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 <i>et al.</i> [Nature 441, 853 (2006)]. We derive an effective Hamiltonian for a lattice loaded with dimers only, and discuss its implications for many-body dynamics of the system. We show that strong on-site repulsion and nearest-neighbor attraction favor clusters of dimers with minimum surface area and uniform, commensurate filling, representing thus incompressible “droplets” of a lattice liquid.

© 2007 Optical Society of America

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