With the high-temperature superconductors a qualitatively new regime in the phenomenology of type-II superconductivity can be accessed. The key elements governing the statistical mechanics and the dynamics of the vortex system are (dynamic) thermal and quantum fluctuations and (static) quenched disorder. The importance of these three sources of disorder can be quantified by the Ginzburg number Gi =(T, /H, sg ) /2, the quantum resistance Qu =(e /A'i(p"/ski, and the critical current-density ratio j,/jo, with j, and jo denoting the depinning and depairing current densities, respectively (p" is the normal-state resistivity and E = m /M (1 denotes the anisotropy parameter). The material parameters of the oxides conspire to produce a large Ginzburg number Gi -10 and a large quantum resistance Qu -10 ', values which are by orders of magnitude larger than in conventional superconductors, leading to interesting effects such as the melting of the vortex lattice, the creation of new vortex-liquid phases, and the appearance of macroscopic quantum phenomena. Introducing quenched disorder into the system turns the Abrikosov lattice into a vortex glass, whereas the vortex liquid remains a liquid. The terms "glass" and "liquid" are defined in a dynamic sense, with a sublinear response p=BE/Bji c characterizing the truly superconducting vortex glass and a finite resistivity p( j~0))0 being the signature of the liquid phase. The smallness of j,/jo allows one to discuss the influence of quenched disorder in terms of the weak collective pinning theory. Supplementing the traditional theory of weak collective pinning to take into account thermal and quantum fluctuations, as well as the new scaling concepts for elastic media subject to a random potential, this modern version of the weak collective pinning theory consistently accounts for a large number of novel phenomena, such as the broad resistive transition, thermally assisted flux flow, giant and quantum creep, and the glassiness of the solid state. The strong layering of the oxides introduces additional new features into the thermodynamic phase diagram, such as a layer decoupling transition, and modifies the mechanism of pinning and creep in various ways. The presence of strong (correlated) disorder in the form of twin boundaries or columnar defects not only is technologically relevant but also provides the framework for the physical realization of novel thermodynamic phases such as the Bose glass. On a macroscopic scale the vortex system exhibits self-organized criticality, with both the spatial and the temporal scale accessible to experimental investigations.

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A weakly biased normal-metal-superconductor junction is considered as a potential device injecting entangled pairs of quasi-particles into a normal-metal lead. The two-particle states arise from Cooper pairs decaying into the normal lead and are characterized by entangled spin-and orbital degrees of freedom. The separation of the entangled quasi-particles is achieved with a fork geometry and normal leads containing spin-or energy-selective filters. Measuring the current-current cross-correlator between the two normal leads allows to probe the efficiency of the entanglement (cond-mat/0009193).PACS 03.67.Hk,72.70.+m,74.50.+r The nonlocal nature of quantum mechanics has been demonstrated theoretically [1] using entangled pairs of particles several decades ago. Recently, potential applications of this entanglement have been found in quantum cryptography [2], in quantum teleportation [3], and in quantum computing [4]. It is thus necessary to search for practical ways to produce such pairs given a specific interaction between particles. While past experiments have focused on pairs of photons [5] propagating in vacuum, attention is now turning to electronic systems [6], where this entanglement interaction can be stronger while coherence can still be maintained over appreciable distances in mesoscopic conductors. A scheme was recently presented [7] which discussed the entanglement of electrons via the exchange interaction in pairs of quantum dots. Here, we propose a rather robust electronic entanglement scheme based on the Andreev reflection of electrons and holes at the boundary between a normal metal and a superconductor.The basic concept underlying the microscopic description of superconductivity is the formation of Cooper pairs. A normal metal in vicinity to a superconductor bears the trace of this phenomenon through the presence of Bogoliubov quasi-particles, or through the non-vanishing of the Gor'kov Green function [8] F = c k↑ c −k↓ (c kσ denote the usual electron annihilation operators). While in a superconductor F = ∆/λ is a consequence of a nonzero gap parameter ∆ (λ is the pairing potential), the coherence surviving in the adjacent normal metal can be understood through the presence of evanescent Cooper pairs. These involve two electrons with entangled spin-and orbital degrees of freedom, carrying opposite spins in the case of usual s-wave pairing and with kinetic energies above and below the superconductor chemical potential. This proximity effect has been illustrated in several recent experiments [9].In order to detect this entanglement and implement it for applications, it is necessary to achieve a spatial separation between the two constituent electrons. The entanglement apparatus which is proposed here consists of a mesoscopic normal-metal-superconductor (NS) junction with normal leads arranged in a fork geometry (see Fig. 1). Using appropriate spin-or energy-selective filters in the two normal leads the quasi-particle pairs are properly separated and their entanglement can be quantified through a c...

