# Probing Stark-induced nonlinear phase variation with opto-optical modulation

## TL;DR

This paper demonstrates how opto-optical modulation can probe and control Stark-induced phase variations in helium atoms, revealing nonlinear effects and state-dependent emission redirection.

## Contribution

It extends opto-optical modulation techniques to measure state-resolved Stark phase variations and shows control over emission redirection via IR beam shaping.

## Key findings

- Redirection of emission differs between 1s2p and Rydberg states.
- IR-induced Stark phase depends nonlinearly on intensity.
- Phase accumulation can change sign at moderate intensities.

## Abstract

We extend the recently developed technique of opto-optical modulation (OOM) to probe state-resolved ac-Stark-induced phase variations of a coherently excited ensemble of helium atoms. In a joint experimental and theoretical study, we find that the spatial redirection of the resonant emission from the OOM process is different for the low-lying 1s2p state as compared with the higher-lying Rydberg states, and that this redirection can be controlled through the spatial characteristics of the infrared (IR) probe beam. In particular, we observe that the intensity dependence of the IR-induced Stark phase on the 1s2p emission is nonlinear, and that the phase accumulation changes sign for moderate intensities. Our results suggest that OOM, combined with precise experimental shaping of the probe beam, could be used to measure the Stark-induced phase shifts of excited states.