Gas-to-soliton transition of attractive bosons on a spherical surface

Abstract

We investigate the ground-state properties of N bosons with attractive zero-range interactions characterized by the scattering length a > 0 and confined to the surface of a sphere of radius R. We present the analytic solution of the problem for N = 2, mean-field analysis for N→∞, and exact diffusion Monte Carlo results for intermediate N. For finite N, we observe a smooth crossover from the uniform state in the limit a/R≫1 (weak attraction) to a localized state at small a/R (strong attraction). With increasing N, this crossover narrows down to a discontinuous transition from the uniform state to a soliton of size ∼R/N. The two states are separated by an energy barrier, tunneling under which is exponentially suppressed at large N. The system behavior is marked by a peculiar competition between space-curvature effects and beyond-mean-field terms, both breaking the scaling invariance of a two-dimensional mean-field theory.