“…A nano-mechanical resonator [1], which explores the interaction between light and mechanical motion, provides an important platform in fundamental physics and has various applications, such as the fundamental test of quantum theory [2,3], quantum information processing [4], high-precision measurements [5], optomechanically induced transparency [6], optomechanical storage [7], normal mode splitting [8], high-precision measurement [9,10], state transfer at different optical wavelengths [11], quantum entanglement [12], optomechanically induced transparency [13], and nonlinear quantum optomechanics [14]. In recent years, much attention has been paid to optomechanical systems involving multiple * Author to whom any correspondence should be addressed.…”