QUROPE Quantum Information Processing and Communication in Europe

We study two many-body systems of bosons interacting via an infinite three-body contact repulsion in a lattice: a pairs quasicondensate induced by correlated hopping and the discrete version of the Pfaffian wave function. We propose to experimentally realize systems characterized by such interaction by means of a proper spin-1 lattice Hamiltonian: spin degrees of freedom are locally mapped into occupation numbers of emerging bosons, in a fashion similar to spin-1/2 and hardcore bosons. Such a system can be realized with ultracold spin-1 atoms in a Mott insulator with a filling factor of 1. The high versatility of these setups allows us to engineer spin-hopping operators breaking the SU(2) symmetry, as needed to approximate interesting bosonic Hamiltonians with three-body hardcore constraint. For this purpose we combine bichromatic spin-independent superlattices and Raman transitions to induce a different hopping rate for each spin orientation. Finally, we illustrate how our setup could be used to experimentally realize the first setup, that is, the transition to a pairs quasicondensed phase of the emerging bosons. We also report on a route toward the realization of a discrete bosonic Pfaffian wave function and list some open problems for reaching this goal.