  Sensitive and accurate rotation sensing is a critical requirement for
applications such as inertial navigation [1], north-finding [2], geophysical
analysis [3], and tests of general relativity [4]. One effective technique used
for rotation sensing is Sagnac interferometry, in which a wave is split,
traverses two paths that enclose an area, and then recombined. The resulting
interference signal depends on the rotation rate of the system and the area
enclosed by the paths [5]. Optical Sagnac interferometers are an important
component in present-day navigation systems [6], but suffer from limited
sensitivity and stability. Interferometers using matter waves are intrinsically
more sensitive and have demonstrated superior gyroscope performance [7-9], but
the benefits have not been large enough to offset the substantial increase in
apparatus size and complexity that atomic systems require. It has long been
hoped that these problems might be overcome using atoms confined in a guiding
potential or trap, as opposed to atoms falling in free space [10-12]. This
allows the atoms to be supported against gravity, so a long measurement time
can be achieved without requiring a large drop distance. The guiding potential
can also be used to control the trajectory of the atoms, causing them to move
in a circular loop that provides the optimum enclosed area for a given linear
size [13]. Here we use such an approach to demonstrate a rotation measurement
with Earth-rate sensitivity.
