Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD's) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be extended to the quantum-diffusive limit when the average electron tunneling rate is very large compared to the extra change of the tunneling rate due to the presence of the electron in the dot closer to the PC. We find that in both quantum-jump and quantum-diffusive cases, the conditional dynamics of the CQD system can be described by the stochastic Schrodinger equations for its conditioned state vector if and only if the information carried away from the CQD system by the PC reservoirs can be recovered by the perfect detection of the measurements.

Quantum measurement of coherent tunnelling between quantum dots

We describe the conditional and unconditional dynamics of two coupled quantum dots when one dot is subjected to a measurement of its occupation number by coupling it to a third readout dot via the Coulomb interaction. The readout dot is coupled to source and drain leads under weak bias, and a tunnel current flows through a single bound state when energetically allowed. The occupation of the quantum dot near the readout dot shifts the bound state of the readout dot from a low conducting state to a high conducting state. The measurement is made by continuously monitoring the tunnel current through the readout dot. We show that there is a difference between the time scale for the measurement-induced decoherence between the localized states of the dots, and the time scale on which the system becomes localized due to the measurement.

Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement

We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.

Single-electron measurements with a micromechanical resonator

A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge.

An in situ study of photosynthetic oxygen exchange and electron transport rate in the marine macroalga Ulva lactuca (Chlorophyta)

Direct comparisons between photosynthetic O-2 evolution rate and electron transport rate (ETR) were made in situ over 24 h using the benthic macroalga Ulva lactuca (Chlorophyta), growing and measured at a depth of 1.8 m, where the midday irradiance rose to 400-600 mumol photons m(-2) s(-1). O-2 exchange was measured with a 5-chamber data-logging apparatus and ETR with a submersible pulse amplitude modulated (PAM) fluorometer (Diving-PAM). Steady-state quantum yield ((Fm'-Ft)/Fm') decreased from 0.7 during the morning to 0.45 at midday, followed by some recovery in the late afternoon. At low to medium irradiances (0-300 mumol photons m(-2) s(-1)), there was a significant correlation between O-2 evolution and ETR, but at higher irradiances, ETR continued to increase steadily, while O-2 evolution tended towards an asymptote. However at high irradiance levels (600-1200 mumol photons m-(2) s(-1)) ETR was significantly lowered. Two methods of measuring ETR, based on either diel ambient light levels and fluorescence yields or rapid light curves, gave similar results at low to moderate irradiance levels. Nutrient enrichment (increases in [NO3-], [NH4+] and [HPO42-] of 5- to 15-fold over ambient concentrations) resulted in an increase, within hours, in photosynthetic rates measured by both ETR and O-2 evolution techniques. At low irradiances, approximately 6.5 to 8.2 electrons passed through PS II during the evolution of one molecule of O-2, i.e., up to twice the theoretical minimum number of four. However, in nutrient-enriched treatments this ratio dropped to 5.1. The results indicate that PAM fluorescence can be used as a good indication of the photosynthetic rate only at low to medium irradiances.

Temperature dependence of polaronic transport through single molecules and quantum dots

Motivated by recent experiments on electric transport through single molecules and quantum dots, we investigate a model for transport that allows for significant coupling between the electrons and a boson mode isolated on the molecule or dot. We focus our attention on the temperature-dependent properties of the transport. In the Holstein picture for polaronic transport in molecular crystals the temperature dependence of the conductivity exhibits a crossover from coherent (band) to incoherent (hopping) transport. Here, the temperature dependence of the differential conductance on resonance does not show such a crossover, but is mostly determined by the lifetime of the resonant level on the molecule or dot.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Magnetic polarization currents in double quantum dot devices

We investigate coherent electron transport through a parallel circuit of two quantum dots (QDs), each of which has a single tunable. energy level. Electrons tunnelling via each dot from the left lead interfere with each other at the right lead. It is shown that due to the quantum interference of tunnelling electrons the double QD device is magnetically polarized by coherent circulation of electrons on the closed path through the dots and the leads. By varying the energy level of each dot one can make the magnetic states of the device be up-, non- or down-polarized. It is shown that for experimentally accessible temperatures and applied biases the magnetic polarization currents Should be sufficiently large to observe with current nanotechnology.

Quantum transport and integrability of the Anderson model for a quantum dot with multiple leads

We show that an Anderson Hamiltonian describing a quantum dot connected to multiple leads is integrable. A general expression for the nonlinear conductance is obtained by combining the Bethe ansatz exact solution with Landauer-Buttiker theory. In the Kondo regime, a closed form expression is given for the matrix conductance at zero temperature and when all the leads are close to the symmetric point. A bias-induced splitting of the Kondo resonance is possible for three or more leads. Specifically, for N leads, with each at a different chemical potential, there can be N-1 Kondo peaks in the conductance.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Progress in silicon-based quantum computation

We review progress at the Australian Centre for Quantum Computer Technology towards the fabrication and demonstration of spin qubits and charge qubits based on phosphorus donor atoms embedded in intrinsic silicon. Fabrication is being pursued via two complementary pathways: a 'top-down' approach for near-term production of few-qubit demonstration devices and a 'bottom-up' approach for large-scale qubit arrays with sub-nanometre precision. The 'top-down' approach employs a low-energy (keV) ion beam to implant the phosphorus atoms. Single-atom control during implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure. In contrast, the 'bottom-up' approach uses scanning tunnelling microscope lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. In both cases, surface electrodes control the qubit using voltage pulses, and dual single-electron transistors operating near the quantum limit provide fast read-out with spurious-signal rejection.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Enhanced optical properties of the GaAsN/GaAs quantum-well structure by the insertion of InAs monolayers

Microstructural and optical properties of InAs-inserted and reference single GaAsN/GaAs quantum-well (QW) structures grown by metalorganic chemical vapor deposition were investigated using cross-sectional transmission electron microscopy and photoluminescence (PL). Significant enhancement of PL intensity and a blueshift of PL emission were observed from the InAs-inserted GaAsN/GaAs QW structure, compared with the single GaAsN/GaAs QW structure. Strain compensation and In-induced reduction of N incorporation are suggested to be two major factors affecting the optical properties. (C) 2004 American Institute of Physics.