Ultrahigh-resolution laser spectroscopy of antihydrogen atoms in a magnetic trap could open a new field of challenging tests of the fundamental CPT theorem. The required laser cooling and laser spectroscopy techniques are also essential for future experiments on the gravitational acceleration of antimatter. Laser cooling of antihydrogen can be done on the strong 1S-2P transition at Lyman-alpha (121.56 nm). We describe the first source of continuous coherent Lyman-alpha radiation and its possible application in experiments with antihydrogen. [References: 21]
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