Fundamental modes in a waveguide pipe twisted by inverted nonlinear double-well potential

We study the fundamental modes trapped in a rotating ring with the local strength of the linear and nonlinear potentials modulated as V (? ? ?z) and ? V (? ? ?z), respectively, where ? is the azimuthal angle and the modulation pattern is V (?) ?cos2?, which is a double-well profile in the domain of ? ? ? ? < ?. The model, based on the nonlinear Schr?dinger equation with periodic boundary conditions, applies to light propagation in a twisted waveguiding pipe, and to a Bose?Einstein condensate loaded into a toroidal trap under the action of a rotating ?-out-of-phase linear potential and nonlinear pseudopotential, induced by means of a rotating optical field and the Feshbach resonance, respectively. In the case of self-focusing, three types of fundamental trapped modes are identified, one symmetric and two asymmetric. This is different from the recently considered setting with purely linear or nonlinear rotating potential. In that setting, only two fundamental modes can be found. The shapes and stability of these modes, together with the transitions between them, are investigated in the first rotational Brillouin zone. The symmetry breaking, which transforms the symmetric mode into the asymmetric ones, is strongly affected by the modulation depth and the rotation speed of V (?, ?). The ground-state mode is identified among these three types, and the evolution of an unstable asymmetric mode, which is chiefly trapped in one potential well, features Josephson oscillations between the two wells.

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