Bloch Oscillations of Ultracold Atoms: A Tool for a Metrological Determination ofh/mRb

Abstract

We use Bloch oscillations in a horizontal moving standing wave to transfer a large number of photon recoils to atoms with a high efficiency ($99.5\%$ per cycle). By measuring the photon recoil of ${}^{87}\mathrm{Rb}$, using velocity-selective Raman transitions to select a subrecoil velocity class and to measure the final accelerated velocity class, we have determined $h/m_{\mathrm{Rb}}$ with a relative precision of 0.4 ppm. To exploit the high momentum transfer efficiency of our method, we are developing a vertical standing wave setup. This will allow us to measure $h/m_{\mathrm{Rb}}$ better than ${10}^{-8}$ and hence the fine structure constant $\alpha$ with an uncertainty close to the most accurate value coming from the ($g-2$) determination.