Effective-range signatures in quasi-1D matter waves: sound velocity and solitons

We investigate ultracold and dilute bosonic atoms under strong transverse harmonic confinement using a 1D modified Gross-Pitaevskii equation (1D MGPE), which accounts for the energy dependence of the two-body scattering amplitude within an effective-range expansion. We study sound waves and solitons of the quasi-1D system, comparing the 1D MGPE results with the 1D GPE ones. We find that when the finite-size nature of the interaction is taken into account, the speed of sound and the density profiles of both dark and bright solitons show relevant quantitative changes with respect to predictions given by the standard 1D GPE.