Large energy superpositions via Rydberg dressing

We propose to create superposition states of over 100 strontium atoms 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 an order of 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.