Full dynamics of two-membrane cavity optomechanics

Year: 2025

Authors: Li WL., Li XL., Li Y., Marzioni F., Piergentili P., Rasponi F., Vitali D.

Autors Affiliation: Northeastern Univ, Coll Sci, Shenyang 110819, Peoples R China; Chinese Univ Hong Kong, Dept Phys, Shatin, Hong Kong, Peoples R China; Univ Camerino, Sch Sci & Technol, Phys Div, I-62032 Camerino, Italy; Ist Nazl Fis Nucl, Sez Perugia, Via A Pascoli, I-06123 Perugia, Italy; Univ Naples Federico II, Dept Phys, I-80126 Naples, Italy; CNR INO, Largo Enrico Fermi 6, I-50125 Florence, Italy.

Abstract: In a two-membrane cavity optomechanical setup, two semitransparent membranes placed within an optical Fabry-P & eacute;rot cavity lead to a nontrivial dependence of the frequency of a mode of the optical cavity on the membranes’ positions, which is due to interference. However, the system dynamics is typically described by a radiation-pressure-force treatment in which the frequency shift is expanded, stopping at first order in the membrane displacements. In this paper, we study the full dynamics of the system obtained by considering the exact nonlinear dependence of the optomechanical interaction between two membranes’ vibrational modes and the driven cavity mode. We then compare this dynamics with the standard treatment based on the Hamiltonian linear interaction, and we find the conditions under which the two dynamics may significantly depart from each other. In particular, we see that a parameter regime exists in which the customary first-order treatment provides distinct and incorrect predictions for the synchronization of two self-sustained mechanical limit cycles and for Gaussian entanglement of the two membranes in the case of two-tone driving.

Journal/Review: PHYSICAL REVIEW A

Volume: 112 (5)      Pages from: 53524-1  to: 53524-13

More Information: W.L. is supported by the National Natural Science Foundation of China (Grant No. 12304389) and the Scientific Research Foundation of NEU (Grant No. 01270021920501*115). F.M., P.P., F.R., and D.V. acknowledge financial support of PNRR MUR Project No. PE0000023-NQSTI (Italy).
KeyWords: Radiation-pressure; Quantum; Oscillator; Mirror
DOI: 10.1103/5wbx-36ws