  The ultimate stability of atomic clocks is limited by the quantum noise of
the atoms. To reduce this noise it has been suggested to use entangled atomic
ensembles with reduced atomic noise. Potentially this can push the stability
all the way to the limit allowed by the Heisenberg uncertainty relation, which
is denoted the Heisenberg limit. In practice, however, entangled states are
often more prone to decoherence, which may prevent reaching this performance.
Here we present an adaptive measurement protocol that in the presence of a
realistic source of decoherence enables us to get near Heisenberg limited
stability of atomic clocks using entangled atoms. The protocol may thus realize
the full potential of entanglement for quantum metrology despite the
detrimental influence of decoherence.
