The main challenge
The main challenge when creating atoms of antihydrogen is to bring an antiproton and a positron close enough together for a long enough time.
(a) One way to do this is to begin with a cylindrical electromagnetic trap in a "nested well" configuration, which causes the oppositely charged antiprotons and positrons to occupy different regions of z, the axis of the cylinder. Antihydrogen atoms are then created by mixing the particles, but this leaves them with too much kinetic energy for precision spectroscopy. (b) The ATRAP collaboration has come up with a new way to create antihydrogen using an "adjacent well" configuration. Here, laser-excited caesium atoms (Cs*) first produce excited positronium atoms (Ps*) when they pass through a well filled with positrons, via the charge-exchange reaction Cs* + e+→Ps* + Cs+. These go on to produce excited antihydrogen atoms (H-bar*) when they pass through the adjacent well filled with antiprotons via the reaction Ps* + p-bar→H-bar* + e-.