Precise measurement of h/mRb using 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(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(Rb) is 4.591 359 29 (6)x10(-9) m(2) 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.