Towards laser spectroscopy of antihydrogen

Cold antihydrogen atoms in a magnetic trap will open up a fascinating field of very precise CPT tests by ultrahigh-resolution laser spectroscopy. Equally exciting is the prospect for experiments on the gravitational acceleration of antimatter. For both types of experiment it is of great importance to have antihydrogen as cold as possible. Laser cooling of antihydrogen can be done on the strong 1S-2P transition at Lyman-α (121.56 nm). The highest cooling efficiency, lowest temperature, and best magnetic sublevel selectivity is expected for continuous coherent radiation. We present an account of the first source for continuous coherent radiation at Lyman-α and discuss possible applications in experiments with antihydrogen.