TY - JOUR

T1 - Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

AU - Hacker, Nir

AU - Malomed, Boris A.

N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/3

Y1 - 2021/3

N2 - 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 carries 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.

AB - 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 carries 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.

KW - Bose-Einstein condensates

KW - Dynamical chaos

KW - Ground states

KW - Josephson oscillations

KW - Perturbation theory

KW - Spontaneous symmetry breaking

KW - Thomas-Fermi approximation

UR - http://www.scopus.com/inward/record.url?scp=85102370134&partnerID=8YFLogxK

U2 - 10.3390/sym13030372

DO - 10.3390/sym13030372

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AN - SCOPUS:85102370134

SN - 2073-8994

VL - 13

SP - 1

EP - 23

JO - Symmetry

JF - Symmetry

IS - 3

M1 - 372

ER -