Superfluidity versus Anderson localization in a dilute Bose gas

We consider the motion of a quasi one dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic, dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples.Comment: 4 pages, 3 figures, final published versio

Bound and resonance states of the nonlinear Schroedinger equation in simple model systems

The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight into the features of stationary bound, scattering and resonance states of the nonlinear Schroedinger equation. For the single delta potential, the influence of the potential strength and the nonlinearity is studied as well as the transition from bound to scattering states. Furthermore, the properties of resonance states for a repulsive delta-shell potential are discussed.Comment: 19 pages, 10 figure

Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasi-bound states of the quantum dot.Comment: 23 pages, 16 figure

Anderson localization of a weakly interacting one dimensional Bose gas

We consider the phase coherent transport of a quasi one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow identified in [T. Paul et al., Phys. Rev. Lett. 98, 210602 (2007)], we focus here on the supersonic stationary regime where Anderson localization exists. We generalize the diffusion formalism of Dorokhov-Mello-Pereyra-Kumar to include interaction effects. It is shown that interactions modify the localization length and also introduce a length scale L* for the disordered region, above which most of the realizations of the random potential lead to time dependent flows. A Fokker-Planck equation for the probability density of the transmission coefficient that takes this new effect into account is introduced and solved. The theoretical predictions are verified numerically for different types of disordered potentials. Experimental scenarios for observing our predictions are discussed.Comment: 20 pages, 13 figure

Tunnelling rates for the nonlinear Wannier-Stark problem

We present a method to numerically compute accurate tunnelling rates for a Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii equation. Our method is based on a sophisticated real-time integration of the complex-scaled Gross-Pitaevskii equation, and it is capable of finding the stationary eigenvalues for the Wannier-Stark problem. We show that even weak nonlinearities have significant effects in the vicinity of very sensitive resonant tunnelling peaks, which occur in the rates as a function of the Stark field amplitude. The mean-field interaction induces a broadening and a shift of the peaks, and the latter is explained by analytic perturbation theory

Multi-barrier resonant tunneling for the one-dimensional nonlinear Schr\"odinger Equation

For the stationary one-dimensional nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-) analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a single quantum well (respectively a double barrier) complicated (looped) structures are observed in the transmission coefficient which can be identified as the result of symmetry breaking similar to the emergence of self-trapping states in double well potentials. Furthermore it is shown that these results are well reproduced by a nonlinear oscillator model based on a small number of resonance eigenfunctions of the corresponding linear system.Comment: 22 pages, 11 figure

The PHENIX Experiment at RHIC

The physics emphases of the PHENIX collaboration and the design and current status of the PHENIX detector are discussed. The plan of the collaboration for making the most effective use of the available luminosity in the first years of RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program available at http://www.rhic.bnl.gov/phenix

A study of one-dimensional transport of Bose-Einstein condensates using exterior complex scaling

We numerically investigate the one-dimensional transport of Bose-Einstein condensates in the context of guided atom lasers using a mean-field description of the condensate in terms of a spatially discretized Gross-Pitaevskii equation. We specifically consider a waveguide configuration in which spatial inhomogeneities and nonvanishing atom-atom interactions are restricted to a spatially localized scattering region of finite extent. We show how the method of smooth exterior complex scaling can be implemented for this particular onfiguration in order to efficiently absorb the outgoing flux within the waveguide. A numerical comparison with the introduction of a complex absorbing potential as well as with the analytically exact elimination of the dynamics of the free non-interacting motion outside the scattering region, giving rise to transparent boundary conditions, clearly confirms the accuracy and efficiency of the smooth exterior complex scaling method

Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method

We study the decay dynamics of an interacting Bose�Einstein condensate in the presence of a metastable trapping potential from which the condensate can escape via tunneling through finite barriers. The time-dependent decay process is reproduced by means of the instantaneous decay rates of the condensate at a given population of the quasi-bound state, which are calculated with the method of complex scaling. Both for the case of a double-barrier potential as well as for the case of a tilted periodic potential, we find pronounced deviations from a monoexponential decay behavior, which would generally be expected in the absence of the atom�atom interaction