Topological px+ipyp_{x}+ip_{y} Superfluid Phase of a Dipolar Fermi Gas in a 2D Optical Lattice

In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological $p_{x}+ip_{y}$ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a 2D square optical lattice with this attractive interaction at low temperatures. The $p_{x}+ip_{y}$ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. In the weak-coupling limit, the p-wave superfluid phase is stable for all filling factors. As the interaction strength increases, it is stable close to filling factors $n=0$ or $n=1$, and phase separation takes place in between. When the interaction strength is above a threshold, the system is phase separated for any $0<n<1$. The transition temperature of the $p_{x}+ip_{y}$ superfluid state is estimated and the implication for experiments is discussed.Comment: 10 pages, 4 figure

Free boson representation of DYℏ(sl^(M+1∣N+1))DY_{\hbar}(\hat{sl} (M+1|N+1)) at level one

We construct a realization of the central extension of super-Yangian double $DY_{\hbar}(\hat{sl}(M+1|N+1))$ at level-one in terms of free boson fields with a continuous parameter.Comment: 9 pages, latex, reference revise

Halo Shape and Relic Density Exclusions of Sommerfeld-Enhanced Dark Matter Explanations of Cosmic Ray Excesses

Dark matter with Sommerfeld-enhanced annihilation has been proposed to explain observed cosmic ray positron excesses in the 10 GeV to TeV energy range. We show that the required enhancement implies thermal relic densities that are too small to be all of dark matter. We also show that the dark matter is sufficiently self-interacting that observations of elliptical galactic dark matter halos exclude large Sommerfeld enhancement for light force carriers. Resonant Sommerfeld enhancement does not modify these conclusions, and the astrophysical boosts required to resolve these discrepancies are disfavored, especially when significant self-interactions suppress halo substructure.Comment: 4 pages, discussion and references added, published versio

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Analytic description of atomic interaction at ultracold temperatures II: Scattering around a magnetic Feshbach resonance

Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$, and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary $l$, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary $l$, (b) rigorous definitions of "broad" and "narrow" resonances of arbitrary $l$ and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.Comment: 13 pages, 4 figure

Robust H∞ control of time-varying systems with stochastic non-linearities: the finite-horizon case

The official published version can be obtained from the link below.This paper is concerned with the robust H∞ control problem for the class of uncertain non-linear discrete time-varying stochastic systems with a covariance constraint. All the system parameters are time-varying and the uncertainties enter into the state matrix. The non-linearities under consideration are described by statistical means and they cover several classes of well-studied non-linearities. The purpose of the addressed problem is to design a dynamic output-feedback controller such that, the H∞ disturbance rejection attenuation level is achieved in the finite-horizon case while the state covariance is not more than an individual upper bound at each time point. An algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that the robust H∞ control problem is solvable if the series of RLMIs is feasible. An illustrative simulation example is given to show the applicability and effectiveness of the proposed algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

An integrated source of broadband quadrature squeezed light

An integrated silicon nitride resonator is proposed as an ultra-compact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing the device. An asymmetric double layer stack waveguide geometry with inverse vertical tapers is proposed for efficient and robust fibre-chip coupling, yielding a simulated total loss of -0.75 dB/facet. We assess the feasibility of the device through a full quantum noise analysis and derive the output squeezing spectrum for intra-cavity pump self-phase modulation. Subject to standard material loss and detection efficiencies, we find that the device holds promises for generating substantial quantum noise squeezing over a bandwidth exceeding 1 GHz. In the low-propagation loss regime, approximately -7 dB squeezing is predicted for a pump power of only 50 mW.Comment: 23 pages, 12 figure

Least-squares finite elements for Stokes problem

A least-squares method based on the first-order velocity-pressure-vorticity formulation for the Stokes problem is proposed. This method leads to a minimization problem rather than to a saddle-point problem. The choice of the combinations of elements is thus not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition. Numerical results are given for the optimal rate of convergence for equal-order interpolations

Quantile Regression Under Random Censoring

No abstract.