Matter Wave Analog of a Fiber-Optic Gyroscope

Confining the propagating wavepackets of an atom interferometer inside a waveguide can substantially reduce the size of the device while preserving high sensitivity. We have realized a two-dimensional Sagnac atom interferometer in which Bose-condensed $^{87}$Rb atoms propagate within a tight waveguide formed by a collimated laser beam, a matter wave analog of the fiber optic gyro (FOG). The condensate is split, reflected, and recombined with a series of Bragg pulses while the waveguide moves transversely so that the wavepacket trajectories enclose an area. Delta-kick cooling is used to prepare low-density atomic wavepackets with a temperature of \SI{3}{\nano \kelvin}. The low density reduces the impact of interatomic interactions, while the low temperature limits the expansion of the wavepacket during the interferometer cycle. The effective enclosed area is $0.8 \text{mm}^2$ with an average fringe contrast of 20\% and underlying contrast up to 60\%. The main source of the reduced average contrast is phase noise caused by mechanical vibrations of the optical components. We present the first measurement of Allan deviation for such an atom rotation sensor, showing that the interferometer phase noise falls with averaging time $\tau$ as $\tau^{-1/2}$ for $\tau$ up to 10,000 seconds. The statistical noise falls below the Earth rotation rate after 30 minutes of averaging.