Antihydrogen is the antimatter mirror of hydrogen in which the electron is replaced by a positron and the proton by an antiproton. The ASACUSA Collaboration intends to measure the ground state hyperfine splitting of antihydrogen (the energy difference between the two states with parallel and antiparallel  electron and proton spins) at the CERN Antiproton Decelerator, with an initial precision of one part per million, to test the symmetry between matter and antimatter. The fundamental symmetry of CPT (combination of charge and parity conjugation and time reversal) predicts that matter and antimatter have equal or sign-opposite properties. However, the puzzling dominance of matter over antimatter in the universe warrants precise measurements of antimatter properties - such as the transition frequencies in antihydrogen atoms - to compare with their matter counterparts. In fact, theories beyond the so far well established Standard Model (such as string theory) predict a violation of the CPT symmetry at some level.

Antihydrogen is the simplest stable atom composed solely of antimatter, and hydrogen is one of the most precisely studied atomic systems. The hydrogen ground state hyperfine splitting of about 1.42 GHz had been measured earlier very accurately by a maser experiment with a relative precision of about 1 part in 10¹². It was also determined recently by ASACUSA, albeit with a more modest precision of a few parts per billion (ref.1) in a hydrogen beam by using the Rabi resonance method, which we will also apply to determine the hyperfine transition frequency of antihydrogen.

Figure 1 shows the behaviour of the two hyperfine states of antihydrogen which split to four when switching an external magnetic field (Breit-Rabi diagram). The total angular momentum F and its pro- jection M on the quantisation axis are given. With ASACUSA’s setup two transitions, σ₁ and π₁, are accessible. The hyperfine transition frequency can then be determined by measuring one of the transitions at several field strengths and extrapolating to zero field.