  The Sagnac interferometry has been widely used to measure rotation frequency.
Beyond the conventional single-particle Sagnac interferometry, we propose an
atomic Sagnac interferometry via multi-particle entangled states. In our
scheme, an ensemble of entangled two-state Bose atoms are moved in a ring by a
state-dependent rotating potential and then are recombined for interference via
Ramsey pulses after a specific time determined by the state-dependent rotating
potential. The ultimate rotation sensitivity can be improved to the Heisenberg
limit if the initial internal degrees of freedom are entangled. By implementing
parity measurement, the ultimate measurement precision can be saturated and the
achieved measurement precisions approach to the Heisenberg limit. Our results
provide a promising way to exploit many-body quantum entanglement in precision
metrology of rotation sensing.