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Unconventional superconductors exhibit an order parameter symmetry lower than the symmetry of the underlying crystal lattice. Recent phase sensitive experiments on YBa2Cu3O7 single crystals have established the d-wave nature of the cuprate materials, thus identifying unambiguously the first unconventional superconductor [1,2]. The sign change in the order parameter can be exploited to construct a new type of s-wave-d-wave-s-wave Josephson junction exhibiting a degenerate ground state and a double-periodic current-phase characteristic. Here we discuss how to make use of these special junction characteristics in the construction of a quantum computer. Combining such junctions together with a usual s-wave link into a SQUID loop we obtain what we call a 'quiet' qubit -a solid state implementation of a quantum bit which remains optimally isolated from its environment.PACS numbers: 85.25. Cp, 85.25.Hv, 89.80.+h Quantum computers take advantage of the inherent parallelism of the quantum state propagation, allowing them to outperform classical computers in a qualitative manner. Although the concept of quantum computation has been introduced quite a while ago [3], wide spread interest has developed only recently when specific algorithms exploiting the character of coherent state propagation have been proposed [4]. Here we deal with the device aspect of quantum computers, which is florishing in the wake of the recent successes achieved on the algorithmic side. Two conflicting difficulties have to be faced by all hardware implementations of quantum computation: while the computer must be scalable and controllable, the device should be almost completely detached from the environment during operation in order to minimize phase decoherence. The most advanced propositions are based on trapped ions [5,6], photons in cavities [7], NMR spectroscopy of molecules [8], and various solid state implementations based on electrons trapped in quantum dots [9], the Coulomb blockade in superconducting junction arrays [10,11], or the flux dynamics in Superconducting Quantum Interference Devices (SQUIDs) [12]. Nanostructured solid state quantum gates offer the attractive feature of large scale integrability, once the limitations due to decoherence can be overcome [13].Here we propose a new device concept for a (quantum) logic gate exploiting the unusual symmetry properties of unconventional superconductors. The basic idea is sketched in Fig. 1: connecting the positive (100) and negative (010) lobes of a d-wave superconductor with a s-wave material produces the famous π-loop with a current carrying ground state characteristic of d-wave symmetry [1]. Here we make use of an alternative geometry and match the s-wave superconductors (S) to the (110) boundaries of the d-wave (D) material. As a consequence, the usual Josephson coupling ∝ (1 − cos φ) vanishes due to symmetry reasons and we arrive at a bistable device, where the leading term in the coupling takes the form E d cos 2φ with minima at φ = ±π/2 (here, φ denotes the gauge invariant phas...

We study the excitation spectrum of strongly correlated lattice bosons for the Mott-insulating phase and for the superfluid phase close to localization. Within a Schwinger-boson mean-field approach we find two gapped modes in the Mott insulator and the combination of a sound mode (Goldstone) and a gapped (Higgs) mode in the superfluid. To make our findings comparable with experimental results, we calculate the dynamic structure factor as well as the linear response to the optical lattice modulation introduced by Stöferle et al. [Phys. Rev. Lett. 92, 130403 (2004)]. We find that the puzzling finite frequency absorption observed in the superfluid phase could be explained via the excitation of the gapped (Higgs) mode. We check the consistency of our results with an adapted f -sum-rule and propose an extension of the experimental technique by Stöferle et al. to further verify our findings.

All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Proposals based on quantum optics naturally emphasize the aspect of optimal isolation [1][2][3], while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques [4][5][6][7][8]. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation [9][10][11], however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev [12], holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer liquid groundstate can be used in the construction of topologically stable qubits and discuss their implementation using Josephson junction arrays.Any quantum computer has to incorporate some fault tolerance as we cannot hope to eliminate all the various sources of decoherence. Amazing progress has been made in the development of quantum error correction schemes [13] which are based on redundant multi-qubit encoding of the quantum data combined with error detection-and recovery steps through appropriate manipulation of the data. Error correction schemes are generic (and hence are applicable to any hardware implementation), but require repeated active interference with the computer during run-time; the delocalization of the data, often in a hierarchical structure, boosts the system size by a factor 10 2 to 10 3 . Delocalization of the quantum information is also at the heart of topological quantum computing [12], however, the stabilization against decoherence is entirely deferred to the hardware level (hence it is tied to the specific implementation) and is achieved passively. In searching for a physical implementation of topological qubits one strives for an extended (many body) quantum system where the Hilbert space of quantum states decomposes into mutually orthogonal sectors, each sector remaining isolated under the action of local perturbations. Choosing the two qubit states from groundstates in different sectors protects these states from unwanted mixing through noise; protection from leakage within the sector has to be secured through a gapped excitation spectrum. As no local operator can interfere with these states, global operators must be found (and implemented) allowing for the manipulation of the qubit state.A promising candidate fulfilling the above requirements is the quantum dimer system [14][15][16]: recent quantum Monte Carlo simulations of the dimer model on a triangular lattice provide evidence for a gapped liquid ...

We show that a two-dimensional atomic mixture of bosons and fermions cooled into their quantum degenerate states and subject to an optical lattice develops a supersolid phase characterized by the simultaneous presence of a nontrivial crystalline order and phase order. This transition is in competition with phase separation. We determine the phase diagram of the system and propose an experiment allowing for the observation of the supersolid phase.