Abstract
We propose to subject two Bose-Einstein condensates to a periodic
potential, so that one condensate undergoes the Mott-insulator transition
to a state with precisely one atom per lattice site. We show that
photoassociation of heteronuclear molecules within each lattice site
is described by the quantum optical Jaynes-Cummings Hamiltonian.
In analogy with studies of this Hamiltonian with cavity fields and
trapped ions, we are thus able to engineer quantum optical states
of atomic matter wave fields and we are able to reconstruct these
states by quantum state tomography.
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