Quantum signatures in quadratic optomechanics

TL;DR

This paper explores quantum effects in quadratic optomechanical systems, demonstrating observable phenomena like frequency shifts and phonon statistics without requiring single-photon strong coupling, and proposes experimental methods to measure these effects.

Contribution

It introduces methods to detect quantum effects and phonon statistics in quadratic optomechanics without the need for strong coupling, expanding experimental possibilities.

Findings

Zero-point energy causes measurable mechanical frequency shifts.

Phonon statistics can be inferred from cavity transmission.

Mechanical quantum states exhibit collapse and revivals.

Abstract

We analyze quantum effects occurring in optomechanical systems where the coupling between an optical mode and a mechanical mode is quadratic in displacement (membrane-in-the-middle geometry). We show that it is possible to observe quantum effects in these systems without achieving the single-photon strong coupling regime. We find that zero-point energy causes a mechanical frequency shift, and we propose an experimental way to measure it. Further, we show that it is possible to determine the phonon statistics from the cavity transmission, and propose a way to infer the resonator's temperature based on this feature. For completeness, we revisit the case of an isolated system and show that different types of mechanical quantum states can be created, depending on the initial cavity state. In this situation, mechanical motion undergoes collapse and revivals, and we compute the collapse and revival times, as well as the degree of squeezing.