Trapping and spectroscopy of hydrogen

I review the results and techniques used by the MIT H↑ group to achieve a fractional resolution of 2 parts in 1012 in the 1S-2S transition in hydrogen [Cesar, D. Fried, T. Killian, A. Polcyn, J. Sandberg, I.A. Yu, T. Greytak, D. Kleppner and J. Doyle, Two-photon spectroscopy of trapped atomic hydrogen, Phys. Rev. Lett. 77 (1996) 255.] With some improvements, this system should deliver 100 times higher resolution with an improved signal count rate getting us closer to an old advertised goal of a precision of 1 part in 1018. While these developments are very important for the proposed test of the CPT theorem through the comparison with anti-hydrogen, some of the techniques used with hydrogen are not applicable to anti-hydrogen and I discuss some difficulties and alternatives for the trapping and spectroscopy of anti-hydrogen