Hermitian and non-Hermitian normal-mode splitting in an optically-levitated nanoparticle

Abstract

Normal-mode splitting is a hallmark of strong coupling between two coupled harmonic oscillators. Here, we report the realization of strong coupling in the optically-levitated nanoparticle system via feedback. A silica nanoparticle is trapped by a tightly focused laser travelling in free space, which is regarded as a harmonic oscillators. An external electric oscillator is then phase-locked to the nanoparticle’s motion as another harmonic oscillator, which is modulated on the trapping laser to feedback and interact with the nanoparticle. Therefore, a highly manipulatable coupled-harmonic oscillator system is built in our platform and the normal-mode splitting is realized with strong coupling in both Hermitian and non-Hermitian cases. Moreover, since the coupling between the two harmonic oscillators induced by the feedback is flexibly manipulated, the normal-mode splitting following the cooling or heating effect is simultaneously observed. This method could be useful for further studying quantum mechanical Hamiltonian and non-Hermitian phenomena of an optically-levitated nanoparticle.