  Optical lattice clocks can now resolve the height difference below 1 mm
within an atomic ensemble by means of gravitational redshift with integration
over sufficient amount of time. Further improvement in the stability enables
the clocks to resolve the height difference of subsystems within an atomic
ensemble that is conventionally interrogated as a single coherent spin state in
a single Ramsey sequence, resulting in the dephasing of the coherent spin
state. This effect is observable with a clock of a stability of $\lesssim
10^{-21}$ by introducing a single-layer-resolved imaging system for a
three-dimensional optical lattice, and limits the 1 s stability of the clock
around $10^{-19}$ for an atomic ensemble distributing symmetrically for the
three axes, which is also a signal of the decoherence. With atoms in an
entangled state, this can be the first observation of the decoherence of a
quantum state by a gravitational effect, and the suppression of other
systematic shifts to observe this decoherence seems feasible.
