  We propose to create superposition states of over 100 Strontium atoms being
in a ground state or metastable optical clock state, using the Kerr-type
interaction due to Rydberg state dressing in an optical lattice. The two
components of the superposition can differ by of order 300 eV in energy,
allowing tests of energy decoherence models with greatly improved sensitivity.
We take into account the effects of higher-order nonlinearities, spatial
inhomogeneity of the interaction, decay from the Rydberg state, collective
many-body decoherence, atomic motion, molecular formation and diminishing
Rydberg level separation for increasing principal number.
