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

Overview

This work addresses the theoretical treatment of laser-induced hyperfine transitions in muonic hydrogen when using multi-pass cell geometries designed to enhance laser fluence. Standard fluence distribution calculations based on ray-tracing methods neglect optical interference effects and consequently can lead to overestimation of transition probabilities, as they underestimate saturation effects. The study develops a quantitative framework to bound the magnitude of interference-induced corrections to transition probability calculations in such systems.

Methods and approach

A model-based approach was developed to estimate maximal possible interference effects for specified laser and multi-pass cell parameters without requiring detailed knowledge of intra-cavity field distributions. The methodology provides an upper bound on the reduction in laser-induced transition probability relative to calculations that neglect these effects. Numerical evaluation was performed using experimental parameters relevant to muonic hydrogen hyperfine spectroscopy.

Key Findings

Evaluation of the theoretical upper bound under the experimental conditions investigated demonstrates that interference effects in the multi-pass cell can be safely neglected for muonic hydrogen. The numerical evaluation shows that under their experimental conditions, such effects do not significantly impact the transition probability calculations.

Implications

The work demonstrates that simplified ray-tracing-based fluence calculations are adequate for muonic hydrogen transition probability estimation under the experimental operating conditions examined. The methodology developed provides a generalizable framework applicable to other coherent light experiments employing multi-pass cell configurations, enabling systematic assessment of interference contributions without full electromagnetic field modeling. Future experiments operating at higher laser intensities or with different cell geometries can employ this approach to determine when more sophisticated field calculations become necessary.