Cheng Equation: A Revisit Through Symmetry Analysis

The symmetry analysis of the Cheng Equation is performed. The Cheng Equation is reduced to a first-order equation of either Abel's Equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati Equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng Equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae journa

Continuous loading of 1^{1}S0_{0} calcium atoms into an optical dipole trap

We demonstrate an efficient scheme for continuous trap loading based upon spatially selective optical pumping. We discuss the case of $^{1}$S$_{0}$ calcium atoms in an optical dipole trap (ODT), however, similar strategies should be applicable to a wide range of atomic species. Our starting point is a reservoir of moderately cold ($\approx 300 \mu$K) metastable $^{3}$P$_{2}$-atoms prepared by means of a magneto-optic trap (triplet-MOT). A focused 532 nm laser beam produces a strongly elongated optical potential for $^{1}$S$_{0}$-atoms with up to 350 $\mu$K well depth. A weak focused laser beam at 430 nm, carefully superimposed upon the ODT beam, selectively pumps the $^{3}$P$_{2}$-atoms inside the capture volume to the singlet state, where they are confined by the ODT. The triplet-MOT perpetually refills the capture volume with $^{3}$P$_{2}$-atoms thus providing a continuous stream of cold atoms into the ODT at a rate of $10^7$s$^{-1}$. Limited by evaporation loss, in 200 ms we typically load $5 \times 10^5$ atoms with an initial radial temperature of 85 $\mu$K. After terminating the loading we observe evaporation during 50 ms leaving us with $10^5$ atoms at radial temperatures close to 40 $\mu$K and a peak phase space density of $6.8 \times 10^{-5}$. We point out that a comparable scheme could be employed to load a dipole trap with $^{3}$P$_{0}$-atoms.Comment: 4 pages, 4 figure

Formation of a topological non-Fermi liquid in MnSi

Fermi liquid theory provides a remarkably powerful framework for the description of the conduction electrons in metals and their ordering phenomena, such as superconductivity, ferromagnetism, and spin- and charge-density-wave order. A different class of ordering phenomena of great interest concerns spin configurations that are topologically protected, that is, their topology can be destroyed only by forcing the average magnetization locally to zero. Examples of such configurations are hedgehogs (points at which all spins are either pointing inwards or outwards) or vortices. A central question concerns the nature of the metallic state in the presence of such topologically distinct spin textures. Here we report a high-pressure study of the metallic state at the border of the skyrmion lattice in MnSi, which represents a new form of magnetic order composed of topologically non-trivial vortices. When long-range magnetic order is suppressed under pressure, the key characteristic of the skyrmion lattice - that is, the topological Hall signal due to the emergent magnetic flux associated with their topological winding - is unaffected in sign or magnitude and becomes an important characteristic of the metallic state. The regime of the topological Hall signal in temperature, pressure and magnetic field coincides thereby with the exceptionally extended regime of a pronounced non-Fermi-liquid resistivity. The observation of this topological Hall signal in the regime of the NFL resistivity suggests empirically that spin correlations with non-trivial topological character may drive a breakdown of Fermi liquid theory in pure metals

Waveguide-based OPO source of entangled photon pairs

In this paper we present a compact source of narrow-band energy-time entangled photon pairs in the telecom regime based on a Ti-indiffused Periodically Poled Lithium Niobate (PPLN) waveguide resonator, i.e. a waveguide with end-face dielectric multi-layer mirrors. This is a monolithic doubly resonant Optical Parametric Oscillator (OPO) far below threshold, which generates photon pairs by Spontaneous Parametric Down Conversion (SPDC) at around 1560nm with a 117MHz (0.91 pm)- bandwidth. A coherence time of 2.7 ns is estimated by a time correlation measurement and a high quality of the entangled states is confirmed by a Bell-type experiment. Since highly coherent energy-time entangled photon pairs in the telecom regime are suitable for long distance transmission and manipulation, this source is well suited to the requirements of quantum communication.Comment: 13 page

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.This work has been supported by the Dept. of Science & Technology (DST), Govt. of India under PURSE programme

A versatile source of polarisation entangled photons for quantum network applications

We report a versatile and practical approach for generating high-quality polarization entanglement in a fully guided-wave fashion. Our setup relies on a high-brilliance type-0 waveguide generator producing paired photon at a telecom wavelength associated with an advanced energy-time to polarisation transcriber. The latter is capable of creating any pure polarization entangled state, and allows manipulating single photon bandwidths that can be chosen at will over five orders of magnitude, ranging from tens of MHz to several THz. We achieve excellent entanglement fidelities for particular spectral bandwidths, i.e. 25 MHz, 540 MHz and 100 GHz, proving the relevance of our approach. Our scheme stands as an ideal candidate for a wide range of network applications, ranging from dense division multiplexing quantum key distribution to heralded optical quantum memories and repeaters.Comment: 5 figure

Integrated optical source of polarization entangled photons at 1310 nm

We report the realization of a new polarization entangled photon-pair source based on a titanium-indiffused waveguide integrated on periodically poled lithium niobate pumped by a CW laser at $655 nm$. The paired photons are emitted at the telecom wavelength of $1310 nm$ within a bandwidth of $0.7 nm$. The quantum properties of the pairs are measured using a two-photon coalescence experiment showing a visibility of 85%. The evaluated source brightness, on the order of $10^5$ pairs $s^{-1} GHz^{-1} mW^{-1}$, associated with its compactness and reliability, demonstrates the source's high potential for long-distance quantum communication.Comment: There is a typing mistake in the previous version in the visibility equation. This mistake doesn't change the result