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We consider an isotropic spin-degenerate interacting uniform $D$-dimensional electron gas (DDEG) with $D > 1$ within the Luttinger-Ward (LW) formalism. We derive the asymptotically exact semiclassical/infrared limit of the LW functional at large distances, $r \gg \lambda_F$, and large times, $\tau \gg 1/E_F$, where $\lambda_F$ and $E_F$ are the Fermi wavelength and the Fermi energy, respectively. The LW functional is represented by skeleton diagrams, each skeleton diagram consists of appropriately connected dressed fermion loops. First, we prove that every $D$-dimensional skeleton diagram consisting of a single fermion loop is reduced to a one-dimensional (1D) fermion loop with the same diagrammatic structure, which justifies the name dimensional reduction. This statement, combined with the fermion loop cancellation theorem (FLCT), agrees with results of multidimensional bosonization. Here we show that the backscattering and the spectral curvature, both explicitly violate the FLCT and both are irrelevant for a 1DEG, become relevant at $D > 1$ and $D > 2$, respectively. The reason for this is a strong infrared divergence of the skeleton diagrams containing multiple fermion loops at $D > 1$. These diagrams, which are omitted within the multidimensional bosonization approaches, account for the non-collinear scattering processes. Thus, the dimensional reduction provides the framework to go beyond predictions of the multidimensional bosonization. A simple diagrammatic structure of the reduced LW functional is another advantage of our approach. The dimensional reduction technique is also applicable to the thermodynamic potential and various approximations, from perturbation theory to self-consistent approaches., Comment: 15 pages, 4 figures

Semiconductor qubits are appealing for building quantum processors as they may be densely integrated due to small footprint. However, a high density raises the issue of noise correlated across different qubits, which is of practical concern for scalability and fault tolerance. Here, we analyse and quantify in detail the degree of noise correlation in a pair of neighbouring silicon spin qubits ~100 nm apart. We evaluate all a-priori independent auto- and cross- power spectral densities of noise as a function of frequency. We reveal strong inter-qubit noise correlation with a correlation strength as large as ~0.7 at ~1 Hz (70% of the maximum in-phase correlation), even in the regime where the spin-spin exchange interaction contributes negligibly. We furthermore find that fluctuations of single-spin precession rates are strongly correlated with exchange noise, giving away their electrical origin. Noise cross-correlations have thus enabled us to pinpoint the most influential noise in the present device among compelling mechanisms including nuclear spins. Our work presents a powerful tool set to assess and identify the noise acting on multiple qubits and highlights the importance of long-range electric noise in densely packed silicon spin qubits.

The spin-orbit interaction lies at the heart of quantum computation with spin qubits, research on topologically non-trivial states, and various applications in spintronics. Hole spins in Ge/Si core/shell nanowires experience a spin-orbit interaction that has been predicted to be both strong and electrically tunable, making them a particularly promising platform for research in these fields. We experimentally determine the strength of spin-orbit interaction of hole spins confined to a double quantum dot in a Ge/Si nanowire by measuring spin-mixing transitions inside a regime of spin-blockaded transport. We find a remarkably short spin-orbit length of $\sim$65 nm, comparable to the quantum dot length and the interdot distance. We additionally observe a large orbital effect of the applied magnetic field on the hole states, resulting in a large magnetic field dependence of the spin-mixing transition energies. Strikingly, together with these orbital effects, the strong spin-orbit interaction causes a significant enhancement of the $g$-factor with magnetic field.The large spin-orbit interaction strength demonstrated is consistent with the predicted direct Rashba spin-orbit interaction in this material system and is expected to enable ultrafast Rabi oscillations of spin qubits and efficient qubit-qubit interactions, as well as provide a platform suitable for studying Majorana zero modes.

Sub-gap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically non-trivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete sub-gap states in a long nanowire segment. In addition to sub-gap states with a standard magnetic field dependence, we find topologically trivial sub-gap states that are independent of the external magnetic field, i.e. that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates.

Single-spin qubits in semiconductor quantum dots proposed by Loss and DiVincenzo (LD qubits) hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity and tunable coupling to the electric field. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers.

