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 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.

Trapping wave fields in an expulsive potential by means of linear coupling

“…In particular, codimension-one exact solutions of the half-trapped system, corresponding to κ = 0, were recently found in Ref. [56]. In the latter case, all the exact solutions are of the BIC type.…”

“…In fact, the linear version of the system is the most relevant one, as the existence of a trapped states in the system with linearly-coupled components subject to the action of the confining and expulsive potentials is not obvious -in particular, because the straightforward definition of spectra does not directly apply to such a system. A half-trapped linearly-coupled system, including the trapping HO potential in one component and no potential in the other, was considered recently [56], but, to the best of our knowledge, trapped-antitrapped systems were not addressed before.…”

Controlling Matter-Wave Smooth Positons in Bose–Einstein Condensates

“…Consequently, investigating the distinctive features of matter waves (solitons, breathers, and rogue waves) becomes highly intriguing given their spatial and temporal localization, particularly in the context of BEC experiments. Motivated by these achievements, extensive research has been dedicated to investigating localized matter waves within quasi-onedimensional BECs [17][18][19][20][21][22][23][24]. Furthermore, studies focusing on the variable coefficient NLS equation have unveiled the possibility of manipulating and enhancing these localized profiles through the utilization of inhomogeneity parameters [5][6][7][25][26][27][28][29][30][31].…”