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Physics Letters A

Confinement of bright matter-wave solitons on top of a pedestal-shaped potential

Kh. Kh. Ismailov, Bakhtiyor B. Baizakov, F. Kh. Abdullaev

Published Nov 12, 2021• 1 citation
Publisher
DOI
10.1016/j.physleta.2021.127831

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Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons with the main emphasis on the possibility to trap them on top of a pedestal-shaped potential. In numerical simulations, we observed that moving solitons return from the borders of the potential and remain trapped for a sufficiently long time. The shuttle motion of the soliton is accompanied by shedding some amount of matter at each reflection from the borders of the trap, thus reducing its norm. The one- and two- soliton configurations are considered. A discontinuous jump of trajectories of colliding solitons has been discussed. The time-shift observed in a step-like decay of the moving soliton's norm in the two-soliton configuration is linked to the trajectory jump phenomenon. The obtained results can be of interest for the design of new soliton experiments with Bose-Einstein condensates.

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Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons with the main emphasis on the possibility to trap them on top of a pedestal-shaped potential. In numerical simulations, we observed that moving solitons return from the borders of the potential and remain trapped for a sufficiently long time. The shuttle motion of the soliton is accompanied by shedding some amount of matter at each reflection from the borders of the trap, thus reducing its norm. The one- and two- soliton configurations are considered. A discontinuous jump of trajectories of colliding solitons has been discussed. The time-shift observed in a step-like decay of the moving soliton's norm in the two-soliton configuration is linked to the trajectory jump phenomenon. The obtained results can be of interest for the design of new soliton experiments with Bose-Einstein condensates.
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science—and in physics in particular. Flat-top solitons are a novel type of bright solitons that have not been well explored in pure nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold atoms with spatially modulated repulsive interactions is proposed and shown to support a vast variety of stable flat-top matter-wave solitons, including one-dimensional flat-top fundamental and multipole solitons, and two-dimensional flat-top fundamental and vortex solitons. We demonstrate that by varying the relevant physical parameters (nonlinearity coefficient and chemical potential), the ordinary bright (Gaussian) solitons can transform into the novel flat-top solitons. The (in)stability domains of the flat-top soliton families are checked by means of linear stability analysis and reconfirmed by direct numerical simulations. This model is generic in the contexts of nonlinear optics and Bose–Einstein condensates, which provides direct experimental access to observe the predicted solutions.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.