Precise determination of the ratio h/m u: a way to link microscopic mass to the new kilogram

The ratio h/m(u) between the Planck constant and the unified atomic mass constant should have a special status in the framework of the future international system of units. Currently (before the redefinition), this ratio allowed the comparison between determinations of h (watt balance) and determinations of m(u) (the XRCD method). In the future SI, as the Planck constant h will be fixed, the ratio h/m(u) will ensure the realization of the new kilogram (quantum kilogram) at the atomic scale. Furthermore as the Avogadro constant will be fixed, the carbon molar mass M(C-12), which will no longer be equal to 12 g . mol(-1), will be determined from m(u). This ratio is also key data for the realization of the kilogram at the macroscopic scale using the XRCD method. In this paper we present the state of the art on experiments that provide the most precise value of the ratio h/m(u). We focus on the one that is based on the measurement of the atomic recoil due to the photon momentum.