Quantum signatures in quadratic optomechanics

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.

arXiv comment7 pages, 6 figures, 2nd version

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• Quadratic optomechanical cooling of a cavity-levitated nanosphere
• Coherent coupling completes an unambiguous optomechanical classification framework
• Nonlinear optomechanical systems with quasi-periodic and chaotic dynamics
• Temporal evolution of a driven optomechanical system in the strong coupling regime
• Time crystal optomechanics
• High-Dimensional Entanglement of Photonic Angular Qudits
• Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings
• Dynamics and Spectral Response of linear-quadratic optomechanical interaction: Effects of pure dephasing