Rotation measurement using a grating-echo interferometer

We discuss a proof-of-principle measurement of rotation using a grating echo atom interferometer. Cold atoms are launched horizontally across the excitation beams and rotation is measured as a phase shift in the echo signal due to the Sagnac effect. Radiofrequencies for the excitation beams are derived from phase-locked loops, referenced to a Rb clock. These excitation beams are pulsed, counter-propagating, blue-detuned travelling waves, having a small frequency difference ($\delta$) with respect to each other. The experiment requires the application of two such pulses, separated by t=T, with the second pulse having opposite k-vectors to the first. The atomic density grating formed in the vicinity of t=2T is detected by applying a travelling-wave read-out pulse, in the presence of a counter-propagating interrogation pulse, which is detuned from the readout by 10 MHz. The effect of rotation manifests as a phase shift in the beat note between the interrrogation beam and the back-scattered signal. The magnitude of the Sagnac shift is varied by changing the launch velocity of the atomic cloud. Averaging the signal as a function of $\delta$ over T generates a ground-state Ramsey fringe pattern with a shifted central fringe.