  We propose a method of controlling two- and three-body interactions in an
ultracold Bose gas in any dimension. The method requires us to have two coupled
internal single-particle states split in energy such that the upper state is
occupied virtually but amply during collisions. By varying system parameters
one can switch off the two-body interaction while maintaining a strong
three-body one. The mechanism can be implemented for dipolar bosons in the
bilayer configuration with tunnelling or in an atomic system by using
radio-frequency fields to couple two hyperfine states. One can then aim to
observe a purely three-body-interacting gas, dilute self-trapped droplets, the
paired superfluid phase, Pfaffian state, and other exotic phenomena.
