Precise measurement ofh∕mRbusing Bloch oscillations in a vertical optical lattice: Determination of the fine-structure constant

Bloch oscillations in a frequency-chirped optical lattice are a powerful tool to transfer coherently many photon momenta to atoms. We have used this method to measure accurately the ratio $h∕m_{\mathrm{Rb}}$. In this paper we detail the experimental procedure and we present a complete analysis of the different systematic effects. They yield a global relative uncertainty of 13 parts per ${10}^9$ (ppb). The measured value of $h∕m_{\mathrm{Rb}}$ is $4.59135929\left(6\right)\times {10}^{-9}{\mathrm{m}}^2{\mathrm{s}}^{-1}$. The deduced value of the fine-structure constant is ${\alpha }^{-1}=137.03599884$ (91) with a relative uncertainty of $6.7\mathrm{ppb}$.