  We investigate the effects of stimulated scattering of optical lattice
photons on atomic coherence times in a state-of-the art ${}^{87}\mathrm{Sr}$
optical lattice clock. Such scattering processes are found to limit the
achievable coherence times to less than 12 s (corresponding to a quality factor
of $1 \times 10^{16}$), significantly shorter than the predicted 145(40) s
lifetime of ${}^{87}\mathrm{Sr}$'s excited clock state. We suggest that
shallow, state-independent optical lattices with increased lattice constants
can give rise to sufficiently small lattice photon scattering and motional
dephasing rates as to enable coherence times on the order of the clock
transition's natural lifetime. Not only should this scheme be compatible with
the relatively high atomic density associated with Fermi-degenerate gases in
three-dimensional optical lattices, but we anticipate that certain properties
of various quantum states of matter can be used to suppress dephasing due to
tunneling.
