Quantum sensitivity limit of a Sagnac hybrid interferometer based on slow-light propagation in ultracold gases

The light-matter-wave Sagnac interferometer based on ultraslow light proposed recently in Zimmer and Fleischhauer, Phys. Rev. Lett. 92, 253201 (2004), is analyzed in detail. In particular the effect of confining potentials is examined and it is shown that the ultraslow light attains a rotational phase shift equivalent to that of a matter wave, if and only if the coherence transfer from light to atoms associated with slow light is associated with a momentum transfer and if an ultracold gas in a ring trap is used. The quantum sensitivity limit of the Sagnac interferometer is determined and the minimum detectable rotation rate calculated. It is shown that the slow-light interferometer allows for a significantly higher signal-to-noise ratio as possible in current matter-wave gyroscopes.