Cavity optomechanical systems are the cross field of quantum optics and classical physics, which study the mixed interactions between light field and mechanical motion. As cavity optomechanical systems develop, scientists have discovered the phenomenon of inverse electromagnetically induced transparency (IEIT). We propose a new system that inserts two transmissive active mirrors into an optical cavity to form a structure of an optical cavity and two mechanical oscillators. A beam of pump light and a beam of probe light are emitted from the left side, while there is only one beam of probe light on the right side. Driven by the three beams of light, the system can still undergo the IEIT phenomenon, and the cavity field energy is equal to the energy sum of the two mechanical oscillators after adjusting the cavity field power and the parameter n (the ratio of two mechanical oscillators b₁ and b₂ to coupling coefficients). When a mechanical oscillator is added and driven by the same cavity field power, the coupling effect is better than that of a single oscillator, and the mechanical oscillator energy can also be controlled by adjusting the parameter n. Our study may have good application prospects in filtering, quantum information processing, quantum communication, and other fields.

Beginning with a new optomechanical system model, we investigate the composition of the system and provide definitions for each parameter. The obtained Hamiltonian is solved by Heisenberg equations of motion, factorization, and other methods, and the relationship between the cavity field and the output field is established. Finally, the relationship between cavity field energy and mechanical oscillator energy under different parameters is explored to conduct further analysis.

The results indicate that when n is set as different values, it can all satisfy εoutL+=εoutR+=0, which means that the IEIT phenomenon occurs. The satisfied condition is G2=2κn2+1 (Fig. 2), and the coupling effect is significantly enhanced. When n=0, only the mechanical oscillator b2 has energy, as shown in Fig. 3(b), while under n=1, mechanical oscillators b₁ and b₂ have the same energy, as shown in Fig. 3(d). Figs. 4(b), 4(c), 5(b), and 5(c) respectively represent the energy possessed by the mechanical oscillators b₁ and b₂ at n=0.5 and n=1.5. By comparing with the energy of the cavity field, when IEIT occurs, number of photons in the cavity probe is equal to the sum of mechanical excitations. Adjusting n can achieve energy distribution adjustment.

We propose a composite multimode cavity optomechanical system, which consists of a control field and two probe fields driven by an optical resonant cavity coupled with two mechanical oscillators. The parameters in this system are controlled, including the coupling strength between the mechanical oscillator and the cavity photon, and the ratio between the coupling strengths of the mechanical oscillators. Numerical results show that this cavity optomechanical system can realize the IEIT phenomenon and further discuss the energy residency problem. Additionally, the coupling effect of the system is significantly enhanced with the action of two mechanical oscillators. By adjusting the cavity field power and the coupling relationship between the mechanical oscillators and the cavity, the system will have potential applications in filtering, energy distribution regulation, quantum communication, and energy storage.