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].
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