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arXiv:quant-ph/0109045 · Physical Review Letters

Impurity Scattering Induced Entanglement of Ballistic Electrons

A. T. Costa, Sougato Bose

Published Dec 11, 2001• 62 citations
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Abstract

We show how entanglement between two conduction electrons is generated in the presence of a localized magnetic impurity embedded in an otherwise ballistic conductor of special geometry. This process is a generalization of beam-splitter mediated entanglement generation schemes with a localized spin placed at the site of the beam splitter. Our entangling scheme is unconditional and robust to randomness of the initial state of the impurity. The entangled state generated manifests itself in noise reduction of spin-dependent currents.

DOI
10.1103/physrevlett.87.277901

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We show how entanglement between two conduction electrons is generated in the presence of a localized magnetic impurity embedded in an otherwise ballistic conductor of special geometry. This process is a generalization of beam-splitter mediated entanglement generation schemes with a localized spin placed at the site of the beam splitter. Our entangling scheme is unconditional and robust to randomness of the initial state of the impurity. The entangled state generated manifests itself in noise reduction of spin-dependent currents.
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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 report experimental research into the possibility of using shot noise mea-surements to detect the entangled states of electron spins. The study is part of the effort towards the demonstration of the use of electron spins as quantum bits (qubits) for quantum computing and quantum information processing. Electrons are electrically injected into two neighboring quantum dots and interact with each other through the exchange coupling, after which they tunnel out of the dots and are incident on a beam splitter, which introduces quantum interference between electron states. Depending on the state of the electrons exiting the dots, the outgoing states of electrons scattering off the beam splitter are different, corresponding to different shot noise in the electrical currents flowing into the channels after the beam splitter. Our experimental data is consistent with most theoretical predictions and provides initial evidence of electron spin entanglement. A comprehensive study of the shot noise in mesoscopic semiconductor tunnel barriers is also reported. Besides the theoretically predicted full shot noise, sup-pressed and enhanced shot noise are also observed. Normal conductance measure-ments and numerical simulations are done to understand the shot noise deviation. Our study shows that shot noise in mesoscopic systems is extremely sensitive to the microscopic details, such as potential disorder and impurity configuration.
The spin-dependent scattering process in a system of a topological insulator and a quantum dot is studied. The unitary scattering process is viewed as a gate transformation applied to an initial state of two electrons. Due to the randomness imposed through the impurities and alloying-induced effects of band parameters, the formalism of the random unitary gates is implemented. For quantifying entanglement in the system, we explored concurrence and ensemble-averaged R\'enyi entropy. We found that an applied external magnetic field leads to long-range entanglement on distances much larger than the confinement length. We showed that topological features of itinerant electrons sustain the formation of robust long-distance entanglement, which survives even in the presence of strong disorder.
We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. We find conditions for the impurity spins to be maximally entangled with a significant success probability. We then consider a more realistic description which includes both the forward and backscattering amplitudes. In this scenario, we obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling. We find that our scheme allows us to entangle the impurities maximally with a significant probability.
We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively largely inhibit the electron transport or make the wire completely transparent for any electron spin state. In the latter case, a resonance condition can always be found, representing an anomalous behaviour compared to typical decoherence induced by magnetic impurities. We provide an explanation for these phenomena in terms of the Hamiltonian symmetries. Finally, a scheme to generate maximally entangled spin states of the two impurities via electron scattering is proposed.