Antibunching in an optomechanical oscillator

We theoretically analyze antibunching of the phonon field in an optomechanical oscillator employ- ing the membrane-in-the-middle geometry. More specifically, a single-mode mechanical oscillator is quadratically coupled to a single-mode cavity field in the regime in which the cavity dissipation is a dominant source of damping, and adiabatic elimination of the cavity field leads to an effective cubic nonlinearity for the mechanics. We show analytically in the weak coupling regime that the mechan- ics displays a chaotic phonon field for small optomechanical cooperativity, whereas an antibunched single-phonon field appears for large optomechanical cooperativity. This opens the door to control of the second-order correlation function of a mechanical oscillator in the weak coupling regime

Convergence of the restricted Nelder-Mead algorithm in two dimensions

The Nelder-Mead algorithm, a longstanding direct search method for unconstrained optimization published in 1965, is designed to minimize a scalar-valued function f of n real variables using only function values, without any derivative information. Each Nelder-Mead iteration is associated with a nondegenerate simplex defined by n+1 vertices and their function values; a typical iteration produces a new simplex by replacing the worst vertex by a new point. Despite the method's widespread use, theoretical results have been limited: for strictly convex objective functions of one variable with bounded level sets, the algorithm always converges to the minimizer; for such functions of two variables, the diameter of the simplex converges to zero, but examples constructed by McKinnon show that the algorithm may converge to a nonminimizing point. This paper considers the restricted Nelder-Mead algorithm, a variant that does not allow expansion steps. In two dimensions we show that, for any nondegenerate starting simplex and any twice-continuously differentiable function with positive definite Hessian and bounded level sets, the algorithm always converges to the minimizer. The proof is based on treating the method as a discrete dynamical system, and relies on several techniques that are non-standard in convergence proofs for unconstrained optimization.Comment: 27 page

Angular Power Spectra of the COBE DIRBE Maps

The angular power spectra of the infrared maps obtained by the DIRBE (Diffuse InfraRed Background Experiment) instrument on the COBE satellite have been obtained by two methods: the Hauser-Peebles method previously applied to the DMR maps, and by Fourier transforming portions of the all-sky maps projected onto a plane. The two methods give consistent results, and the power spectrum of the high-latitude dust emission is C_\ell \propto \ell^{-3} in the range 2 < \ell < 300.Comment: ApJ in press. 15 pages with 5 included figure

Shaping an ultracold atomic soliton in a travelling wave laser beam

An ultracold wave packet of bosonic atoms loaded into a travelling laser wave may form a many-atom soliton.This is disturbed by a homogeneous force field, for example by the inevitable gravitation. The wave packet is accelerated and therefore the laser frequency appears to be chirped in the rest frame of the atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a time dependent nonlinearity coefficient which amounts to a damping or antidamping, respectively. The accelerated packet solution remains a soliton which changes its shape adiabatically. Similarly, an active shaping can be obtained in the force-free case by chirping the laser frequency thus representing a way of coherent control of the soliton form. The experimental consequences are discussed.Comment: 5 pages, Latex, to published in Europhys. Let

Current Approaches to HR Strategies: Inside-Out vs. Outside-In

In an effort to determine the best practices with regard to Human Resource (HR) strategies, we conducted interviews with HR executives knowledgeable about their HR strategies from 20 companies, and gathered archival materials such as the HR strategy documents from 9 of the companies. We found that the content, process, and evaluation of the HR strategies can each be classified as focusing primarily on the HR function, the people of the firm, or the business. We provide some examples of ways that firms can move from an HR focused to a business-focused HR strategy