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 the atoms. We have used this method to measure accurately the ratio h/m_{Rb}. In this paper we detail the experimental procedure and we present a complete analysis of the different systematic effects. They yield to a global relative uncertainty of 13 ppb. The measured value of h/m_{Rb} is 4.591 359 29 (6)\times10^{-9}~m^2\cdot s^{-1}. The deduced value of the fine structure constant is \alpha^{-1}=137.035 998 84 (91) with a relative uncertainty of 6.7 ppb.