A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

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.

Indications of coherence-incoherence crossover in layered metallic transport

For many strongly correlated metals with layered crystal structure the temperature dependence of the interlayer resistance is different to that of the intralayer resistance. We consider a small polaron model which exhibits this behavior, illustrating how the interlayer transport is related to the coherence of quasiparticles within the layers. Explicit results are also given for the electron spectral function, interlayer optical conductivity, and the interlayer magnetoresistance. All these quantities have two contributions: one coherent (dominant at low temperatures) and the other incoherent (dominant at high temperatures).

Non-ideal monitoring of a qubit state using a quantum tunnelling device

We propose a model for non-ideal monitoring of the state of a coupled quantum dot qubit by a quantum tunnelling device. The non-ideality is modelled using an equivalent measurement circuit. This allows realistically available measurement results to be related to the state of the quantum system (qubit). We present a quantum trajectory that describes the stochastic evolution of the qubit state conditioned by tunnelling events (i.e. current) through the device. We calculate and compare the noise power spectra of the current in an ideal and a non-ideal measurement. The results show that when the two qubit dots are strongly coupled the non-ideal measurement cannot detect the qubit state precisely. The limitation of the ideal model for describing a realistic system maybe estimated from the noise spectra.

Enhanced spin injection efficiency in ferromagnet/semiconductor tunnel junctions

Within the ballistic transport picture, we have investigated the spin-polarized transport properties of a ferromagnetic metal/two-dimensional semiconductor (FM/SM) hybrid junction and an FM/FM/SM structure using quantum tunnelling theory. Our calculations indicate explicitly that the low spin injection efficiency (SIE) from an FM into an SM, compared with a ferromagnet/normal metal junction, originates from the mismatch of electron densities in the FM and SM. To enhance the SIE from an FM into an SM, we introduce another FM film between them to form FM/FM/SM double tunnel junctions, in which the quantum interference effect will lead to the current polarization exhibiting periodically oscillating behaviour, with a variation according to the thickness of the middle FM film and/or its exchange energy strength. Our results show that, for some suitable values of these parameters, the SIE can reach a very high level, which can also be affected by the electron density in the SM electrode.

Entanglement of two-mode Bose-Einstein condensates

We investigate the entanglement characteristics of two general bimodal Bose-Einstein condensates-a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and, thus, the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the two modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

The gap equations for spin singlet and triplet ferromagnetic superconductors

We derive gap equations for superconductivity in coexistence with ferromagnetism. We treat singlet and triplet states With either equal spin pairing (ESP) or opposite spin pairing (OSP) states, and study the behaviour of these states as a function of exchange splitting. For the s-wave singlet state we find that our gap equations correctly reproduce the Clogston-Chandrasekhar limiting behaviour and the phase diagram of the Baltensperger-Sarma equation (excluding the FFLO region). The singlet superconducting order parameter is shown to be independent of exchange splitting at zero temperature, as is assumed in the derivation of the Clogston-Chandrasekhar limit. P-wave triplet states of the OSP type behave similarly to the singlet state as a function of exchange splitting. On the other hand, ESP triplet states show a very different behaviour. In particular, there is no Clogston-Chandrasekhar limiting and the superconducting critical temperature, T-C, is actually increased by exchange splitting.

Competition between disorder and exchange splitting in superconducting ZrZn2

We propose a simple picture for the occurrence of superconductivity and the pressure dependence of the superconducting critical temperature, T-SC, in ZrZn2. According to our hypothesis the pairing potential is independent of pressure, but the exchange splitting, E-xc leads to a pressure dependence in the (spin dependent) density of states at the Fermi level, D-sigma (epsilon(F)). Assuming p-wave pairing T-SC is dependent on D-sigma (epsilonF) which ensures that, in the absence of non-magnetic impurities, T-SC decreases as pressure is applied until it reaches a minimum in the paramagnetic state. Disorder reduces this minimum to zero, this gives the illusion that the superconductivity disappears at the same pressure as ferromagnetism does.

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.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

A maximum density rule for surfaces of quasicrystals

Motivated by Bravais' rule, of wide validity for crystals, we introduce a maximum density rule for the surfaces of quasicrystals and use it to determine the 5-, 2- and 3-fold bulk terminations in a geometric icosahedral model of i-AlPdMn and i-AlCuFe that represent surfaces.

The effects of J-gate potential and interfaces on donor exchange coupling in the Kane quantum computer architecture

We calculate the electron exchange coupling for a phosphorus donor pair in silicon perturbed by a J-gate potential and the boundary effects of the silicon host geometry. In addition to the electron-electron exchange interaction we also calculate the contact hyperfine interaction between the donor nucleus and electron as a function of the varying experimental conditions. Donor separation, depth of the P nuclei below the silicon oxide layer and J-gate voltage become decisive factors in determining the strength of both the exchange coupling and hyperfine interaction-both crucial components for qubit operations in the Kane quantum computer. These calculations were performed using an anisotropic effective-mass Hamiltonian approach. The behaviour of the donor exchange coupling as a function of the parameters varied in this work provides relevant information for the experimental design of these devices.

Measuring a photonic qubit without destroying it

Measuring the polarization of a single photon typically results in its destruction. We propose, demonstrate, and completely characterize a quantum nondemolition (QND) scheme for realizing such a measurement nondestructively. This scheme uses only linear optics and photodetection of ancillary modes to induce a strong nonlinearity at the single-photon level, nondeterministically. We vary this QND measurement continuously into the weak regime and use it to perform a nondestructive test of complementarity in quantum mechanics. Our scheme realizes the most advanced general measurement of a qubit to date: it is nondestructive, can be made in any basis, and with arbitrary strength.