A trapped ion in an optical cavity: numerical study of an optomechanical transition in the few-photon regime

TL;DR

This paper investigates the quantum behavior of a trapped ion coupled to an optical cavity in the few-photon regime, revealing increased entropy and entanglement near the optomechanical transition without clear metastability signatures.

Contribution

It provides a numerical quantum analysis of the optomechanical transition in a trapped ion-cavity system, especially in the low-photon regime where semiclassical models fail.

Findings

Entropy and entanglement increase near the transition

No clear metastability signatures in the quantum spectrum

Quantum features differ from semiclassical predictions

Abstract

We consider an optomechanical system composed by a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus in a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity of the system transitions or when the mean photon number is low. Here we provide a numerical analysis of the fully quantum state in the few-photon regime, exploring the features of the asymptotic state across the transition and analyzing possible markers of semiclassical bistability. We find an increase in the entropy of the system and of the entanglement in the transition region, but no clear signatures of metastability in the spectrum of the evolution.