An analytical study of resonant transport of Bose-Einstein condensates

Abstract

We study the stationary nonlinear Schrödinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the transport properties of the system analytically in terms of ingoing and outgoing waves. Resonances and bound states are obtained analytically. The transmitted flux shows a bistable behaviour. Novel crossing scenarios of eigenstates similar to beak--to--beak structures are observed for a repulsive mean-field interaction. It is proven that resonances transform to bound states due to an attractive nonlinearity and vice versa for a repulsive nonlinearity, and the critical nonlinearity for the transformation is calculated analytically. The bound state wavefunctions of the system satisfy an oscillation theorem as in the case of linear quantum mechanics. Furthermore, the implications of the eigenstates on the dymamics of the system are discussed.

RevTeX4, 16 pages, 19 figures

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Cited by in corpus (28)

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• Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
• Nonlinear Spectral Singularities and Lasing Threshold Condition
• Barrier transmission for the one-dimensional nonlinear Schrödinger equation: resonances and transmission profiles
• Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
• Stationary Nonlinear Schrödinger Equation on Simplest Graphs: Boundary conditions and exact solutions
• Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
• Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential
• Transport of ultracold Bose gases beyond the Gross-Pitaevskii description
• Transport and interaction blockade of cold bosonic atoms in a triple-well potential
• The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions
• Resonance States and Quantum Tunneling of Bose Einstein condensates in a 3D shallow trap
• Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials
• Nonlinear Scattering of a Bose-Einstein Condensate on a Rectangular Barrier
• Stationary waves on nonlinear quantum graphs II: Application of canonical perturbation theory in basic graph structures
• Multiple-scale analysis for resonance reflection by a one-dimensional rectangular barrier in the Gross-Pitaevskii problem
• Multi-barrier resonant tunneling for the one-dimensional nonlinear Schrödinger Equation
• Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap
• Quantum Scattering States in a Nonlinear Coherent Medium
• Transmission resonances in above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential
• Realization of the driven nonlinear Schrödinger equation with stationary light
• Barrier transmission for the Nonlinear Schrödinger Equation: Surprises of nonlinear transport
• Power dependent switching of nonlinear trapping by local photonic potentials
• Higher order transmission resonances in above-barrier reflection of ultra-cold atoms
• Stationary transport above the critical velocity in a one-dimensional superflow past an obstacle