# Ionic vibration induced transparency and Autler-Townes splitting

## TL;DR

This paper investigates how ionic vibrations induce transparency and Autler-Townes splitting in the absorption spectrum of a two-level ion in a trap, revealing control via laser tuning to vibrational sidebands.

## Contribution

It demonstrates the emergence of vibration-induced transparency and Autler-Townes splitting through Jaynes-Cummings and anti-Jaynes-Cummings interactions in a trapped ion system.

## Key findings

- Vibration-induced transparency appears when tuning to the red sideband.
- Autler-Townes splitting observed when tuning to the blue sideband.
- Constructs a three-level system model for the ion-vibration interaction.

## Abstract

In this work, the absorption spectrum of a two-level ion in a linear Paul trap is investigated, the ion is supposed to be driven by two orthogonal laser beams, the one along the axial of the trap acts as the control light beam, the other as probe beam. When the frequency of the control laser is tuned to the first red sideband of the ionic transition, the coupling between the internal states of the ion and vibrational mode turns out to be a Jaynes-Cummings (JC) Hamiltonian, which together with the coupling between the probe beam and the two-level ion constructs a {\Lambda}-type three-level structure. In this case the transparency window may appear in the absorption spectrum of the probe light, which is induced by the ionic vibration and is very similar to the cavity induced transparency [1996 Opt. Commun. 126 230-235]. On the other hand, when the frequency of the control laser is tuned to the first blue sideband of the ionic transition, the two-level ion and vibrational mode are governed by an anti-Jaynes-Cummings (anti-JC) Hamiltonian, the total system including the probe beam forms a V -type threelevel structure. And the Autler-Townes splitting in the absorption spectrum is found.