Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

Abstract

We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO's ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carry over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas-Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

arXiv commentto be published in journal Symmetry (special issue on Symmetry and Mesoscopic Physics)

References in corpus (29)

• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Resonantly Trapped Bound State in the Continuum Laser
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Theory of Nonlinear Matter Waves in Optical Lattices
• Motion of dark solitons in trapped Bose-Einstein condensates
• Macroscopic quantum self-trapping and Josephson oscillations of exciton-polaritons
• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• Solitons in combined linear and nonlinear lattice potentials
• Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates
• Domain walls of relative phase in two-component Bose-Einstein condensates
• Quantized Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity
• "Embedded solitons": solitary waves in resonance with the linear spectrum
• Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations. Application to two-component Bose-Einstein condensates
• Optical Weak Link between Two Spatially Separate Bose-Einstein Condensates
• Numerical Solution of the Two-Dimensional Gross-Pitaevskii Equation for Trapped Interacting Atoms
• A numerical approach to the ground and excited states of a Bose-Einstein condensed gas confined in a completely anisotropic trap
• Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates
• Networks of nonlinear superconducting transmission line resonators
• Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas
• Oscillations of dark solitons in trapped Bose-Einstein condensates
• Dark soliton decay due to trap anharmonicity in atomic Bose-Einstein condensates
• Coherent-perfect-absorber and laser for bound states in a continuum
• Thermalization in a one-dimensional integrable system
• Thermalization of a quantum Newton's cradle in a one-dimensional quasicondensate
• Probing quasi-integrability of the Gross-Pitaevskii equation in a harmonic-oscillator potential
• Dynamical suppression of tunneling and spin switching of a spin-orbit-coupled atom in a double-well trap
• One- and two-dimensional modes in the complex Ginzburg-Landau equation with a trapping potential
• Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions
• Solitons and nonlinear dynamics in dual-core optical fibers