Collective Dynamics of Bose--Einstein Condensates in Optical Cavities

Recent experiments on Bose--Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system -- superradiance. The time dependent nature of these experiments demands consideration of collective dynamics. Here we establish a rich phase diagram, accessible by quench experiments, with distinct regimes of dynamics separated by non-equilibrium phase transitions. We include the key effects of cavity leakage and the back-reaction of the cavity field on the condensate. Proximity to some of these phase boundaries results in critical slowing down of the decay of many-body oscillations. Notably, this slow decay can be assisted by large cavity losses. Predictions include the frequency of collective oscillations, a variety of multi-phase co-existence regions, and persistent optomechanical oscillations described by a damped driven pendulum. These findings open new directions to study collective dynamics and non-equilibrium phase transitions in matter-light systems.Comment: 5 pages, 5 figure

A study of charge storage in silicon oxide resulting from non-penetrating electron irradiation

Charge storage in silicon dioxide resulting from electron irradiatio

Morphological trends in the molars of fossil rodents from the Fayum Depression, Egypt

While many of the mammalian taxa from the Fayum of Egypt, such as the primates and hyraxes, have been well-studied, little is known about the rodents. Species described to date have all been referred to the endemic family Phiomyidae. Many rodent species from this family have been named and their importance to biogeography addressed, but what this fauna can reveal about the palaeoenvironment of the Fayum has yet to be determined. The study of palaeoenvironmental trends begins with a general examination of species diversity and morphology of the specific rodent lineages. A statistical analysis of available molar measurements of Fayum rodents estimates general size and shape trends and changes in rodent diversity through the stratigraphic sequence of the Fayum. This analysis finds stability in species diversity and an increase in the average body size of taxa using molar length as an estimate of body size. The body size pattern of the rodents is similar to the pattern found among the Fayum primates. Analysis of molar length and width has been performed to test whether these variables could discriminate accurately between taxa. If molars that are too worn to be identified by cusp pattern can be identified confidently based on length and width, more specimens could be included in future analyses and a more accurate depiction of the small mammal fauna attained. Length is significantly different between most of the species, and several species can be identified by length and width alone. Length and width relationships were consistent for species within the same genus.National Science Foundatio

A hill-sliding strategy for initialization of Gaussian clusters in the multidimensional space

A hill sliding technique was devised to extract Gaussian clusters from the multivariate probability density estimate of sample data for the first step of iterative unsupervised classification. Each cluster was assumed to posses a unimodal normal distribution. A clustering function proposed distinguished elements of a cluster under formation from the rest in the feature space. Initial clusters were extracted one by one according to the hill sliding tactics. A dimensionless cluster compactness parameter was proposed as a universal measure of cluster goodness and used satisfactorily in test runs with LANDSAT multispectral scanner data. The normalized divergence, defined by the cluster divergence divided by the entropy of the entire sample data, was utilized as a general separability measure between clusters. An overall clustering objective function was set forth in terms of cluster covariance matrices, from which the cluster compactness measure could be deduced. Minimal improvement of initial data partitioning was evaluated by this objective function in eliminating scattered sparse data points. The hill sliding clustering technique developed herein has the potential applicability to decomposition any multivariate mixture distribution into a number of unimodal distributions when an appropriate distribution function to the data set is employed

Polaritons and Pairing Phenomena in Bose--Hubbard Mixtures

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations.Comment: 4 pages, 3 figure

Bayesian inversion for finite fault earthquake source models I—theory and algorithm

The estimation of finite fault earthquake source models is an inherently underdetermined problem: there is no unique solution to the inverse problem of determining the rupture history at depth as a function of time and space when our data are limited to observations at the Earth’s surface. Bayesian methods allow us to determine the set of all plausible source model parameters that are consistent with the observations, our a priori assumptions about the physics of the earthquake source and wave propagation, and models for the observation errors and the errors due to the limitations in our forward model. Because our inversion approach does not require inverting any matrices other than covariance matrices, we can restrict our ensemble of solutions to only those models that are physically defensible while avoiding the need to restrict our class of models based on considerations of numerical invertibility. We only use prior information that is consistent with the physics of the problem rather than some artefice (such as smoothing) needed to produce a unique optimal model estimate. Bayesian inference can also be used to estimate model-dependent and internally consistent effective errors due to shortcomings in the forward model or data interpretation, such as poor Green’s functions or extraneous signals recorded by our instruments. Until recently, Bayesian techniques have been of limited utility for earthquake source inversions because they are computationally intractable for problems with as many free parameters as typically used in kinematic finite fault models. Our algorithm, called cascading adaptive transitional metropolis in parallel (CATMIP), allows sampling of high-dimensional problems in a parallel computing framework. CATMIP combines the Metropolis algorithm with elements of simulated annealing and genetic algorithms to dynamically optimize the algorithm’s efficiency as it runs. The algorithm is a generic Bayesian Markov Chain Monte Carlo sampler; it works independently of the model design, a priori constraints and data under consideration, and so can be used for a wide variety of scientific problems. We compare CATMIP’s efficiency relative to several existing sampling algorithms and then present synthetic performance tests of finite fault earthquake rupture models computed using CATMIP

Given-new effects on the duration of gestures and of words in face-to-face dialogue

The given-new contract entails that speakers must distinguish for their addressee whether references are new or already part of their dialogue. Past research had found that, in a monologue to a listener, speakers shortened repeated words. However, the notion of the given-new contract is inherently dialogic, with an addressee and the availability of co-speech gestures. Here, two face-to-face dialogue experiments tested whether gesture duration also follows the given-new contract. In Experiment 1, four experimental sequences confirmed that when speakers repeated their gestures, they shortened the duration significantly. Experiment 2 replicated the effect with spontaneous gestures in a different task. This experiment also extended earlier results with words, confirming that speakers shortened their repeated words significantly in a multimodal dialogue setting, the basic form of language use. Because words and gestures were not necessarily redundant, these results offer another instance in which gestures and words independently serve pragmatic requirements of dialogue

Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors

We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point correlation function, which exhibits a new kind of universal behavior characteristic of disordered conductors. Systems with orthogonal and symplectic symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of Oxford), to appear in Phys. Rev. B (Rapid Communication

Ising Deconfinement Transition Between Feshbach-Resonant Superfluids

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group (DMRG) and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.Comment: 4 pages, 4 figure