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][11][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.A small number of trapped-atom Sagnac interferometers have been demonstrated in the past [14-18], but none have been used to make a quantitative rotation measurement. The largest enclosed areas have been achieved using a linear interferometer that is translated along a direction perpendicular to the interferometer axis [19], but this approach may not be well-suited for inertial measurements in a moving vehicle. Here, we demonstrate a true two-dimensional interferometer configuration in which atoms travel in circular trajectories through a static confining potential. We obtain an effective enclosed area of 0.50 mm 2 , compared to areas of 0.20 mm 2 reported by Wu et al.[15] and 0.35 mm 2 recently obtained by the Los Alamos group [18]. Our approach is readily scalable to weaker traps and multiple orbits by the atoms, making larger areas feasible.Another key advance is the use of dual counterpropagating interferometer measurements. Here, two Sagnac interferometers are implemented at the same time in the same trap, with atoms travelling at opposite velocities over the same paths. This technique was developed for free space interferometers [8], and allows the common-mode rejection of interferometric phases from accelerations, laser noise, background fields, and other effects that can mask the rotation signal. The Sagnac effect itself is differential and can be extracted by comparing the two individual measurements. This technique is likely to be essential for any practical rotation-sensing system, but has not previously been demonstrated in a trapped-atom s...

We theoretically investigate a proposed scheme to use an atomic δ-kicked rotor resonance for high-precision measurements of accelerations and the photon recoil frequency. Although the technique offers rapid scaling of the measurement sensitivity with pulse number, it also features a high sensitivity to initial atomic momentum. We find that for realistic atom sources, the momentum sensitivity significantly limits the achievable precision. We consider several different variations on the technique, but find similar limitations in all cases.

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We present a variant of the time-orbiting potential trap suitable for Bose-Einstein condensate atom interferometers, which provides weak, cylindrically symmetric confinement as well as support for the atoms against gravity. This trapping configuration is well-suited for the implementation of a compact atom interferometer based gyroscope. The trap is made up of six coils, which were produced using photolithographic techniques and take up a modest volume of approximately 1 cubic inch inside a vacuum chamber. The trapping frequencies and thermal characteristics of the trap are presented, showing cylindrical symmetry and scalability of the trapping frequencies from 1 Hz to 8 Hz in the symmetry plane.