Accurate measurement of the fine-structure constant α is of the utmost need for testing the Standard Model using low energy experiments. At the Laboratoire Kastler Brossel, we are developing an experiment to determine α using a measurement of the ratio $h/m$ between the Planck constant and the mass of an atom. Our experiment uses an atom interferometer to measure the recoil velocity of atom that absorbs a photon.
Using a determination of α, one can calculate the electron g-factor. Comparison of this value with the direct measurement can be used to test the Standard Model with an unprecedented accuracy. It allows to put constraints on possible candidate particles from dark sector. It seams now that it will possible in the near future to test the puzzle of the anomalous magnetic moment of the muon, where a 3.6 $\sigma$ tension exists between experiment and theory, in the electron sector.