We present a technique for manipulating the nuclear spins and the emission polarization from a single optically active quantum dot. When the quantum dot is tunnel coupled to a Fermi sea, we have discovered a natural cycle in which an electron spin is repeatedly created with resonant optical excitation. The spontaneous emission polarization and the nuclear spin polarization exhibit a bistability. For a sigma(+) pump, the emission switches from sigma(+) to sigma(-) at a particular detuning of the laser. Simultaneously, the nuclear spin polarization switches from positive to negative. Away from the bistability, the nuclear spin polarization can be changed continuously from negative to positive, allowing precise control via the laser wavelength., Comment: 4 pages main article + 7 pages supplement, 4 + 2 figures

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spin-orbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects in the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order. The theory, which is confirmed by numerical transport calculations, allows us to investigate the entire range from the weak to the previously unexplored strong spin-orbit regime, where the spin rotation time is shorter than the momentum relaxation time., Comment: 5 pages, 1 figure, RevTex, submitted to Physical Review Letters

We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a Bose-Einstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state, which can be tested by probing two parts of the spin system separately, but only in a narrow regime around the threshold coupling. Around the resonance, the size of this regime is inversely proportional to the number of spins and shrinks down to zero for infinite systems. This spin entanglement is a non-perturbative effect and is also missed by the mean-field approximation.

The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for fractional quantum Hall states by including correlation effects. A transition of the direction of the spin-polarization is predicted at specific values of the Zeeman energy. We show that these values can be expressed in terms of the pair-correlation function, and thus provide information about the microscopic ground state. We examine the particular examples of the Laughlin wavefunctions and the 5/2-Pfaffian state. We also include effects of the nuclear bath.

We review recent advances on the theory of spin qubits in nanostructures. We focus on four selected topics. First, we show how to form spin qubits in the new and promising material graphene. Afterwards, we discuss spin relaxation and decoherence in quantum dots. In particular, we demonstrate how charge fluctations in the surrounding environment cause spin decay via spin--orbit coupling. We then turn to a brief overview of how one can use electron-dipole spin resonance (EDSR) to perform single spin rotations in quantum dots using an oscillating electric field. The final topic we cover is the spin-spin coupling via spin-orbit interaction which is an alternative to the usual spin-spin coupling via the Heisenberg exchange interaction., Comment: 18 pages, 8 figures, submitted to JPSJ Special Topics: Advances in Spintronics

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear spin bath. Due to the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of ~pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit., Comment: Main text: 4 pages, 3 figures, Supplementary material: 2 pages, 3 figures

Using canonical transformations we diagonalize approximately the Hamiltonian of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows us to obtain the energy dispersion relations and the wavefunctions with good accuracy, even in systems with relatively strong Rashba coupling. With these eigenstates one can calculate the non-equilibrium spin densities induced by applying bias voltages across the sample. We focus on the $z$-component of the spin density, which is related to the spin Hall effect., Comment: 4 pages, 4 figures

We investigate a mesoscopic setup composed of a small electron droplet (dot) coupled to a larger quantum dot (grain) also subject to Coulomb blockade as well as two macroscopic leads used as source and drain. An exotic Kondo ground state other than the standard SU(2) Fermi liquid unambiguously emerges: an SU(4) Kondo correlated liquid. The transport properties through the small dot are analyzed for this regime, through boundary conformal field theory, and allow a clear distinction with other regimes such as a two-channel spin state or a two-channel orbital state., Comment: 13 pages, 3 figures

We report electrical transport measurements through a semiconducting single-walled carbon nanotube (SWNT) with three additional top-gates. At low temperatures the system acts as a double quantum dot with large inter-dot tunnel coupling allowing for the observation of tunnel-coupled molecular states extending over the whole double-dot system. We precisely extract the tunnel coupling and identify the molecular states by the sequential-tunneling line shape of the resonances in differential conductance., Comment: 5 pages, 4 figures

Two quantum dots with tunable mutual tunnel coupling have been embedded in a two-terminal Aharonov-Bohm geometry. Aharonov-Bohm oscillations are investigated in the cotunneling regime. Visibilities of more than 0.8 are measured indicating that phase-coherent processes are involved in the elastic and inelastic cotunneling. An oscillation-phase change of pi is detected as a function of bias voltage at the inelastic cotunneling onset., Comment: 4 pages, 4 figures

