  We investigate the dynamics of Rydberg electrons excited from the ground
state of ultracold atoms trapped in an optical lattice. We first consider a
lattice comprising an array of double-well potentials, where each double well
is occupied by two ultracold atoms. We demonstrate the existence of molecular
states with equilibrium distances of the order of experimentally attainable
inter-well spacings and binding energies of the order of 10^3 GHz. We also
consider the situation whereby ground-state atoms trapped in an optical lattice
are collectively excited to Rydberg levels, such that the charge-density
distributions of neighbouring atoms overlap. We compute the hopping rate and
interaction matrix elements between highly-excited electrons separated by
distances comparable to typical lattice spacings. Such systems have tunable
interaction parameters and a temperature ~10^{-4} times smaller than the Fermi
temperature, making them potentially attractive for the study and simulation of
strongly correlated electronic systems.
