The goal of the ASACUSA-CUSP collaboration at the Antiproton Decelerator of CERN is to measure the ground-state hyperfine splitting of antihydrogen using an atomic spectroscopy beamline. A milestone was achieved in 2012 through the detection of 80 antihydrogen atoms 2.7 meters away from their production region. This was the first observation of cold antihydrogen atoms in a magnetic field free region. In parallel to the progress on the antihydrogen production, the spectroscopy beamline was tested with a source of hydrogen. This led to a measurement at a relative precision of 2.7x 10^(-9) which constitues the most precise measurement of the hydrogen hyperfine splitting in a beam. Further measurements with an upgraded hydrogen apparatus are motivated by CPT and Lorentz violation tests in the framework of the Standard Model Extension. Unlike for hydrogen, the antihydrogen experiment is complicated by the difficulty of synthesizing enough cold antiatoms in ground-state. The first antihydrogen quantum states scan at the entrance of the spectroscopy apparatus was realized in 2016 and is presented here. The prospects for a ppm measurement are also discussed.
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