Quantum liquid of repulsively bound pairs of particles in a lattice

Abstract

Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms---``dimers''---have recently been prepared by Winkler et al. [Nature (London) 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications for the many-body dynamics of the system. We find that the dimer-dimer interaction includes strong on-site repulsion and nearest-neighbor attraction which always dominates over the dimer kinetic energy at low temperatures. The dimers then form incompressible, minimal-surface ``droplets'' of a quantum lattice liquid. For low lattice filling, the effective Hamiltonian can be mapped onto the spin-$1∕2$ $XXZ$ model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.