We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows to measure the coupling strength and temperature and hence a full characterization of the system.Josephson dynamics between weakly coupled macroscopic wave functions have been observed in superconductors [1,2], superfluid Helium [3,4], and recently using Bose-Einstein condensates in double well potentials [5][6][7]. The bosonic Josephson junction (BJJ) is especially interesting, as particle interactions lead to additional dynamical modes such as quantum self trapping or π phase modes [5,8] and finite temperature leads to enhanced fluctuations of the observables [9]. In contrast to other implementations, the BJJ enables complete experimental control over all relevant system parameters such as the coupling strength or relative population together with direct access to the conjugate observables number and phase. Theoretical work has mostly employed a twomode approach to describe the finite temperature equilibrium system and dynamical properties [8,10].One-dimensional (1D) Josephson junctions show a significantly enriched physical behavior, as the two involved wave functions can not be described by single quantum modes any more. The non-interacting 1D junction represents an implementation of the Sine-Gordon Hamiltonian which occurs in widespread areas of physics [11,12]. In the 1D bosonic junction interactions and finite temperature are expected to cause dynamical instabilities of the classical Josephson modes [13]. Whether quasi-static phenomena such as quantum self-trapping persist in 1D is issue of ongoing discussion [14].In this work we realize and fully characterize a onedimensional bosonic Josephson junction using quantum degenerate Bose gases in a tunable double well potential. The finite temperature equilibrium state is marked by the competing effects of thermally driven phase fluctuations and phase locking due to tunnel coupling. Fluctuations of the relative population are < 1 % and can be neglected [9]. We probe the coherence properties of the coupled system by performing matter wave interferometry. Comparing the statistical distribution function of twopoint phase correlations to a stochastic model [10,15], we measure the coupling energy or the temperature of [16,17]. We characterize two-point phase correlations of the system by measuring the statistical properties of the difference of relative phases ∆ϕ(z) = ϕ(z) − ϕ(z ).the system.The experiments are performed in a horizontally orientated double well potential, generated on an atom chip using radio-frequency (RF) induced adiabatic states [18,19]. Different double well paramet...

We present a steepest descent energy minimization scheme for micromagnetics. The method searches on a curve that lies on the sphere which keeps the magnitude of the magnetization vector constant. The step size is selected according to a modified Barzilai-Borwein method. Standard linear tetrahedral finite elements are used for space discretization. For the computation of static hysteresis loops the steepest descent minimizer is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two. The speed up on a graphic processor is 4.8 as compared to the fastest single-core CPU implementation.

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two onedimensional systems, either independent or tunnel-coupled and compare with the Luttinger-liquid theory. PACS numbers: 03.75.Hh,67.85.-d Measurement of fluctuations and their correlations yields important information on regimes and phases of many-body quantum systems [1]. In ultracold atomic systems, these correlations revealed the Mott insulator phase of bosonic [2] and fermionic [3] atoms in optical lattices, they allowed detection of correlated atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates [4] and Hanbury-Brown-Twiss correlation for non-degenerate metastable 3 He and 4 He atoms [5] and in atom lasers [6]. Furthermore, they have allowed studies of dephasing [7] and have been employed as noise thermometer [8,9].

Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically-induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly-nonlocal interactions of optical fields in one dimension.Comment: 16 pages, including appendices and 5 figure

The Schrödinger-Poisson-Xα (S-P-Xα) model is a "local one particle approximation" of the time dependent Hartree-Fock equations. It describes the time evolution of electrons in a quantum model respecting the Pauli principle in an approximate fashion which yields an effective potential that is the difference of the nonlocal Coulomb potential and the third root of the local density. We sketch the formal derivation, existence and uniqueness analysis of the S-P-Xα model with/without an external potential.In this paper we deal with numerical simulations based on a time-splitting spectral method, which was used and studied recently for the nonlinear Schrödinger (NLS) equation in the semiclassical regime and shows much better spatial and temporal resolution than finite difference methods. Extensive numerical results of position density and Wigner measures in 1d, 2d and 3d for the S-P-Xα model with/without an external potential are presented. These results give an insight to understand the interplay between the nonlocal ("weak") and the local ("strong") nonlinearity.

Abstract.We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing, elliptic-elliptic Davey-Stewartson systems and simultaneous blowup at multiple locations in the focusing elliptic-elliptic system. Also the modeling of exact soliton type solutions for the hyperbolic-elliptic (DS2) system is studied.Mathematics Subject Classification. 35Q55, 65M12, 65M70, 76B45.

Abstract. We apply Wigner transform techniques to the analysis of the Dufort-Frankel difference scheme for the Schrödinger equation and to the continuous analogue of the scheme in the case of a small (scaled) Planck constant (semiclassical regime). In this way we are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant tends to zero. The theory developed in this paper is not based on local and global error estimates and does not depend on whether or not caustics develop. Numerical test examples are presented to help interpret the theory and to compare the Dufort-Frankel scheme to other difference schemes for the Schrödinger equation.

We numerically model the evolution of a pair of coherently split quasicondensates. A truly one-dimensional case is assumed, so that the loss of the (initially high) coherence between the two quasicondensates is due to dephasing only, but not due to the violation of integrability and subsequent thermalization (which are excluded from the present model). We confirm the subexponential time evolution of the coherence between two quasicondensates ∝ exp[−(t/t 0 ) 2/3 ], experimentally observed by Hofferberth et al. [Nature 449, 324 (2007)]. The characteristic time t 0 is found to scale as the square of the ratio of the linear density of a quasicondensate to its temperature, and we analyze the full distribution function of the interference contrast and the decay of the phase correlation.