extracted from shot noise measurements. Possible two particle sources are Cooper pairs emitted from superconductors or even simpler electron-hole pairs generated at tunnel contacts or generated dynamically with the help of oscillating potentials.
Mesoscopic shot noise is not only probabilistic: it has features which reflect quantum mechanical entanglement. We discuss recent proposals of orbital entanglement generation and detection in mesoscopic coherent conductors. Orbital entanglement avoids the difficulty of manipulating spin and leads to simpler structures. Orbital entanglement schemes invoke two two‐particle sources. The index of the source plays the role of a pseudo‐spin. The rotation of qubits can be implemented with beam‐splitters or even just quantum point contacts. Entanglement is detected via violation of a Bell inequality. The necessary correlations can be extracted from shot noise measurements.
In this article we discuss our two recent proposals on producing and detecting of entangled states in quantum conductors. First we analyze a setup where two electrons are scattered on a quantum dot with Coulomb repulsion and became orbitally entangled. Second, for identical noninteracting particles we suggest an operating scheme for the deliberate generation of spin‐entangled electron pairs in a normal‐metal mesoscopic structure with a fork geometry. The spin‐entangled pair is created through a post‐selection in the two branches of the fork. We also make comments on different ways of producing and quantifying the degree of entanglement.