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We have built an atom interferometer that can measure , the local acceleration due to gravity, with a resolution of after a single measurement cycle, after 1 min and after two days of integration time. The difference between our value for and one obtained by a falling corner-cube optical interferometer is. The atom interferometer uses velocity-selective stimulated Raman transitions and laser-cooled caesium atoms in an atomic fountain. We extend previous methods of analysing the interferometer to include the effects of a gravitational gradient. We also present detailed experimental and theoretical studies of potential systematic errors and noise sources.

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The basic physical principles behind atom interferometers based on optical pulses of light are summarized. This method of atom interferometry is based on measurements in the time and frequency domain and is an inherently precise measurement technique. After a brief discussion of some of the important technical requirements for good fringe accuracy and visibility, we describe an interferometer that has measured the acceleration of an atom due to gravity with a resolution better than one part in 10 10 . We project that the absolute accuracy of our measurement will be of the order of a few parts in 10 9 . We also describe an interferometer experiment that measures the recoil energy shift of an atom when it absorbs a photon. When combined with the value of the Rydberg constant and the mass ratios M Cs /m p and m p /m e , one can obtain a value for α, the fine structure constant. Currently, we have an experimental resolution ∆α/α ∼ 10 −8 after two hours of integration time and are studying the systematic effects that affect the measurement.

We present a test of the local Lorentz invariance of post-Newtonian gravity by monitoring Earth's gravity with a Mach-Zehnder atom interferometer that features a resolution of about 8×10−9 g/ √ Hz, the highest reported thus far. Expressed within the standard model extension (SME) or Nordtvedt's anisotropic universe model, the analysis limits four coefficients describing anisotropic gravity at the ppb level and three others, for the first time, at the 10ppm level. Using the SME we explicitly demonstrate how the experiment actually compares the isotropy of gravity and electromagnetism.PACS numbers: 03.75. Dg, 11.30.Cp, 11.30.Qc, 04.25.Nx The description of gravitation by a dynamic geometry of space-time, Einstein's general relativity (GR), is based on the Einstein equivalence principle. This encompasses the universality of free fall (UFF), local position invariance (LPI), and local Lorentz invariance (LLI), which also underlies the non-gravitational standard model of particle physics. Attempts to unify GR and the standard model have failed so far. This suggests that one of their foundations might be violated at some level of precision [1]. So far, tests of the UFF and LPI have not identified violations [1]. LLI has been tested experimentally for many sectors of the standard model, such as for photons ('Maxwell sector'), electrons, protons, and neutrons [1,2,3]. No Lorentz violation has been identified, although the coverage of parameter space is still incomplete. Far less attention, however, has been paid to the LLI of the gravitational ('Einstein') sector, in spite of the pioneering work of Nordtvedt and Will in the 1970ies. Motivated by that fact that anisotropies arise in various theories of gravity other than GR [4], they have ruled out a Lorentz-violating anisotropy in gravity by searching for an anomalous time-dependence of the acceleration of free fall g on Earth [4,5,6].The success of GR and the standard model implies that any Lorentz violations are tiny. This and the relative weakness of gravity means that only exceptionally sensitive experiments can hope to detect Lorentz violation in gravity. A relatively recent addition to these is precision atom interferometry [7,8]. This has been serving, for example, in measurements of the fine structure constant [9], g [10] and its gradient [11], the Sagnac effect [12], and Newton's constant G [13] with sensitivities that compare favorably with other state-of-the-art instruments. One reason for its outstanding precision is that the motion of neutral atoms can realize a freely falling frame to a * Electronic address: holgerm@stanford.edu high accuracy and that this motion can be interrogated by laser radiation in a tremendously precise way. As a result, tests of post-Newtonian gravity with atom interferometry have been proposed that could rival or exceed the precision of classical ones [14].Here, we report on a first step in this direction: We describe the highest resolution atomic gravimeter reported thus far [15]. We then analyze the influence of Lorentz violat...