Numerical ab initio variational calculations of the transition probabilities and ac Stark shifts in two-photon transitions of antiprotonic helium atoms driven by two counter-propagating laser beams are presented. We found that sub-Doppler spectroscopy is, in principle, possible by exciting transitions of the type $(n,L)\to (n-2,L-2)$ between antiprotonic states of principal and angular momentum quantum numbers $n~L-1~35$, first by using highly monochromatic, nanosecond laser beams of intensities ${10}^4–{10}^5$ W/cm${}^2$, and then by tuning the virtual intermediate state close (e.g., within 10–20 GHz) to the real state $(n-1,L-1)$ to enhance the nonlinear transition probability. We expect that ac Stark shifts of a few MHz or more will become an important source of systematic error at fractional precisions of better than a few parts in ${10}^9$. These shifts can, in principle, be minimized and even canceled by selecting an optimum combination of laser intensities and frequencies. We simulated the resonance profiles of some two-photon transitions in the regions $n=30–40$ of the $\overline{p}$${}^4\mathrm{He}$${}^{+}$ and $\overline{p}$${}^3\mathrm{He}$${}^{+}$ isotopes to find the best conditions that would allow this.

• Received 9 February 2010

DOI:https://doi.org/10.1103/PhysRevA.81.062508