Quantum noise and mixedness of a pumped dissipative non-linear oscillator

Evolutions of quantum noise, characterized by quadrature squeezing parameter and Fano factor, and of mixedness, quantified by quantum von Neumann and linear entropies, of a pumped dissipative non-linear oscillator are studied. The model can describe a signal mode interacting with a thermal reservoir in a parametrically pumped cavity with a Kerr non-linearity. It is discussed that the initial pure states, including coherent states, Fock states, and finite superpositions of coherent states evolve into the same steady mixed state as verified by the quantum relative entropy and the Bures metric. It is shown analytically and verified numerically that the steady state can be well approximated by a nonclassical Gaussian state exhibiting quadrature squeezing and sub-Poissonian statistics for the cold thermal reservoir. A rapid increase is found in the mixedness, especially for the initial Fock states and superpositions of coherent states, during a very short time interval, and then for longer evolution times a decrease in the mixedness to the same, for all the initial states, and relatively low value of the nonclassical Gaussian state.Comment: 10 pages, 12 figure

Singular projective varieties and quantization

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This allows for generalization to the case of singular varieties. The set-up is explained in the first part of the contribution. The second part of the contribution is of tutorial nature. Necessary notions, concepts, and results of algebraic geometry appearing in this approach to quantization are explained. In particular, the notions of projective varieties, embeddings, singularities, and quotients appearing in geometric invariant theory are recalled.Comment: 21 pages, 3 figure

Entanglement generation in continuously coupled parametric generators

We investigate a compact source of entanglement. This device is composed of a pair of linearly coupled nonlinear waveguides operating by means of degenerate parametric downconversion. For the vacuum state at the input the generalized squeeze variance and logarithmic negativity are used to quantify the amount of nonclassicality and entanglement of output beams. Squeezing and entanglement generation for various dynamical regimes of the device are discussed.Comment: 6 pages, 7 figure

Effective Hamiltonians in quantum optics: a systematic approach

We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter, dictated by the process under consideration, becomes small, we immediately get a diagonal effective Hamiltonian that correctly represents the dynamics for arbitrary states and long times. We extend the technique to su(3) and su(N), finding the corresponding effective Hamiltonians when some resonance conditions are fulfilled.Comment: 13 Pages, no figures, submitted for publicatio

Actuation of Micro-Optomechanical Systems Via Cavity-Enhanced Optical Dipole Forces

We demonstrate a new type of optomechanical system employing a movable, micron-scale waveguide evanescently-coupled to a high-Q optical microresonator. Micron-scale displacements of the waveguide are observed for milliwatt(mW)-level optical input powers. Measurement of the spatial variation of the force on the waveguide indicates that it arises from a cavity-enhanced optical dipole force due to the stored optical field of the resonator. This force is used to realize an all-optical tunable filter operating with sub-mW control power. A theoretical model of the system shows the maximum achievable force to be independent of the intrinsic Q of the optical resonator and to scale inversely with the cavity mode volume, suggesting that such forces may become even more effective as devices approach the nanoscale.Comment: 4 pages, 5 figures. High resolution version available at (http://copilot.caltech.edu/publications/CEODF_hires.pdf). For associated movie, see (http://copilot.caltech.edu/research/optical_forces/index.htm

Reverse mathematics, well-quasi-orders, and Noetherian spaces

A quasi-order Q induces two natural quasi-orders on P(Q) P(Q) , but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on P(Q) P(Q) preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on P(Q) P(Q) are Noetherian, which means that they contain no infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) P(Q) P(Q) is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA0 over RCA0. To state these theorems in RCA0 we introduce a new framework for dealing with second-countable topological spaces

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Systematic review of methodologies used to assess mastectomy flap viability

BACKGROUND Accurate prediction of mastectomy skin flap viability is vital as necrosis causes significant morbidity, potentially compromising results and delaying oncological management. Traditionally assessed by clinical judgement, a more objective evaluation can be provided using intraoperative imaging modalities. This systematic review aimed to compare all intraoperative techniques for assessment of mastectomy flap viability. METHODS A systematic literature review was performed using MEDLINE and Embase databases. Primary outcomes reported included specificity, sensitivity and predictive values of each test, and mean rates of mastectomy flap necrosis and reoperation. Secondary outcomes included cost analysis. RESULTS Some 18 studies were included. Designs were prospective cohort study (8), retrospective case series (4), prospective case series (3), retrospective case–control study (1), prospective pilot trial (1) and cost analysis study (1). The studies compared indocyanine green angiography (ICGA) (16 studies) and fluorescein dye angiography (FA) (3 studies) with clinical judgement. Sensitivity and specificity were highest for ICGA (5 studies) ranging from 38 to 100 and 68 to 91 per cent respectively. Both methods overpredicted necrosis. Mean rates of flap necrosis and reoperation decreased with ICGA (7·9 and 5·5 per cent respectively) and FA (3 and 0 per cent) compared with clinical judgement (19·4 and 12·9 per cent). Two studies were designed to define numerical parameters corresponding to perfusion using intraoperative techniques. Two studies performed a cost analysis for ICGA; one claimed a cost benefit and the other advocated its use in high‐risk patients only. CONCLUSION ICGA and FA are potentially useful tools for mastectomy flap assessment. However, the predictive accuracy is subject to the specific settings and model of equipment used. Current recommendations support their use in high‐risk patients

First experimental results of very high accuracy centroiding measurements for the neat astrometric mission

NEAT is an astrometric mission proposed to ESA with the objectives of detecting Earth-like exoplanets in the habitable zone of nearby solar-type stars. NEAT requires the capability to measure stellar centroids at the precision of 5e-6 pixel. Current state-of-the-art methods for centroid estimation have reached a precision of about 2e-5 pixel at two times Nyquist sampling, this was shown at the JPL by the VESTA experiment. A metrology system was used to calibrate intra and inter pixel quantum efficiency variations in order to correct pixelation errors. The European part of the NEAT consortium is building a testbed in vacuum in order to achieve 5e-6 pixel precision for the centroid estimation. The goal is to provide a proof of concept for the precision requirement of the NEAT spacecraft. In this paper we present the metrology and the pseudo stellar sources sub-systems, we present a performance model and an error budget of the experiment and we report the present status of the demonstration. Finally we also present our first results: the experiment had its first light in July 2013 and a first set of data was taken in air. The analysis of this first set of data showed that we can already measure the pixel positions with an accuracy of about 1e-4 pixel.Comment: SPIE conference proceeding