We discuss laser cooling of antihydrogen atoms in a magnetic trap down to the millikelvin range using radiation at Lyman‐alpha. This is very important to suppress residual Zeeman shifts and broadenings in future high‐resolution laser‐spectroscopy of antihydrogen. Even colder antihydrogen temperatures in the sub‐millikelvin range are desirable for experiments on antimatter gravity. We discuss novel methods to obtain antihydrogen atoms at these ultracold temperatures.

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