Antiprotonic helium and CPT invariance

We review recent progress in the laser and microwave spectroscopy of antiprotonic helium atoms ((p) over bar He+ e(-) - (p) over bar - He++) carried out at CERN's Antiproton Decelerator facility (AD). Laser transitions were here induced between Rydberg states (n, l) and (n +/- 1, l - 1) of (p) over bar He+ (n similar to 40 and l less than or similar to n - 1 being the principal and orbital angular momentum quantum numbers of the antiproton orbit). Successive refinements in the experimental techniques improved the fractional precision on the (p) over bar He+ frequencies from 3 parts in 10(6) to similar to 1 part in 10(8). These included a radiofrequency quadrupole decelerator, which reduced the energy of the antiprotons from 5.3 MeV (the energy of the beam emerging from AD) to similar to 100 keV. This enabled the production of (p) over bar He+ in ultra-low density targets, where collisional effects with other helium atoms are negligible. A continuous wave pulse-amplified dye laser, stabilized against a femtosecond optical frequency comb, was then used to measure the (p) over bar He+ frequencies with ppb-scale precision. This progress in the experimental field was matched by similar advances in computing methods for evaluating the expected transition frequencies in three-body QED calculations. The comparison of experimental (nu(exp)) and theoretical (nu(th)) frequencies for seven transitions in (p) over bar He-4(+) and five in (p) over bar (3) He+ yielded an antiproton-to-electron mass ratio of m((p) over bar)/m(e) = 1836.152 674(5). This agrees with the known proton-to-electron mass ratio at the level of similar to 2x 10(-9). The experiment also set a limit on any CPT-violating difference between the antiproton and proton charges and masses, (Qp - vertical bar Q((p) over bar)vertical bar)/Qp similar to (m(p)-m((p) over bar))/mp < 2 x 10(-9) to a 90% confidence level. If on the other hand we assume the validity of the CPT invariance, the m((p) over bar)/m(e) result can be taken to be equal to m(p)/m(e). This can be used as an input to future adjustments of fundamental constants. The hyperfine structure of a state in (p) over bar He-4(+) has also been measured by microwave spectroscopy to a precision of 3 x 10(-5). This corresponds to the accuracy of the most precise three-body QED calculations. Further increases in the experimental precision may soon yield an improvement in the value of the antiproton magnetic moment.