Calculation of transition probabilities and ac Stark shifts in two-photon laser transitions of antiprotonic helium

TL;DR

This paper presents ab initio calculations of transition probabilities and ac Stark shifts in two-photon laser transitions of antiprotonic helium, suggesting possible sub-Doppler spectroscopy and methods to minimize systematic errors.

Contribution

The study provides the first detailed ab initio analysis of two-photon transition probabilities and ac Stark shifts in antiprotonic helium, including strategies to reduce systematic errors.

Findings

Sub-Doppler spectroscopy is feasible with specific two-photon transitions.

ac Stark shifts of a few MHz can be minimized or canceled.

Optimal laser parameters can enhance transition probabilities.

Abstract

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)->(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 \bar{p}^4He^+ and \bar{p} ^3He^+ isotopes to find the best conditions that would allow this.