Precise Determination of the Ratio h/m u : A Way to Link Microscopic Mass to the New Kilogram

The ratio $h/m_{\mathrm{u}}$ 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. As the Planck constant $h$ will be fixed, the ratio $h/m_{\mathrm{u}}$ will ensure the realization of the new kilogram (quantum kilogram) at the atomic scale. Furthermore, this ratio becomes a key data for the realization of the kilogram at the macroscopic scale using the XRCD method. The ratio $h/m_{\mathrm{u}}$ can be precisely determined from the measurement of the atomic recoil due to the absorption of a photon momentum. In this conference we will present the lastest developments of our experiment in Paris that aims to measure precisely the recoil of rubidium atom using atom interferometry.