Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability representation. The problem of SIC-POVM existence is formulated in terms of symbols of operators associated with a star-product quantization scheme. We show that SIC-POVMs (if they do exist) must obey general rules of the star product, and, starting from this fact, we derive new relations on SIC-projectors. The case of qubits is considered in detail, in particular, the relation between the SIC probability representation and other probability representations is established, the connection with mutually unbiased bases is discussed, and comments to the Lie algebraic structure of SIC-POVMs are presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop "Nonlinearity and Coherence in Classical and Quantum Systems" held at the University "Federico II" in Naples, Italy on December 4, 2009 in honor of Prof. Margarita A. Man'ko in connection with her 70th birthday, minor misprints are corrected in the second versio

The Drinfel'd twisted XYZ model

We construct a factorizing Drinfel'd twist for a face type model equivalent to the XYZ model. Completely symmetric expressions for the operators of the monodromy matrix are obtained.Comment: 15 pages, 4 figures, second preprint no. added, reference [14] added, typos correcte

Divergent diagrams of folds and simultaneous conjugacy of involutions

In this work we show that the smooth classification of divergent diagrams of folds (f(1),..., f(s)) : (R-n, 0) -> (R-n x(...)xR(n), 0) can be reduced to the classification of the s-tuples (p(1)., W) of associated involutions. We apply the result to obtain normal forms when s = 2. We also present a brief discussion on applications of our results to the study of discontinuous vector fields and discrete reversible dynamical systems.12465767

Three-body interactions with cold polar molecules

We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective interaction potentials is based on a microscopic understanding of the underlying molecular physics, and follows from a well controlled and systematic expansion into many-body interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearest-neighbor two-body and three-body interaction. As an illustration, we study the one-dimensional Bose-Hubbard model with dominant three-body interaction and derive its phase diagram.Comment: 8 pages, 4 figure

Effect of phase fluctuation and dephasing on the dynamics of entanglement generation in a correlated emission laser

A detailed study of the effects of phase fluctuation and dephasing on the dynamics of the entanglement generated from a coherently pumped correlated emission laser is presented. It is found that the time evolution of the entanglement is significantly reliant on the phase fluctuation and dephasing, particularly, at early stages of the lasing process. In the absence of external driving radiation, the degree of entanglement and intensity turns out to attain a maximum value just before starting to exhibit oscillation which dies at longer time scale. However, in case the driving mechanism is on, the oscillatory nature disappears due to the additional induced coherent superposition and the degree of entanglement would be larger at steady state. Moreover, the degree of entanglement as predicted by the logarithmic negativity and the Duan-Giedke-Cirac-Zoller criteria exhibits a similar nature when there is no driving radiation, although such a trend is eroded with increasing strength of the pumping radiation at longer time scale. The other important aspect of the phase fluctuation and dephasing is the possibility of relaxing the time at which the maximum entanglement is detected.Comment: 10 pages, 10 figure

Microwave amplification with nanomechanical resonators

Sensitive measurement of electrical signals is at the heart of modern science and technology. According to quantum mechanics, any detector or amplifier is required to add a certain amount of noise to the signal, equaling at best the energy of quantum fluctuations. The quantum limit of added noise has nearly been reached with superconducting devices which take advantage of nonlinearities in Josephson junctions. Here, we introduce a new paradigm of amplification of microwave signals with the help of a mechanical oscillator. By relying on the radiation pressure force on a nanomechanical resonator, we provide an experimental demonstration and an analytical description of how the injection of microwaves induces coherent stimulated emission and signal amplification. This scheme, based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices, and, at the same time, has a high potential to reach quantum limited operation. With a measured signal amplification of 25 decibels and the addition of 20 quanta of noise, we anticipate near quantum-limited mechanical microwave amplification is feasible in various applications involving integrated electrical circuits.Comment: Main text + supplementary information. 14 pages, 3 figures (main text), 18 pages, 6 figures (supplementary information

Guidelines for the monitoring of Rosalia alpina

Copyright Alessandro Campanaro et al. Rosalia alpina (Linnaeus, 1758) is a large longhorn beetle (Coleoptera: Cerambycidae) which is protected by the Habitats Directive and which typically inhabits beech forests characterised by the presence of mature, dead (or moribund) and sun-exposed trees. A revision of the current knowledge on systematics, ecology and conservation of R. alpina is reported. The research was carried out as part of the LIFE MIPP project which aims to find a standard monitoring method for saproxylic beetles protected in Europe. For monitoring this species, different methods were tested and compared in two areas of the Apennines, utilising wild trees, logs and tripods (artificially built with beech woods), all potentially suitable for the reproduction of the species. Even if all methods succeeded in the survey of the target species, these results showed that the use of wild trees outperformed other methods. Indeed, the use of wild trees allowed more adults to be observed and required less intensive labour. However, monitoring the rosalia longicorn on wild trees has the main disadvantage that they can hardly be considered “standard sampling units”, as each tree may be differently attractive to adults. Our results demonstrated that the most important factors influencing the attraction of single trunks were wood volume, sun-exposure and decay stage. Based on the results obtained during the project LIFE MIPP, as well as on a literature review, a standard monitoring method for R. alpina was developed

Entangled Mechanical Oscillators

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations like Schrodinger's cat, which exists in a superposition of alive and dead states entangled with a radioactive nucleus. Such situations are not observed in nature. This may simply be due to our inability to sufficiently isolate the system of interest from the surrounding environment -- a technical limitation. Another possibility is some as-of-yet undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. One system ubiquitous to nature where entanglement has not been previously demonstrated is distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator.Comment: 7 pages, 2 figure

The Calcitonin and Glucocorticoids Combination: Mechanistic Insights into Their Class-Effect Synergy in Experimental Arthritis

PMCID: PMC3564948This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Resolved Sideband Cooling of a Micromechanical Oscillator

Micro- and nanoscale opto-mechanical systems provide radiation pressure coupling of optical and mechanical degree of freedom and are actively pursued for their ability to explore quantum mechanical phenomena of macroscopic objects. Many of these investigations require preparation of the mechanical system in or close to its quantum ground state. Remarkable progress in ground state cooling has been achieved for trapped ions and atoms confined in optical lattices. Imperative to this progress has been the technique of resolved sideband cooling, which allows overcoming the inherent temperature limit of Doppler cooling and necessitates a harmonic trapping frequency which exceeds the atomic species' transition rate. The recent advent of cavity back-action cooling of mechanical oscillators by radiation pressure has followed a similar path with Doppler-type cooling being demonstrated, but lacking inherently the ability to attain ground state cooling as recently predicted. Here we demonstrate for the first time resolved sideband cooling of a mechanical oscillator. By pumping the first lower sideband of an optical microcavity, whose decay rate is more than twenty times smaller than the eigen-frequency of the associated mechanical oscillator, cooling rates above 1.5 MHz are attained. Direct spectroscopy of the motional sidebands reveals 40-fold suppression of motional increasing processes, which could enable reaching phonon occupancies well below unity (<0.03). Elemental demonstration of resolved sideband cooling as reported here should find widespread use in opto-mechanical cooling experiments. Apart from ground state cooling, this regime allows realization of motion measurement with an accuracy exceeding the standard quantum limit.Comment: 13 pages, 5 figure