# High-intensity two-frequency photoassociation spectroscopy of a weakly bound molecular state: theory and experiment

## TL;DR

This paper combines experimental and theoretical approaches to study high-intensity two-frequency photoassociation of weakly bound molecular states, revealing nonlinear features and providing models for analyzing complex spectra.

## Contribution

It introduces a simple three-level model and Floquet-based formulas that accurately describe high-intensity photoassociation spectra, including nonlinear satellite peaks and Stark shifts.

## Key findings

- Observation of satellite peaks from nonlinear processes
- Accurate modeling of two-photon spectral features
- Development of simple formulas for halo-state energies

## Abstract

We investigate two-frequency photoassociation of a weakly bound molecular state, focusing on a regime where the ac Stark shift is comparable to the halo-state energy. In this "high-intensity" regime, we observe features absent in low-intensity two-frequency photoassociation. We experimentally measure the spectra of $^{86}$Sr atoms coupled to the least bound state of the $^{86}$Sr$_2$ ground electronic channel through an intermediate electronically excited molecular state. We compare the spectra to a simple three-level model that includes a two-frequency drive on each leg of the transition. With numerical solution of the time-dependent Schrodinger equation, we show that this model accurately captures (1) the existence of experimentally observed satellite peaks that arise from nonlinear processes, (2) the locations of the two-photon peak in the spectrum, including ac Stark shifts, and (3) in some cases, spectral lineshapes. To better understand these numerical results, we develop an approximate treatment of this model, based on Floquet and perturbation theory, that gives simple formulas that accurately capture the halo-state energies. We expect these expressions to be valuable tools to analyze and guide future two-frequency photoassociation experiments.