Entanglement, Non-linear Dynamics, and the Heisenberg Limit

We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a $N$ qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle $\theta$. The analysis therefore singles out the class of entangled states which are {\it useful} to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the non-linear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.Comment: Phys. Rev. Lett. 102, 100401 (2009

Phase Estimation With Interfering Bose-Condensed Atomic Clouds

We investigate how to estimate from atom-position measurements the relative phase of two Bose-Einstein condensates released from a double-well potential. We demonstrate that the phase estimation sensitivity via the fit of the average density to the interference pattern is fundamentally bounded by shot noise. This bound can be overcome by estimating the phase from the measurement of $\sqrt N$ (or higher) correlation function. The optimal estimation strategy requires the measurement of the $N$-th order correlation function. We also demonstrate that a second estimation method -- based on the detection of the center of mass of the interference pattern -- provides sub shot-noise sensitivity. Yet, the implementation of both protocols might be experimentally challenging.Comment: 4 pages, 2 figure

Analytical Results for the Statistical Distribution Related to Memoryless Deterministic Tourist Walk: Dimensionality Effect and Mean Field Models

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding \mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial non-periodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parameterized by the normalized incomplete beta function I_d = I_{1/4}[1/2,(d+1)/2]. The joint distribution S_{\mu,d}^{(N)}(t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is: S_{1,d}^{(\infty)}(t,p) = [\Gamma(1+I_d^{-1}) (t+I_d^{-1})/\Gamma(t+p+I_d^{-1})] \delta_{p,2}, where t=0,1,2,...,\infty, \Gamma(z) is the gamma function and \delta_{i,j} is the Kronecker's delta. The mean field models are random link model, which corresponds to d \to \infty, and random map model which, even for \mu = 0, presents non-trivial cycle distribution [S_{0,rm}^{(N)}(p) \propto p^{-1}]: S_{0,rm}^{(N)}(t,p) = \Gamma(N)/\{\Gamma[N+1-(t+p)]N^{t+p}\}. The fundamental quantities are the number of explored points n_e=t+p and I_d. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.Comment: 9 pages and 4 figure

Genomic and non-genomic effects of androgens in the cardiovascular system: clinical implications

The principle steroidal androgens are testosterone and its metabolite 5α-dihydrotestosterone (DHT), which is converted from testosterone by the enzyme 5α-reductase. Through the classic pathway with androgens crossing the plasma membrane and binding to the androgen receptor (AR) or via mechanisms independent of the ligand-dependent transactivation function of nuclear receptors, testosterone induces genomic and non-genomic effects respectively. AR is widely distributed in several tissues, including vascular endothelial and smooth muscle cells. Androgens are essential for many developmental and physiological processes, especially in male reproductive tissues. It is now clear that androgens have multiple actions besides sex differentiation and sexual maturation and that many physiological systems are influenced by androgens, including regulation of cardiovascular function [nitric oxide (NO) release, Ca2+ mobilization, vascular apoptosis, hypertrophy, calcification, senescence and reactive oxygen species (ROS) generation]. This review focuses on evidence indicating that interplay between genomic and non-genomic actions of testosterone may influence cardiovascular function

Phase Sensitivity of a Mach-Zehnder Interferometer

The best performance of a Mach-Zehnder interferometer is achieved with the input state |N_T/2 + 1>|N_T/2-1 > + |N_T/2 - 1>|N_T/2+1>, being N_T the total number of atoms/photons. This gives: i) a phase-shift error confidence C_{68%}=2.67/N_T with ii) a single interferometric measurement. Different input quantum states can achieve the Heisenberg scaling ~ 1/N_T but with higher prefactors and at the price of a statistical analysis of two or more independent measurements.Comment: 4 figure

Was the GLE on May 17, 2012 linked with the M5.1-class flare the first in the 24th solar cycle?

