Certainly Unsupervisable States

This paper proposes an abstraction method for compositional synthesis. Synthesis is a method to automatically compute a control program or supervisor that restricts the behaviour of a given system to ensure safety and liveness. Compositional synthesis uses repeated abstraction and simplification to combat the state-space explosion problem for large systems. The abstraction method proposed in this paper finds and removes the so-called certainly unsupervisable states. By removing these states at an early stage, the final state space can be reduced substantially. The paper describes an algorithm with cubic time complexity to compute the largest possible set of removable states. A practical example demonstrates the feasibility of the method to solve real-world problems

Coherent quantum phase slip

A hundred years after discovery of superconductivity, one fundamental prediction of the theory, the coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual to the Josephson effect: whilst the latter is a coherent transfer of charges between superconducting contacts, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations of incoherent phase slip, the CQPS has been only a subject of theoretical study. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors in the vicinity of the superconductor-insulator transition (SIT). Here we report the first direct observation of the CQPS in a strongly disordered indium-oxide (InOx) superconducting wire inserted in a loop, which is manifested by the superposition of the quantum states with different number of fluxes. Similarly to the Josephson effect, our observation is expected to lead to novel applications in superconducting electronics and quantum metrology.Comment: 14 pages, 3 figure

Quantum Measurement and the Aharonov-Bohm Effect with Superposed Magnetic Fluxes

We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\vec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized superposed currents in a superconducting ring and discuss broader implications.Comment: 6 pages, 4 figures; Changes from version 3: corrected typo (not present in versions 1 and 2) in Eq. 8; Changes from version 2: shortened abstract; added refs and material in Section IV. The final publication is available at: http://link.springer.com/article/10.1007/s11128-013-0652-

Quantum phase slip phenomenon in ultra-narrow superconducting nanorings

The smaller the system, typically - the higher is the impact of fluctuations. In narrow superconducting wires sufficiently close to the critical temperature Tc thermal fluctuations are responsible for the experimentally observable finite resistance. Quite recently it became possible to fabricate sub-10 nm superconducting structures, where the finite resistivity was reported within the whole range of experimentally obtainable temperatures. The observation has been associated with quantum fluctuations capable to quench zero resistivity in superconducting nanowires even at temperatures T-->0. Here we demonstrate that in tiny superconducting nanorings the same phenomenon is responsible for suppression of another basic attribute of superconductivity - persistent currents - dramatically affecting their magnitude, the period and the shape of the current-phase relation. The effect is of fundamental importance demonstrating the impact of quantum fluctuations on the ground state of a macroscopically coherent system, and should be taken into consideration in various nanoelectronic applications.Comment: 20 pages, 4 figure

Reversing non-local transport through a superconductor by electromagnetic excitations

Superconductors connected to normal metallic electrodes at the nanoscale provide a potential source of non-locally entangled electron pairs. Such states would arise from Cooper pairs splitting into two electrons with opposite spins tunnelling into different leads. In an actual system the detection of these processes is hindered by the elastic transmission of individual electrons between the leads, yielding an opposite contribution to the non-local conductance. Here we show that electromagnetic excitations on the superconductor can play an important role in altering the balance between these two processes, leading to a dominance of one upon the other depending on the spatial symmetry of these excitations. These findings allow to understand some intriguing recent experimental results and open the possibility to control non-local transport through a superconductor by an appropriate design of the experimental geometry.Comment: 6 pages, 3 figure

Topologically protected quantum bits from Josephson junction arrays

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, while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, 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, 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.Comment: 6 pages, 4 figure

Electrical detection of 31P spin quantum states

In recent years, a variety of solid-state qubits has been realized, including quantum dots, superconducting tunnel junctions and point defects. Due to its potential compatibility with existing microelectronics, the proposal by Kane based on phosphorus donors in Si has also been pursued intensively. A key issue of this concept is the readout of the P quantum state. While electrical measurements of magnetic resonance have been performed on single spins, the statistical nature of these experiments based on random telegraph noise measurements has impeded the readout of single spin states. In this letter, we demonstrate the measurement of the spin state of P donor electrons in silicon and the observation of Rabi flops by purely electric means, accomplished by coherent manipulation of spin-dependent charge carrier recombination between the P donor and paramagnetic localized states at the Si/SiO2 interface via pulsed electrically detected magnetic resonance. The electron spin information is shown to be coupled through the hyperfine interaction with the P nucleus, which demonstrates the feasibility of a recombination-based readout of nuclear spins

Sisyphus cooling and amplification by a superconducting qubit

Laser cooling of the atomic motion paved the way for remarkable achievements in the fields of quantum optics and atomic physics, including Bose-Einstein condensation and the trapping of atoms in optical lattices. More recently superconducting qubits were shown to act as artificial two-level atoms, displaying Rabi oscillations, Ramsey fringes, and further quantum effects. Coupling such qubits to resonators brought the superconducting circuits into the realm of quantum electrodynamics (circuit QED). It opened the perspective to use superconducting qubits as micro-coolers or to create a population inversion in the qubit to induce lasing behavior of the resonator. Furthering these analogies between quantum optical and superconducting systems we demonstrate here Sisyphus cooling of a low frequency LC oscillator coupled to a near-resonantly driven superconducting qubit. In the quantum optics setup the mechanical degrees of freedom of an atom are cooled by laser driving the atom's electronic degrees of freedom. Here the roles of the two degrees of freedom are played by the LC circuit and the qubit's levels, respectively. We also demonstrate the counterpart of the Sisyphus cooling, namely Sisyphus amplification. Parallel to the experimental demonstration we analyze the system theoretically and find quantitative agreement, which supports the interpretation and allows us to estimate system parameters.Comment: 7 pages, 4 figure

Phase-slip induced dissipation in an atomic Bose-Hubbard system

Phase slips play a primary role in dissipation across a wide spectrum of bosonic systems, from determining the critical velocity of superfluid helium to generating resistance in thin superconducting wires. This subject has also inspired much technological interest, largely motivated by applications involving nanoscale superconducting circuit elements, e.g., standards based on quantum phase-slip junctions. While phase slips caused by thermal fluctuations at high temperatures are well understood, controversy remains over the role of phase slips in small-scale superconductors. In solids, problems such as uncontrolled noise sources and disorder complicate the study and application of phase slips. Here we show that phase slips can lead to dissipation for a clean and well-characterized Bose-Hubbard (BH) system by experimentally studying transport using ultra-cold atoms trapped in an optical lattice. In contrast to previous work, we explore a low velocity regime described by the 3D BH model which is not affected by instabilities, and we measure the effect of temperature on the dissipation strength. We show that the damping rate of atomic motion-the analogue of electrical resistance in a solid-in the confining parabolic potential fits well to a model that includes finite damping at zero temperature. The low-temperature behaviour is consistent with the theory of quantum tunnelling of phase slips, while at higher temperatures a cross-over consistent with the transition to thermal activation of phase slips is evident. Motion-induced features reminiscent of vortices and vortex rings associated with phase slips are also observed in time-of-flight imaging.Comment: published in Nature 453, 76 (2008