2021/02/21 by Nir Hacker, Boris A. Malomed, Hacker, Nir +1
Physics and Astronomy · #Advanced Fiber Laser Technologies #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nonlinear Photonic Systems #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Quantum Gases (cond-mat.quant-gas) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2102.10554
openalex publication_date 2021/02/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We consider a two-component linearly-coupled system with the intrinsic cubic\nnonlinearity and the harmonic-oscillator (HO) confining potential. The system\nmodels binary settings in BEC and optics. In the symmetric system, with the HO\ntrap acting in both components, we consider Josephson oscillations (JO)\ninitiated by an input in the form of the HO's ground state (GS) or dipole mode\n(DM), placed in one component. With the increase of the strength of the\nself-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the\ncomponents takes place in the dynamical JO state. Under still stronger\nnonlinearity, the regular JO initiated by the GS input carry over into a\nchaotic dynamical state. For the DM input, the chaotization happens at smaller\npowers than for the GS, which is followed by SSB at a slightly stronger\nnonlinearity. In the system with the defocusing nonlinearity, SSB does not take\nplace, and dynamical chaos occurs in a small area of the parameter space. In\nthe asymmetric half-trapped system, with the HO potential applied to a single\ncomponent, we first focus on the spectrum of confined binary modes in the\nlinearized system. The spectrum is found analytically in the limits of weak and\nstrong inter-component coupling, and numerically in the general case. Under the\naction of the coupling, the existence region of the confined modes shrinks for\nGSs and expands for DMs. In the full nonlinear system, the existence region for\nconfined modes is identified in the numerical form. They are constructed too by\nmeans of the Thomas-Fermi approximation, in the case of the defocusing\nnonlinearity. Lastly, particular (non-generic) exact analytical solutions for\nconfined modes, including vortices, in one- and two-dimensional asymmetric\nlinearized systems are found. They represent bound states in the continuum.\n