Doppler Amplification of Motion of a Trapped Three-Level Ion

TL;DR

This paper investigates the dynamics of a three-level trapped ion system as a phonon laser, focusing on coherent population trapping effects and optimizing laser parameters for improved internal state readout.

Contribution

It extends previous two-level models to three-level ions, specifically $^{138} ext{Ba}^+$, and explores how to optimize laser parameters for better amplification and detection.

Findings

Coherent population trapping alters phonon laser behavior.

Optimized laser parameters enhance amplification gain.

Simulation results guide non-destructive internal state readout.

Abstract

The system of a trapped ion translationally excited by a blue-detuned near-resonant laser, sometimes described as an instance of a phonon laser, has recently received attention as interesting in its own right and for its application to non-destructive readout of internal states of non-fluorescing ions. Previous theoretical work has been limited to cases of two-level ions. Here, we perform simulations to study the dynamics of a phonon laser involving the $\Lambda$-type $^{138}\mbox{Ba}^{+}$ ion, in which coherent population trapping effects lead to different behavior than in the previously studied cases. We also explore optimization of the laser parameters to maximize amplification gain and signal-to-noise ratio for internal state readout.