Figure 1

Schematic diagram of the multimode optomechanical mechanical system. The two movable membranes can be treated as mechanical modes with annihilation operators \(b_{1}\) and \(b_{2}\), which are quadratically coupled to the common cavity mode a. The cavity is driven by a control (probe) field with amplitude \(\varepsilon _{c}(\varepsilon _{p})\), frequency \(\omega _{c}(\omega _{p})\), and phase \(\phi _{c}(\phi _{p})\). In addition, the two membranes are excited by two weak coherent mechanical driving fields with amplitudes \(\varepsilon _{1,2}\), frequency \(\Omega =\omega _{p}-\omega _{c}\), and phases \(\phi _{1,2}\)