The study of CPT invariance with the highest achievable precision in all particle sectors is of fundamental importance for physics. Equally important is the question of the gravitational acceleration of antimatter.
In recent years, impressive progress has been achieved at the Low-Energy Antiproton Ring (LEAR) at CERN in capturing antiprotons in specially designed Penning traps, in cooling them to energies of a few milli-electron volts, and storing them for hours in a small volume of space. Positrons have been accumulated in large numbers in similar traps, and low-energy positron or positronium beams have been generated. Finally, steady progress has been made in trapping and cooling neutral atoms. Thus the ingredients to form antihydrogen at rest are at hand.
This report will describe the techniques available to produce, decelerate, and accumulate antiprotons at low energy, how to generate high-density plasmas of low-energy positrons, and how to combine these two species into antihydrogen.
Once antihydrogen atoms have been formed, they can be captured in magnetic gradient traps and standard spectroscopic methods applied to interrogate their atomic structure with extremely high precision for comparison with the hydrogen atom. In particular, the 1S-2S transition, with a lifetime of the excited state of 122 ms and thereby a natural linewidth of five parts in 
, offers in principle the possibility to directly compare matter and antimatter properties at a level of one part in 
. Other quantities of interest, such as the hyperfine structure splitting of the ground state, will also be discussed.
Finally, we will give a brief outlook into the future and comment on some of the possible antiproton facilities which could be used to continue this field of research well into the next century.
