Abstract:
We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly-coupled components, with the confining harmonic-oscillator (HO) potential acting upon one-component, and an expulsive anti -HO potential acting upon the other. The systems can be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by the variational approximation, and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are obtained for the GS and vortex states in the 2D system. Both the trapped and anti-trapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.
Publications:
N. Hacker and B. A. Malomed, Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps, Symmetry 13, 372 (2021);
Trapping wave fields in an expulsive potential by means of linear coupling, Phys. Rev. E 105, 034213 (2022).
