A promising method for the measurement of the local ac- celeration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave

– An obvious determination of the acceleration of gravity g can be deduced from the measurement of the velocity of falling atoms using a π − π pulses sequence of stimulated Raman transitions. By using a vertical standing wave to hold atoms against gravity, we expect to improve the relative accuracy by increasing the upholding time in the gravity field and to minimize the systematic errors induced by inhomogeneous fields, owing to the very small spatial amplitude of the atomic center-of-mass wavepacket periodic motion. We also propose to use such an experimental setup nearby a Watt balance. By exploiting the g/h (h is the Planck constant) dependence of the Bloch frequency, this should provide a way to link a macroscopic mass to an atomic mass. Introduction. – The dynamics of an atomic wave packet in a periodic potential under the influence of a static force has been extensively analyzed using different physical approaches : in terms of Wannier-Stark resonance states [1], Bloch oscillations [2] or macroscopic quantum interferences induced by tunnelling due to the external acceleration [3](for review see [4]). An interesting configuration occurs when the external force is induced by the acceleration of gravity. In this case the Bloch frequency is equal to νB = mgλ 2h and depends only on the local acceleration of the gravity g, the wavelength of the light λ and some fundamental constants. This frequency is typically in the range 100 Hz − 2000 Hz, and its measurement allows the determination of g. Previous experiments have already been realized using the dynamics of BEC [3, 5] or degenerated Fermi gas [5] in vertical 1-D optical lattice. Kasevich’s group has observed the interference between macroscopic quantum states of BEC atoms confined in a vertical array of optical traps. This interference arises from the tunneling induced by the acceleration of gravity and appears as a train of falling atomic pulses. The acceleration of the gravity g was determined by measuring the spatial period of the pulses train. In Ingusio’s group [5] the Bloch period is straightforwardly deduced from the evolution of the momentum