Two-photon spectroscopy of trapped HD$^+$ ions in the Lamb-Dicke regime

TL;DR

This paper demonstrates the feasibility of high-precision two-photon rovibrational spectroscopy of trapped HD+ ions using a REMPD scheme, achieving sub-Doppler linewidths suitable for fundamental physics tests.

Contribution

It introduces a realistic simulation of two-photon spectroscopy in HD+ ions, showing sub-Doppler resolution in an effective Lamb-Dicke regime with potential for 10^{-14} accuracy.

Findings

Sub-Doppler lines with 100 Hz width are achievable.

Counterpropagating lasers enable Lamb-Dicke regime excitation.

Spectroscopy can test molecular QED and proton-to-electron mass ratio.

Abstract

We study the feasibility of nearly-degenerate two-photon rovibrational spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking advantage of quasi-coincidences in the rovibrational spectrum, the excitation lasers are tuned close to an intermediate level to resonantly enhance two-photon absorption. Realistic simulations of the REMPD signal are obtained using a four-level model that takes into account saturation effects, ion trajectories, laser frequency noise and redistribution of population by blackbody radiation. We show that the use of counterpropagating laser beams enables optical excitation in an effective Lamb-Dicke regime. Sub-Doppler lines having widths in the 100 Hz range can be observed with good signal-to-noise ratio for an optimal choice of laser detunings. Our results indicate the feasibility of molecular spectroscopy at the $10^{-14}$ accuracy level for improved tests of molecular QED, a new determination of the proton-to-electron mass ratio, and studies of the time (in)dependence of the latter.