Phonon amplification in two coupled cavities containing one mechanical resonator

TL;DR

This paper develops a theoretical framework for phonon lasing in coupled optomechanical systems, deriving threshold conditions, analyzing phase diagrams, and highlighting unique phenomena distinct from photon lasing.

Contribution

It introduces a general theory of phonon lasing in coupled cavities, deriving dynamical equations and threshold conditions, and compares phonon lasing with photon lasing.

Findings

Phonon lasing can occur near the threshold in certain parameter regimes.

Distinct phenomena are observed in phonon lasing not seen in photon lasing.

Phase diagrams and second-order correlation functions reveal unique properties of phonon lasing.

Abstract

We study a general theory of phonon lasing [I. S. Grudinin et al., Phys. Rev. Lett. 104, 083901 (2010)] in coupled optomechancial systems. We derive the dynamical equation of the phonon lasing using supermodes formed by two cavity modes. A general threshold condition for phonon lasing is obtained. We also show the differences between phonon lasing and photon lasing, generated by photonic supermodes and two-level atomic systems, respectively. We find that the phonon lasing can be realized in certain parameter regime near the threshold. The phase diagram and second-order correlation function of the phonon lasing are also studied to show some interesting phenomena that cannot be observed in the common photon lasing with the two-level systems.