Laser excitation of muonic 1S hydrogen hyperfine transition: effects of multi-pass cell interference

Calculating the laser-induced transition probability by using the fluence distribution that neglects interference effects (e.g., by employing ray-tracing methods) can lead to an overestimation of this probability, as it underestimates saturation effects. In this paper, we investigate how interference effects in the multi-pass cell, used to enhance the laser fluence, affect the laser-induced transition probability between hyperfine levels in muonic hydrogen, a bound system of a negative muon and a proton. To avoid complications related to the exact knowledge of the intra-cavity field, we develop a simple model that estimates the maximal possible interference effects for given laser and multi-pass cell parameters, thereby providing an upper bound for the resulting decrease in transition probability relative to the case where these effects are neglected. A numerical evaluation of this upper bound for muonic hydrogen shows that, under our experimental conditions, such effects can be safely neglected. Nonetheless, the methodology presented here could be applied to estimate the impact of interference effects on the laser-induced transition probability in other experiments involving coherent light in multi-pass systems.