Pairing in fermionic systems: A quantum information perspective

The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical theory of pairing which would allow to unambiguously characterize and systematically detect paired states. We propose a definition of pairing and develop methods for its detection and quantification applicable to current experimental setups. Pairing is shown to be a quantum correlation different from entanglement, giving further understanding in the structure of highly correlated quantum systems. In addition, we will show the resource character of paired states for precision metrology, proving that the BCS states allow phase measurements at the Heisenberg limit.Comment: 23 pages, 4 figure

Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos

We investigate the probability density of rescaled sum of iterates of sine-circle map within quasi-periodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily to be valid anymore. We discuss here the main characteristics of the central limit behavior of deterministic dynamical systems which exhibit quasi-periodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a q-Gaussian with q<1 as the golden mean value is approached.Comment: 7 pages, 7 figures, 1 tabl

Compensation of Strong Thermal Lensing in High Optical Power Cavities

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors such as Advanced LIGO, we show that strong thermal lenses form in accordance with predictions and that they can be compensated using an intra-cavity compensation plate heated on its cylindrical surface. We show that high finesse ~1400 can be achieved in cavities with internal compensation plates, and that the cavity mode structure can be maintained by thermal compensation. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.Comment: 8 page

Measuring Information Transfer

An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due to common history and input signals. In our new approach, these influences are excluded by appropriate conditioning of transition probabilities. The resulting transfer entropy is able to distinguish driving and responding elements and to detect asymmetry in the coupling of subsystems.Comment: 4 pages, 4 Figures, Revte

Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures

We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{min}$ also depends on the temperature $T$! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a first quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to $T^{-3}$ below.Comment: 12 pages, 5 figures, discussion of results extended, accepted for publication in Phys. Rev.

Realization of low-loss mirrors with sub-nanometer flatness for future gravitational wave detectors

The second generation of gravitational wave detectors will aim at improving by an order of magnitude their sensitivity versus the present ones (LIGO and VIRGO). These detectors are based on long-baseline Michelson interferometer with high finesse Fabry-Perot cavity in the arms and have strong requirements on the mirrors quality. These large low-loss mirrors (340 mm in diameter, 200 mm thick) must have a near perfect flatness. The coating process shall not add surface figure Zernike terms higher than second order with amplitude >0.5 nm over the central 160 mm diameter. The limits for absorption and scattering losses are respectively 0.5 and 5 ppm. For each cavity the maximum loss budget due to the surface figure error should be smaller than 50 ppm. Moreover the transmission matching between the two inputs mirrors must be better than 99%. We describe the different configurations that were explored in order to respect all these requirements. Coatings are done using IBS. The two first configurations based on a single rotation motion combined or not with uniformity masks allow to obtain coating thickness uniformity around 0.2 % rms on 160 mm diameter. But this is not sufficient to meet all the specifications. A planetary motion completed by masking technique has been studied. With simulated values the loss cavity is below 20 ppm, better than the requirements. First experimental results obtained with the planetary system will be presented

Random walks - a sequential approach

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its as- sociated sequential partial sum process under non-standard sampling. The asymptotic behavior differs substantially from the stationary situation, if there is a unit root (random walk component). To obtain meaningful asymptotic results we consider local nonpara- metric alternatives for the drift component. It turns out that the rate of convergence at which the drift vanishes determines whether the asymptotic properties of the monitoring procedure are determined by a deterministic or random function. Further, we provide a theoretical result about the optimal kernel for a given alternative

Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.Comment: 29 pages, 2 figure

Observability and nonlinear filtering

This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability in filter stability is explored. Finally, the results are partially extended to non-compact signal state spaces