Double-passage mechanical cooling in a coupled optomechanical system<xref rid="cpb_28_11_114206fn1" ref-type="fn">*</xref><fn id="cpb_28_11_114206fn1"><label>*</label><p>Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2018MS056) and the National Natural Science Foundation of China (Grant Nos. 11605055 and 11574082).</p></fn>

Double-passage mechanical cooling in a coupled optomechanical system**

Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2018MS056) and the National Natural Science Foundation of China (Grant Nos. 11605055 and 11574082).

Mu Qing-Xia¹, Lang Chao¹, Zhang Wen-Zhao^{2, †}

(a) Schematic of a three-mode optomechanical system. Two cavities (cavity 1 and cavity 2) interact with a common mechanical oscillator, which are also driven by two external laser fields with frequency ω_L1 and ω_L2, respectively. Further, a tunnel coupling J between the two cavity modes is allowed. (b) Level scheme of the linearized Hamiltonian [Eq. (3)] in the displaced frame. Here |0⟩, |1⟩, |n⟩ denote the states of the two cavity modes and the mechanical oscillator, respectively. The blue double arrow represents the transition from the state |0,1,n−1⟩ to the state |1,0,n−1⟩ with coupling strength J.