On May 17, 2012 an M5.1-class flare exploded from the sun. An O-type coronal mass ejection (CME) was also associated with this flare. There was an instant increase in proton flux with peak at $\geq 100$ MeV, leading to S2 solar radiation storm level. In about 20 minutes after the X-ray emission, the solar particles reached the Earth.It was the source of the first (since December 2006) ground level enhancement (GLE) of the current solar cycle 24. The GLE was detected by neutron monitors (NM) and other ground based detectors. Here we present an observation by the Tupi muon telescopes (Niteroi, Brazil, $22^{0}.9 S$, $43^{0}.2 W$, 3 m above sea level) of the enhancement of muons at ground level associated with this M5.1-class solar flare. The Tupi telescopes registered a muon excess over background $\sim 20\%$ in the 5-min binning time profile. The Tupi signal is studied in correlation with data obtained by space-borne detectors (GOES, ACE), ground based neutron monitors (Oulu) and air shower detectors (the IceTop surface component of the IceCube neutrino observatory). We also report the observation of the muon signal possibly associated with the CME/sheath striking the Earth magnetosphere on May 20, 2012. We show that the observed temporal correlation of the muon excess observed by the Tupi muon telescopes with solar transient events suggests a real physical connection between them. Our observation indicates that combination of two factors, the low energy threshold of the Tupi muon telescopes and the location of the Tupi experiment in the South Atlantic Anomaly region, can be favorable in the study and detection of the solar transient events. Our experiment provides new data complementary to other techniques (space and ground based) in the study of solar physics.Comment: 9 pages, 10 figure

Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light

We show that the phase sensitivity $\Delta \theta$ of a Mach-Zehnder interferometer fed by a coherent state in one input port and squeezed-vacuum in the other one is i) independent from the true value of the phase shift and ii) can reach the Heisenberg limit $\Delta \theta \sim 1/N_T$, where $N_T$ is the average number of particles of the input states. We also show that the Cramer-Rao lower bound, $\Delta \theta \propto 1/ \sqrt{|\alpha|^2 e^{2r} + \sinh^2r}$, can be saturated for arbitrary values of the squeezing parameter $r$ and the amplitude of the coherent mode $|\alpha|$ by a Bayesian phase inference protocol.Comment: 4 pages, 4 figure

Using nitrogen concentration and isotopic composition in lichens to spatially assess the relative contribution of atmospheric nitrogen sources in complex landscapes

Reactive nitrogen (Nr) is an important driver of global change, causing alterations in ecosystem biodiversity and functionality. Environmental assessments require monitoring the emission and deposition of both the amount and types of Nr. This is especially important in heterogeneous landscapes, as different land-cover types emit particular forms of Nr to the atmosphere, which can impact ecosystems distinctively. Such assessments require high spatial resolution maps that also integrate temporal variations, and can only be feasibly achieved by using ecological indicators. Our aim was to rank land-cover types according to the amount and form of emitted atmospheric Nr in a complex landscape with multiple sources of N. To do so, we measured and mapped nitrogen concentration and isotopic composition in lichen thalli, which we then related to land-cover data. Results suggested that, at the landscape scale, intensive agriculture and urban areas were the most important sources of Nr to the atmosphere. Additionally, the ocean greatly influences Nr in land, by providing air with low Nr concentration and a unique isotopic composition. These results have important consequences for managing air pollution at the regional level, as they provide critical information for modeling Nr emission and deposition across regional as well as continental scales.Supported by project GISA (funded by private companies: GALP, Repsol, APS, AdSA, AICEP, CARBOGAL, EDP, EuroResinas, KIMAXTRA, REN and GENERG; and managed by local authorities: CCDRA, ARSA and Municipalities of Sines, Santiago do Cacém, Grândola, Álcacer do Sal and Odemira. Further support for researchers from FCT-MCTES (SFRH/BPD/75425/2010, SFRH/BPD/109382/2015 and Investigador FCT contract) and EC-H2020 (NitroPortugal 692331)