  We present and implement a non-destructive detection scheme for the
transition probability readout of an optical lattice clock. The scheme relies
on a differential heterodyne measurement of the dispersive properties of
lattice-trapped atoms enhanced by a high finesse cavity. By design, this scheme
offers a 1st order rejection of the technical noise sources, an enhanced
signal-to-noise ratio, and an homogeneous atom-cavity coupling. We
theoretically show that this scheme is optimal with respect to the photon shot
noise limit. We experimentally realize this detection scheme in an operational
strontium optical lattice clock. The resolution is on the order of a few atoms
with a photon scattering rate low enough to keep the atoms trapped after
detection. This scheme opens the door to various different interrogations
protocols, which reduce the frequency instability, including atom recycling,
zero-dead time clocks with a fast repetition rate, and sub quantum projection
noise frequency stability.
