Linear Trapping Potentials

Abstract

The trapping potential is a necessary ingredient of any setup used in experiments with atomic gases in the BEC state (otherwise, the gas would escape). Similarly, the presence of an effective trap is necessary for building various optical and photonic cavities. Therefore, the analysis of models combining the intrinsic nonlinearity acting in multidimensional settings with the trapping potential is a natural step in the theoretical work. The present chapter aims to summarize basic theoretical results produced by the work in this direction. The results are presented for 2D fundamental (zero-voticity) and vortical states trapped in the HO potential and for similar 3D states trapped in the HO potential, which may be anisotropic. Also considered are two-component 2D states with hidden vorticity, i.e., with opposite vorticities if the two components have equal norms. Stability regions are identified for all these settings. The chapter additionally reports findings for two-component 2D fundamental and vortex states in a linearly coupled system, in which the potential acting on one component is trapping, while the other component is subjected to the action of an expulsive potential. As for experimental results demonstrating the creation of 2D or 3D solitons in trapping potentials, very few of them are available. A recent experimental finding that may be relevant in this respect is the creation of quasi-stable effectively two-dimensional Townes solitons in atomic BEC loaded in a trapping potential [Bakkali-Hassani et al., Phys. Rev. Lett. 127, 023603 (2021)].