The present rate of Supernovae

We present and discuss the most recent determination of the rate of Supernovae in the local Universe. A comparison with other results shows a general agreement on the gross values but still significant differences on the values of the rates of various SN rates in different kinds of galaxies. The rate of SNe, used as a probe of Star Formation, confirms the young progenitor scenario for SNII+Ib/c. The increasing diversity of SNe reflects also in the SN yields which may affect the chemical evolution of the Galaxy but, because of the limited statistics, we cannot estimate the contributions of the new subtypes yet. It is also expected that in a few years observational determinations of the SN rates at various look-back times will be available.Comment: 9 pages, Latex, 1 figure, To appear in the proceedings of the conference "The Chemical Evolution of The Milky Way: Stars versus Clusters", eds. F. Matteucci and F. Giovannelli, Vulcano, Italy, September 20-24 199

Superfluids, Fluctuations and Disorder

We present a field-theory description of ultracold bosonic atoms in presence of a disordered external potential. By means of functional integration techniques, we aim to investigate and review the interplay between disordered energy landscapes and fluctuations, both thermal and quantum ones. Within the broken-symmetry phase, up to the Gaussian level of approximation, the disorder contribution crucially modifies both the condensate depletion and the superfluid response. Remarkably, it is found that the ordered (i.e. superfluid) phase can be destroyed also in regimes where the random external potential is suitable for a perturbative analysis. We analyze the simplest case of quenched disorder and then we move to present the implementation of the replica trick for ultracold bosonic systems. In both cases, we discuss strengths and limitations of the reviewed approach, paying specific attention to possible extensions and the most recent experimental outputs.Comment: 18 pages, 1 figures. Accepted as a Review for the special issue "Quantum Optics for Fundamental Quantum Mechanics" in Applied Science

Telecom photon interface of solid-state quantum nodes

Solid-state spins such as nitrogen-vacancy (NV) center are promising platforms for large-scale quantum networks. Despite the optical interface of NV center system, however, the significant attenuation of its zero-phonon-line photon in optical fiber prevents the network extended to long distances. Therefore a telecom-wavelength photon interface would be essential to reduce the photon loss in transporting quantum information. Here we propose an efficient scheme for coupling telecom photon to NV center ensembles mediated by rare-earth doped crystal. Specifically, we proposed protocols for high fidelity quantum state transfer and entanglement generation with parameters within reach of current technologies. Such an interface would bring new insights into future implementations of long-range quantum network with NV centers in diamond acting as quantum nodes.Comment: 10 pages, 5 figure

Thermal field theory of bosonic gases with finite-range effective interaction

We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes account finite-range effects of the inter-atomic potential. Within the formalism of functional integration from the grand canonical partition function we derive beyond-mean-field analytical results which depend on both scattering length and effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including one-loop Gaussian fluctuation. In the case of zero-range effective interaction we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finite-range results are in quite good agreement with recent zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.Comment: 6 pages, 2 figures, added some equation

Shift of the critical temperature in superconductors: a self-consistent approach

Within the Ginzburg-Landau functional framework for the superconducting transition, we analyze the fluctuation-driven shift of the critical temperature. In addition to the order parameter fluctuations, we also take into account the fluctuations of the vector potential above its vacuum. We detail the approximation scheme to include the fluctuating fields contribution, based on the Hartree-Fock-Bogoliubov-Popov framework. We give explicit results for $d=2$ and $d=3$ spatial dimensions, in terms of easily accessible experimental parameters such as the Ginzburg-Levanyuk number $\text{Gi}_{(d)}$, which is related to the width of the critical region where fluctuations cannot be neglected, and the Ginzburg-Landau parameter $\kappa$, defined as the ratio between the magnetic penetration length and the coherence one.Comment: 12 pages, 2 figures. Layout issue with Fig. 1 fixed. Editorially accepted for publication in Scientific Report

Mixed-state quantum transport in correlated spin networks

Quantum spin networks can be used to transport information between separated registers in a quantum information processor. To find a practical implementation, the strict requirements of ideal models for perfect state transfer need to be relaxed, allowing for complex coupling topologies and general initial states. Here we analyze transport in complex quantum spin networks in the maximally mixed state and derive explicit conditions that should be satisfied by propagators for perfect state transport. Using a description of the transport process as a quantum walk over the network, we show that it is necessary to phase correlate the transport processes occurring along all the possible paths in the network. We provide a Hamiltonian that achieves this correlation, and use it in a constructive method to derive engineered couplings for perfect transport in complicated network topologies

Finite-Range Corrections to the Thermodynamics of the One-Dimensional Bose Gas

The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal corrections to this equation of state taking into account finite-range effects of the inter-atomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the one-dimensional Bose gas thermodynamic quantities like pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.Comment: 6 pages, 2 figures, accepted for publication in Physical Review

Experimentally efficient methods for estimating the performance of quantum measurements

Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a well-defined experimental procedure for estimating the distinguishability measure. Here, we propose the average measurement fidelity and error between quantum measurements as distinguishability measures. We present protocols for obtaining bounds on these quantities that are both estimable using experimentally accessible quantities and scalable in the size of the quantum system. We explain why the bounds should be valid in large generality and illustrate the method via numerical examples.Comment: 20 pages, 1 figure. Expanded details and typos corrected. Accepted versio

Correlation of the rate of Type Ia supernovae with the parent galaxy properties: Light and shadows

The identification of the progenitors of Type Ia Supernovae (SNIa) is extremely important in several astrophysical contexts, ranging from stellar evolution in close binary systems to evaluating cosmological parameters. Determining the distribution of the delay times (DTD) of SNIa progenitors can shed light on their nature. In this paper we investigate on the diagnostic capabilities on the DTD of the correlation between the SNIa rate and the parent galaxy properties by examining its systematics with the various parameters at play: simple stellar population models, the adopted description for the star formation history in galaxies, and the way in which the masses of the galaxies are evaluated. We compute models for the correlations of the SNIa rate with the parent galaxy color and specific star formation rate for a variety of input ingredients, and for a few astrophysically motivated DTD laws. The models are compared to the results of three independent observational surveys. We find that the scaling of the SNIa rate with the properties of the parent galaxy is sensitive to all input ingredients mentioned above. This is a severe limitation on the possibility to discriminate alternative DTDs. In addition, current surveys show some discrepancies for the rate measured in the reddest and bluest galaxies, likely due to limited statistics and inhomogeneity of the observations. For galaxies with intermediate colors the rates are in agreement, leading to a robust determination of the productivity of SNIa from stellar populations of $\simeq$ 0.8 events per 1000 \msun. Large stastistics of SNIa events along with accurate measurements of the star formation history in the galaxies are required to derive firm constraints on the DTD. LSST will achieve these results by providing the homogeneous, unbiased and vast database on both SNIa and galaxies.Comment: Astronomy and Astrophysics in press. Includes one more figure in the appendix. Notice the slight change of titl