We study under-barrier tunneling for a pair of energetically bound bosonic atoms in an optical lattice with a barrier. We identify the conditions under which this exotic molecule tunnels as a point particle with the coordinate given by the bound pair center of mass and discuss the atomic co-tunneling beyond this regime. In particular, we quantitatively analyze resonantly enhanced co-tunneling, where two interacting atoms penetrate the barrier with higher probability than a single atom.
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