Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic

Four-wave mixing near resonance in an atomic vapor can produce relative intensity squeezed light suitable for precision measurements beyond the shot-noise limit. We develop an analytic distributed gain/loss model to describe the competition of mixing and absorption through the non-linear medium. Using a novel matrix calculus, we present closed-form expressions for the degree of relative intensity squeezing produced by this system. We use these theoretical results to analyze experimentally measured squeezing from a $^{85}$Rb vapor and demonstrate the analytic model's utility as an experimental diagnostic.Comment: 10 pages, 5 figure

Quantum Estimation of Parameters of Classical Spacetimes

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves using the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.Comment: 23 pages. This article supersedes arXiv:1108.522

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.

Determining a quantum state by means of a single apparatus

The unknown state \hrho of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix \hrho and the probabilities of occurrence of the eigenvalues of a single and factorized observable of S+A, so that \hrho can be determined by repeated measurements using a single apparatus. If S and A are spins, it suffices to measure simultaneously their $z$-components after a controlled interaction. The most robust setups are determined in this case, for an initially pure or a completely disordered state of A. They involve an Ising or anisotropic Heisenberg coupling and an external field.Comment: 5 pages revte

Quantum Mechanics and Linearized Gravitational Waves

The interaction of classical gravitational waves (GW) with matter is studied within a quantum mechanical framework. The classical equations of motion in the long wave-length limit is quantized and a Schroedinger equation for the interaction of GW with matter is proposed. Due to its quadrapole nature, the GW interacts with matter by producing squeezed quantum states. The resultant hamiltonian is quite different from one would expect from general principles, however. The interaction of GW with the free particle, the harmonic oscillator and the hydrogen atom is then studied using this hamiltonian.Comment: 24 pages, written in REVTE

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page

Spectral Sensitivity in Ray-Finned Fishes: Diversity, Ecology and Shared Descent

A major goal of sensory ecology is to identify factors that underlie sensory-trait variation. One open question centers on why fishes show the greatest diversity among vertebrates in their capacity to detect color (i.e. spectral sensitivity). Over the past several decades, λmax values (photoreceptor class peak sensitivity) and chromacy (photoreceptor class number) have been cataloged for hundreds of fish species, yet the ecological basis of this diversity and the functional significance of high chromacy levels (e.g. tetra- and pentachromacy) remain unclear. In this study, we examined phylogenetic, physiological and ecological patterns of spectral sensitivity of ray-finned fishes (Actinoptergyii) via a meta-analysis of data compiled from 213 species. Across the fishes sampled, our results indicate that trichromacy is most common, ultraviolet λmax values are not found in monochromatic or dichromatic species, and increasing chromacy, including from tetra- to pentachromacy, significantly increases spectral sensitivity range. In an ecological analysis, multivariate phylogenetic latent liability modeling was performed to analyze correlations between chromacy and five hypothesized predictors (depth, habitat, diet, body coloration, body size). In a model not accounting for phylogenetic relatedness, each predictor with the exception of habitat significantly correlated with chromacy: a positive relationship in body color and negative relationships with body size, diet and depth. However, after phylogenetic correction, the only remaining correlated predictor was depth. The findings of this study indicate that phyletic heritage and depth are important factors in fish spectral sensitivity and impart caution about excluding phylogenetic comparative methods in studies of sensory trait variation

Unknown Quantum States: The Quantum de Finetti Representation

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an ``unknown quantum state'' in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point.Comment: 30 pages, 2 figure

Cultural and economic complementarities of spatial agglomeration in the British television broadcasting industry: Some explorations.

This paper considers the processes supporting agglomeration in the British television broadcasting industry. It compares and contrasts the insights offered by the cultural turn in geography and more conventionally economic approaches. It finds that culture and institutions are fundamental to the constitution of production and exchange relationships and also that they solve fundamental economic problems of coordinating resources under conditions of uncertainty and limited information. Processes at a range of spatial scales are important, from highly local to global, and conventional economics casts some light on which firms are most active and successful

Uncertainty-principle noise in vacuum-tunneling transducers

The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular potential barriers and a barrier in which there is a constant electric field. Practical configurations for reaching the quantum limit in measurements of the position of macroscopic bodies with such a class of transducers are studied