A measurement of the fine-structure constant using atom interferometry

Using atom interferometry, we have measured the photon recoil frequency shift for cesium atoms caused by the absorption of up to 200 optical photons. Performing the measurement using cold atoms allowed interaction times as long as 400 ms, corresponding to 2.5 Hz FWHM interference fringes. We have achieved a measurement resolution of 120 ppb from 90 s of data. This is over an order-of-magnitude higher sensitivity than in a previous version of this experiment. We report a value {dollar}Delta fsb{lcub}rm rec{rcub}{dollar} = 30, 012.557 3(16)(7) Hz for the photon recoil shift using the cesium {dollar}Dsb1{dollar} line, where the first 1{dollar}sigma{dollar} error bar is the 52 ppb limit from systematic errors, and the second error bar is the 22 ppb statistical uncertainty after 4 hours of data. The uncertainty in {dollar}Delta fsb{lcub}rm rec{rcub}{dollar} has improved over an order of magnitude from the previous photon recoil measurement.; Combining this recoil-frequency-shift measurement with mass-ratio measurements and an absolute frequency measurement determines a value for the fine-structure constant of {dollar}alphasp{lcub}-1{rcub}{dollar} = 137.036 002 8(77). To within the stated uncertainty, this determination agrees with the value for {dollar}alpha{dollar} obtained from the anomalous magnetic moment of the electron. The largest contributor to the 56 ppb relative uncertainty of this determination of {dollar}alpha{dollar} is the uncertainty in the knowledge of the absolute frequency of the cesium {dollar}Dsb1{dollar} line. The uncertainty in our measurement of {dollar}Delta fsb{lcub}rm rec{rcub}{dollar} limits the relative uncertainty in this {dollar}alpha{dollar} determination to 28 ppb.