Ground-state properties of attractive bosons in mesoscopic 1D ring lattices

We consider a one-dimensional Bose-Hubbard model describing attractive ultracold bosons trapped in an M-site ring optical lattice within a variational su(M)-coherent-state approach where the attractive-boson dynamics is reformulated in terms of (modified) discrete nonlinear Schrodinger equations. The delocalized, exact ground state of this model can be shown to be well represented as a Schrodinger-cat-like state by coherently superimposing the space-localized ground states obtained by our variational approach. In this paper we focus on two aspects of such space-localized (semiclassical) ground states. First, we prove that the (space-like) su(M) coherent states involved in our variational approach can be recast as momentum-like su(M) coherent states. Based on this property we show that the momentum-space boson distribution of Schrodinger-cat-like states exhibits unexpected features. Secondly, we study the low-energy modes of the discrete nonlinear Schrodinger equations showing that, for sufficiently small lattices, the ground state of the system exhibits a transition controlled by the model parameters from a single-pulse (localized) soliton mode to the superfluid (delocalized) mode. The nontrivial dependence of this effect on the lattice size is also discussed.