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arXiv:cond-mat/0012475 · Journal of the Physical Society of Japan

Test of Bell's Inequality using the Spin Filter Effect in Ferromagnetic Semiconductor Microstructures

Shiro Kawabata

Published May 15, 2001• 92 citations
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Abstract

A theoretical proposal for testing Bell's inequality in mesoscopic systems is presented. We show that the entanglement of two electron spins can be detected in the spin filter effect in the mesoscopic semiconductor / ferromagnetic semiconductor / semiconductor junction. The current-current correlation function is calculated by use of the quantum scattering theory and we compare it with the local hidden variable theory. We also discuss the influence of an imperfect spin filter and derive the condition to see the violation of Bell's inequality experimentally.

DOI
10.1143/jpsj.70.1210

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Control over electron-spin states, such as coherent manipulation, filtering and measurement promises access to new technologies in conventional as well as in quantum computation and quantum communication. In this paper, we review recent theoretical proposal of using electron spins in quantum confined structures as qubits. We also present a theoretical proposal for testing Bell's inequality in nano-electronics devices. We show that the entanglement of two electron spins can be detected in the spin filter effect in the nanostructure semiconductor / ferromagnetic semiconductor / semiconductor junction. In particular, we show how to test Bell's inequality via the measurement of the current-current correlation function in this setup.
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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.
Entanglement, viz. the non‐separability of quantum states, is a fundamental prediction of quantum mechanics, which is at odds with the classical perception of reality. Furthermore, it constitutes a resource for quantum computation and quantum communication. Electronic degrees of freedom in nanostructures –in particular the spin –constitute promising candidates to implement quantum information architectures in scalable solid state circuits. In this topical review, we will summarize some efforts to create and detect entanglement in such structures. We concentrate first on entanglement in double quantum dots, since they promise to be viable candidates to produce entanglement by confining electrons to a small interaction region. The quantitative detection of the entanglement through transport measurements can be done via current and noise. Secondly, we concentrate on the creation of spin entanglement at quantum point contacts, which has the advantage that the two electrons are automatically spatially separated. We discuss the possibility of performing a Bell test of non‐local correlations. However, as we will point out, a reliable entanglement detection can be performed by current‐correlation measurements, although they require some trust in the experimental setup. Finally, we present a hierarchy of mesoscopic Bell tests, which could be useful to evaluate theoretical proposals and experimental setups.