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrt{\alpha}$, where $\alpha$ is the coupling strength to the environment. We also explore the calculation of the next order Born approximation: we show that, at the expense of very large computational complexity, interesting physical quantities can be rigorously computed at fourth order using computer algebra, presented completely in an accompanying Mathematica file. We compute the $O(\alpha)$ corrections to the long time behavior of the system density matrix; the result is identical to the reduced density matrix of the equilibrium state to the same order in $\alpha$. All these calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems., Comment: Greatly extended version of short paper cond-mat/0304118. Accompanying Mathematica notebook fop5.nb, available in Source, is an essential part of this work; it gives full details of the fourth-order Born calculation summarized in the text. fop5.nb is prepared in arXiv style (available from Wolfram Research)

We review our recent contributions on shot noise for entangled electrons and spin-polarized currents in novel mesoscopic geometries. We first discuss some of our recent proposals for electron entanglers involving a superconductor coupled to a double dot in the Coulomb blockade regime, a superconductor tunnel-coupled to Luttinger-liquid leads, and a triple-dot setup coupled to Fermi leads. We calculate current and shot noise for spin-polarized currents and entangled/unentangled electron pairs in a beam-splitter geometry with a \textit{local} Rashba spin-orbit (s-o) interaction in the incoming leads. We find \textit{continuous} bunching and antibunching behaviors for the \textit{entangled} pairs -- triplet and singlet -- as a function of the Rashba rotation angle. In addition, we find that unentangled triplets and the entangled one exhibit distinct shot noise. Shot noise for spin-polarized currents shows sizable oscillations as a function of the Rashba phase. This happens only for electrons injected perpendicular to the Rashba rotation axis; spin-polarized carriers along the Rashba axis are noiseless. We find an additional spin rotation for electrons with energies near the crossing of the bands where s-o induced interband coupling is relevant. This gives rise to an additional modulation of the noise for both electron pairs and spin-polarized currents. Finally, we briefly discuss shot noise for a double dot near the Kondo regime., Comment: 35 Kluwer pages, 12 figures - to appear in an upcoming NATO SERIES volume on noise

The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our theoretical proposal for using electron spins in quantum dots as quantum bits. We present single- and two qubit gate mechanisms in laterally as well as vertically coupled quantum dots and discuss the possibility to couple spins in quantum dots via superexchange. We further present the recently proposed schemes for using a single quantum dot as spin-filter and spin read-out/memory device., Comment: 14 pages, 3 figures. To appear in the Proceedins of ``Macroscopic Quantum Coherence and Computing" - MQC2 2000, eds. D. Averin and P. Silvestrini, 2000, Plenum Press, New York

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)

The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant timescales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, parallel controlled-not operations and arbitrary single qubit rotations can be realized. Optical techniques can also be used to measure the spin-state of each quantum dot., Comment: Revised version including a method to realize parallel two-qubit operations

Temperature-dependent magnetization measurements on a series of synthetic ferritin proteins containing from 100 to 3000 Fe(III) ions are used to determine the uncompensated moment of these antiferromagnetic particles. The results are compared with recent theories of macroscopic quantum coherence which explicitly include the effect of this excess moment. The scaling of the excess moment with protein size is consistent with a simple model of finite size effects and sublattice noncompensation., Comment: 4 pages, 3 Postsript figures, 1 table. Submitted to PRB

If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information processing, showing that the famous Shor speedup of integer factoring is just one of a host of important applications for qubits, including cryptography, counterfeit protection, channel capacity enhancement, distributed computing, and others. We review our proposed spin-quantum dot architecture for a quantum computer, and we indicate a variety of first generation materials, optical, and electrical measurements which should be considered. We analyze the efficiency of a two-dot device as a transmitter of quantum information via the ballistic propagation of carriers in a Fermi sea., Comment: 13 pages, latex, one eps figure. Prepared for special issue of J. Mag. Magn. Matl., "Magnetism beyond 2000". Version 2: small revisions and corrections