Equilibrium vortex formation in ultrarapidly rotating two-component Bose-Einstein condensates

Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency \Omega_c is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ?\Omega_c and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.Comment: 7 pages, 7 figure

A detailed study on understanding glycopolymer library and Con A interactions

Synthetic glycopolymers are important natural oligosaccharides mimics for many biological applications. To develop glycopolymeric drugs and therapeutic agents, factors that control the receptor-ligand interaction need to be investigated. A library of well-defined glycopolymers has been prepared by the combination of copper mediated living radical polymerization and CuAAC click reaction via post-functionalization of alkyne-containing precursor polymers with different sugar azides. Employing Concanavalin A as the model receptor, we explored the influence of the nature and densities of different sugars residues (mannose, galactose, and glucose) on the stoichiometry of the cluster, the rate of the cluster formation, the inhibitory potency of the glycopolymers, and the stability of the turbidity through quantitative precipitation assays, turbidimetry assays, inhibitory potency assays, and reversal aggregation assays. The diversities of binding properties contributed by different clustering parameters will make it possible to define the structures of the multivalent ligands and densities of binding epitopes tailor-made for specific functions in the lectin-ligand interaction. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2588–259

Dark pair coherent states of the motion of a trapped ion

We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the X-Y plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly-correlated pair coherent state.Comment: 14 pages, 3 figure

Dynamical Equilibration Across a Quenched Phase Transition in a Trapped Quantum Gas

The formation of an equilibrium quantum state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of non-equilibrium many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously-generated defects, whose emergence obeys a universal scaling law with the quench duration. Much less is known about the ensuing re-equilibrating or "coarse-graining" stage, which is governed by the evolution and interactions of such defects under system-specific and external constraints. In this work we perform a detailed numerical characterization of the entire non-equilibrium process, addressing subtle issues in condensate growth dynamics and demonstrating the quench-induced decoupling of number and coherence growth during the re-equilibration process. Our unique visualizations not only reproduce experimental measurements in the relevant regimes, but also provide valuable information in currently experimentally-inaccessible regimes.Comment: Supplementary Movie Previes: SM-Movie-1: https://youtu.be/3q7-CvuBylg SM-Movie-2: https://youtu.be/-Gymaiv9rC0 SM-Movie-3: https://youtu.be/w-O2SPiw3nE SM-Movie-4: https://youtu.be/P4xGyr4dwK

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure

Spontaneous Crystallization of Skyrmions and Fractional Vortices in the Fast-rotating and Rapidly-quenched Spin-1 Bose-Einstein Condensates

We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on the spin-1 Bose-Einstein condensates. By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions, and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respetively, which can be imaged by using the polarization-dependent phase-contrast method

Nonlinear Decoherence in Quantum State Preparation of a Trapped Ion

We present a nonlinear decoherence model which models decoherence effect caused by various decohereing sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).Comment: 5 pages, Revte