Elastic Multi-Body Interactions on a Lattice

We show that by coupling two hyperfine states of an atom in an optical lattice one can independently control two-, three-, and four-body on-site interactions in a non-perturbative manner. In particular, under typical conditions of current experiments one can have a purely three- or four-body interacting gas of $^{39}$K atoms characterized by on-site interaction shifts of several 100Hz.Comment: 6 pages, 3 figure

Three-Body Interacting Bosons in Free Space

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.Comment: Published version with Supplemental Materia

Ultradilute low-dimensional liquids

We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.Comment: published version + supplemental materia