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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum shot noise: from Schottky to Bell (Keynote Address)

Μ. Büttiker, Peter Samuelsson, Eugene V. Sukhorukov

Published May 23, 2005• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.609386

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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.
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.
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.
In this article, we have discussed about the scattering of charge and spin in spin-resolved mesoscopic systems. We have proposed a method to generate and detect the entanglement of electronic spin and electronic orbital degrees of freedom. It is observed that in a spin-resolved mesoscopic system, all form of entanglement existing between different electronic degrees of freedom can be generated. A method to detect Bell's inequality violation in terms of zero frequency current cross-correlators has been mentioned. Further, we have also studied the effect of quantum interference between spin flip and non-spin flip scattering matrices in determining the current and noise. We have obtained the expression for shot noise of spin and charge current when an arbitrarily polarised charge current is scattered at the spin resolved potential.
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.