Aspects of 1S-2S spectroscopy of trapped antihydrogen atoms

Antihydrogen atoms are now routinely trapped in small numbers. One of the purposes of this effort is to make precision comparisons of the 1S-2S transition in hydrogen and antihydrogen as a precision test of the CPT theorem. We investigate, through calculations and simulations, various methods by which the 1S-2S transition may be probed with only a few trapped atoms. We consider the known constraints from typical experimental geometries, detection methods, sample temperatures, laser light sources etc and we identify a viable path towards a measurement of this transition at the $10^{−1}$1 level in a realistic scenario. We also identify ways in which such a first measurement could be improved upon as a function of projected changes and improvements in antihydrogen synthesis and trapping. These calculations recently guided the first observation of the 1S-2S transition in trapped antihydrogen.