Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential

Abstract

The resonance states and the decay dynamics of the nonlinear Schrödinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed, as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two basis states in terms of a nonlinear, nonhermitian matrix problem.

arXiv comment21 pages, 14 figures

References in corpus (29)

• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Matter-wave interferometry in a double well on an atom chip
• Direct Observation of Second Order Atom Tunnelling
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Wannier-Stark resonances in optical and semiconductor superlattices
• Photonic Bloch oscillations and Zener tunneling in two-dimensional optical lattices
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Noise Thermometry with Two Weakly Coupled Bose-Einstein Condensates
• Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory
• Nonlinear Resonant Transport of Bose Einstein Condensates
• Cold, dilute, trapped bosons as an open quantum system
• Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
• Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement
• Bound and resonance states of the nonlinear Schroedinger equation in simple model systems
• A Primary Noise Thermometer for Ultracold Bose Gases
• Mean-field dynamics of a two-mode Bose-Einstein condensate subject to noise and dissipation
• Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
• Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction
• Complex scaling approach to the decay of Bose-Einstein condensates
• An analytical study of resonant transport of Bose-Einstein condensates
• Barrier transmission for the one-dimensional nonlinear Schrödinger equation: resonances and transmission profiles
• Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances
• Tunnelling rates for the nonlinear Wannier-Stark problem
• Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method
• Statics and dynamics of BEC's in double square well potentials
• Dissipation-driven quantum phase transitions in collective spin systems
• The stationary solutions of G-P equations in double square well
• Nonlinear Dynamics in Double Square Well Potential

Cited by in corpus (25)

• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Exceptional points in the spectra of atoms in external fields
• Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well
• Spectral singularities in PT-symmetric Bose-Einstein condensates
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Dynamical evolutions in non-Hermitian triple-well system with complex potential
• Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{P}\mathcal{T}$-symmetric double-delta trap
• Calculating resonance positions and widths using the Siegert approximation method
• Exceptional points in bichromatic Wannier-Stark systems
• Multi-barrier resonant tunneling for the one-dimensional nonlinear Schrödinger Equation
• Interaction-induced decoherence in non-Hermitian quantum walks of ultracold Bosons
• PT-symmetric gain and loss in a rotating Bose-Einstein condensate
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Closed system approach to open systems: Tunneling decay of interacting cold bosons in an optical lattice
• Transmission resonances in above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates
• Matter-wave scattering on a BEC in a double-well potential
• Trapping of quantum particles and light beams by switchable potential wells
• Higher order transmission resonances in above-barrier reflection of ultra-cold atoms
• Matter wave propagation above a step potential within the cubic-nonlinear Schrödinger equation