Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply-bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body s-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasi-universal, or strongly non-universal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body s-wave scattering length as, as > 0. In the weakly-to medium-stronglyinteracting regime, one of the states approaches the energy obtained for a hard core interaction model. This state is identified as the energetically lowest-lying "BEC state". Structural properties are also presented.PACS numbers:

We study the ground state properties of a system of N harmonically trapped bosons of mass m interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle E0/N ≈ 2.5N 1/3h ω and two-body contact C2/N ≈ 16N 1/6 mω/h for a Bose gas on resonance, where ω is the trap frequency.

We describe a diabatic protocol to prepare a strongly-interacting Bose-Einstein condensate in a regime where neither an adiabatic ramp nor a direct diabatic quench are desirable. This protocol is expected to achieve a nearly unit population transfer to the strongly-interacting ground state for realistic experimental parameters for 85 Rb. The protocol matches the initial and final density profiles by modifying the trap along with the scattering length during the quench. The protocol should reveal several properties of the strongly-interacting Bose gas, and enable further investigation of beyond mean-field corrections to the Gross-Pitaevskii equation.