Leonid I. Glazman

Electron liquids and solids in one dimension

Even though bulk metallic systems contain a very large number of strongly interacting electrons, their properties are well described within Landaus Fermi liquid theory of non-interacting quasiparticles. Although many higher-dimensional systems can be successfully understood on the basis of such non-interacting theories, this is not possible for one-dimensional systems. When confined to narrow channels, electron interaction gives rise to such exotic phenomena as spin–charge separation and the emergence of correlated-electron insulators. Such strongly correlated electronic behaviour has recently been seen in experiments on one-dimensional carbon nanotubes and nanowires, and this behaviour challenges the theoretical description of such systems.

Observation of High Coherence in Josephson Junction Qubits Measured in a Three-Dimensional Circuit QED Architecture

Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20  μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.

Electron spin decoherence in quantum dots due to interaction with nuclei

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.

Revival of the Kondo effect

This is a popular review of some recent investigations of the Kondo effect in a variety of mesoscopic systems. After a brief introduction, experiments are described where a scanning tunneling microscope measures the surroundings of a magnetic impurity on a metal surface. In another set of experiments, Kondo effect creates a number of characteristic features in the electron transport through small electronic devices -- semiconductor quantum dots or single-molecule transistors which can be tuned by applying appropriate gate voltages. The article contains 5 color figures, photo of Jun Kondo, but no equations.

Quantum effects in Coulomb blockade

Abstract We review the quantum interference effects in a system of interacting electrons confined to a quantum dot. The review starts with a description of an isolated quantum dot. We discuss the random matrix theory (RMT) of the one-electron states in the dot, present the universal form of the interaction Hamiltonian compatible with the RMT, and derive the leading corrections to the universal interaction Hamiltonian. Next, we discuss a theoretical description of a dot connected to leads via point contacts. Having established the theoretical framework to describe such an open system, we discuss its transport and thermodynamic properties. We review the evolution of the transport properties with the increase of the contact conductances from small values to values ∼e2/πℏ. In the discussion of transport, the emphasis is put on mesoscopic fluctuations and the Kondo effect in the conductance.

Persistent currents in normal metal rings.

Normally Persistent In superconductors, currents are expected to flow persistently without dissipation. Quantum mechanics predicts that such persistent currents should also exist in normal mesoscopic metal rings. However, the predicted effect is small, which has made the detection of these currents difficult. Bleszynski-Jayich et al. (p. 272; see the Perspective by Birge) have developed a sensitive technique based on a nanomechanical resonator. An array of aluminum rings on the end of a resonator was fabricated to monitor the shift in frequency of the resonator as the rings were threaded with quanta of magnetic-field flux, setting up currents in the rings. In agreement with a theoretical scenario put forward over a decade ago, the results could be described with a model based on non-interacting electrons. A nanomechanical resonator is used to detect weak persistent currents that flow in resistive metal rings Quantum mechanics predicts that the equilibrium state of a resistive metal ring will contain a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. We have developed a technique for detecting persistent currents that allows us to measure the persistent current in metal rings over a wide range of temperatures, ring sizes, and magnetic fields. Measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons.

Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets

Quiet, Please One approach for building quantum computers is based on superconductors with appropriately designed components to control the pairs of charges flowing through the circuits. However, at the single-electron level, required quantum noise—generated by quantum fluctuations and throwing offset charges into the device—presents a real problem in manipulating the delicate quantum states of the qubits. Manucharyan et al. (p. 113) present a clever piece of quantum circuit engineering that can suppress the effect of the quantum noise and allow the quantum circuit to operate without disturbance. Circuit engineering was used to mitigate the effects of quantum noise in superconducting quantum circuits. The promise of single Cooper-pair quantum circuits based on tunnel junctions for metrology and quantum information applications is severely limited by the influence of offset charges: random, slowly drifting microscopic charges inherent in many solid-state systems. By shunting a small junction with the Josephson kinetic inductance of a series array of large-capacitance tunnel junctions, thereby ensuring that all superconducting islands are connected to the circuit by at least one large junction, we have realized a new superconducting artificial atom that is totally insensitive to offset charges. Yet its energy levels manifest the anharmonic structure associated with single Cooper-pair effects, a useful component for solid-state quantum computation.

Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result, the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrödinger equation with twisted boundary conditions.

One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined to a 1D trap. We review existing results for various dynamic correlation functions, in particular the density structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and discuss its impact on the transport properties of 1D systems at finite temperatures. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.

Electron spin evolution induced by interaction with nuclei in a quantum dot

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling. We show that the usual treatment of the problem based on the Markovian approximation is impossible because the correlation time for the nuclear magnetic field seen by the electron spin is itself determined by the flip-flop processes. The decay of the electron spin correlation function is not exponential but rather power (inverse logarithm) law-like. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by hN/A, where N is the number of nuclei inside the dot and A is a hyperfine constant. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.