We report an experimental measurement of a light wavelength at which the ac electric polarizability equals zero for 87 Rb atoms in the F = 2 ground hyperfine state. The experiment uses a condensate interferometer both to find this 'tune-out' wavelength and to accurately determine the light polarization for it. The wavelength lies between the D1 and D2 spectral lines at 790.032388(32) nm. The measurement is sensitive to the tensor contribution to the polarizability, which has been removed so that the reported value is the zero of the scalar polarizability. The precision is fifty times better than previous tune-out wavelength measurements. Our result can be used to determine the ratio of matrix elements 5P 3/2 ||d||5S 1/2 / 5P 1/2 ||d||5S 1/2 2 = 1.99221(3), a 100-fold improvement over previous experimental values. New theoretical calculations for the tune-out wavelength and matrix element ratio are presented. The results are consistent with the experiment, with uncertainty estimates for the theory about an order of magnitude larger than the experimental precision.

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...

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Atom interferometers using Bose-Einstein condensates are fundamentally limited by a phase diffusion process that arises from atomic interactions. The Gross-Pitaevskii equation is here used to accurately calculate the diffusion rate for a Bragg interferometer. It is seen to agree with a ThomasFermi approximation at large atom numbers and a perturbative approximation at low atom numbers. The diffusion times obtained are generally longer than the coherence times observed in experiments to date.

Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are thus useful for constraining theory and broadening the application of experimental values. Tune-out wavelength measurements to date have focused on zeros of the scalar polarizability, but in general the vector polarizability also contributes. We show here that combined measurements of the vector and scalar polarizabilities can provide more detailed information about the matrix element ratios, and in particular can distinguish small contributions from the atomic core and the valence tail states. These small contributions are the leading error sources in current parity violation calculations for cesium.2 of 12 that of a more easily measured transition. For instance, Herold et al. improved knowledge of the 6P matrix elements in rubidium by a factor of ten by relating them to the better-known 5P elements [4].While these results demonstrate the utility of tune-out spectroscopy, a challenge is that to some degree the frequency of any single response zero depends on all of the accessible states and matrix elements in the atom [2]. To deal with this, theoretical estimates are used for contributions that are not of direct interest. This introduces additional sources of uncertainty and limits the applicability of the measurements to systems where high-quality theoretical estimates are available.We present here a technique to reduce this dependence on theory. Up to now, most studies have centered on the scalar response of the atom, which can be obtained by averaging over the atomic spin states and/or the optical polarization of the light. However, spin-polarized atoms also have a strong vector response, which can be measured by varying the light polarization and the spin orientation. The effect on the tune-out wavelength was measured in a recent study by Schmidt et al. [7] Like the scalar response, the vector response depends on multiple transition matrix elements. However, these elements combine in a different way for the scalar and vector quantities. We show here that by making joint measurements of both responses, different contributions to the electric polarizability can be experimentally resolved. This can lead to improved accuracy and can provide experimental information about matrix elements that cannot easily be observed directly.Of particular significance, it is possible to independently determine the effects of the atomic core and of the infinite manifold of high-lying valence states. The electric polarizability of the ion...