We report on the existence of quantum forces between nearby fragments of correlated matter that result due to the interference effects between the fragments. This effect explains the phenomenon of correlation-assisted tunneling and puts it in a broader context. The magnitude of the reported force depends on the amount of coherence between different locations; it attains a maximum value for fragments in a perfect superfluid state and disappears entirely when the fragments are in the Mott Insulator state. The force can also be explained in terms of the Bohmian quantum potential. We illustrate the implications of this force on the transport of cold atoms through simple potential structures, the triple-well harmonic trap and optical lattices.
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