Quantum Computation and Spin Electronics

In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics. We discuss five criteria for the realization of a quantum computer and consider the implications that these criteria have for quantum computation using the spin states of single-electron quantum dots. Finally, we consider the transport of quantum information via the motion of individual electrons in mesoscopic structures; specific transport and noise measurements in coupled quantum dot geometries for detecting and characterizing electron-state entanglement are analyzed.Comment: 28 pages RevTeX, 4 figures. To be published in "Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics," eds. I. O. Kulik and R. Ellialtioglu (NATO Advanced Study Institute, Turkey, June 13-25, 1999

Topological Quantum Gates with Quantum Dots

We present an idealized model involving interacting quantum dots that can support both the dynamical and geometrical forms of quantum computation. We show that by employing a structure similar to the one used in the Aharonov-Bohm effect we can construct a topological two-qubit phase-gate that is to a large degree independent of the exact values of the control parameters and therefore resilient to control errors. The main components of the setup are realizable with present technology.Comment: 8 pages, 3 figures, submitted to Jour. of Opt. B (special issue on Quantum Computing

Semiclassical theory of spin-polarized shot noise in mesoscopic diffusive conductors

We study fluctuations of spin-polarized currents in a three-terminal spin-valve system consisting of a diffusive normal metal wire connected by tunnel junctions to three ferromagnetic terminals. Based on a spin-dependent Boltzmann-Langevin equation, we develop a semiclassical theory of charge and spin currents and the correlations of the currents fluctuations. In the three terminal system, we show that current fluctuations are strongly affected by the spin-flip scattering in the normal metal and the spin polarizations of the terminals, which may point in different directions. We analyze the dependence of the shot noise and the cross-correlations on the spin-flip scattering rate in the full range of the spin polarizations and for different magnetic configurations. Our result demonstrate that noise measurements in multi-terminal devices allow to determine the spin-flip scattering rate by changing the polarizations of ferromagnetic terminals.Comment: 12 pages, 5 figure

Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons

We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots each of which is tunnel-coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin-singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance which allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.Comment: 11 double-column pages, 2 figures, REVTeX, minor revision

Spin current shot noise as a probe of interactions in mesoscopic systems

It is shown that the spin resolved current shot noise can probe attractive or repulsive interactions in mesoscopic systems. This is illustrated in two physical situations : i) a normal-superconducting junction where the spin current noise is found to be zero, and ii) a single electron transistor (SET), where the spin current noise is found to be Poissonian. Repulsive interactions may also lead to weak attractive correlations (bunching of opposite spins) in conditions far from equilibrium. Spin current shot noise can be used to measure the spin relaxation time $T_1$, and a set-up is proposed in a quantum dot geometry.Comment: 5 pages, 4 Figures, revised version, added reference

Noise of entangled electrons : bunching and antibunching

Addressing the feasibility of quantum communication with entangled electrons in an interacting many-body environment, we propose an interference experiment using a scattering setup with an entangler and a beam splitter. It is shown that, due to electron-electron interaction, the spin correlation of the entangled singlet and triplet states is reduced by z(F)(2) in a conductor described by Fermi liquid theory. We calculate the quasiparticle weight factor z(F) for a two-dimensional electron system. The current noise for electronic singlet states turns out to be enhanced (bunching behavior), while it is reduced for triplet states (antibunching). Within standard scattering theory, we find that the Fano factor (noise-to-current ratio) for singlets is twice as large as for independent classical particles and is reduced to zero for triplets

Noise of a quantum dot system in the cotunneling regime

We study the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. The various regimes of weak and strong, elastic and inelastic cotunneling are analyzed for quantum dot systems (QDS) with few-level, nearly degenerate, and continuous electronic spectra. We iind that in contrast to sequential tunneling, where the noise is either Poissonian (due to uncorrelated tunneling events) or sub-Poissonian (suppressed by charge conservation on the QDS), the noise in inelastic cotunneling can be super-Poissonian due to switching between QDS states carrying currents of different strengths. In the case of weak cotunneling we prove a nonequilibrium fluctuation-dissipation theorem: which leads to a universal expression for the noise-to-current ratio (Fano factor). In order to investigate strong cotunneling we develop a microscopic theory of cotunneling based on the density-operator formalism and using the projection operator technique. The master equation for the QDS and the expressions for current and noise in cotunneling in terms of the stationary state of the QDS are derived and applied to QDS with a nearly degenerate and continuous spectrum