Coherent control of Fano resonances in a macroscopic four-mirror cavity

We demonstrate coherent control of optomechanically induced transparency and Fano resonances in a four-mirror macroscopic optomechanical cavity, with two movable mirrors, each driven by an external mechanical pump. The variable control of the amplitude and phase of the coherent mechanical pumps provides a means of tuning the shape and nature of the Fano profiles. Further, our scheme shows the occurrence of tunable optomechanical features, even at very low mechanical driving field amplitudes, in macroscopic optomechanical cavities.

Figure 1

Schematic diagram of a four-mirror cavity with two movable mirrors.

Figure 2

Schematic illustration of frequencies used in obtaining Fano line shapes.

Figure 3

The real part of the anti-Stokes field as a function of normalized probe detuning for ${\omega }_{m1}=\mathrm{\Omega }$, ${\varphi }_{m1}=3\pi /2$, and the following parameters: (a) $s_{m1}=5.6$ mN (blue curves), $s_{m1}=2.6$ mN (red curves), and $s_{m1}=0$ and $s_{m2}=0$ (black curves); (b) $s_{m1}=s_{m2}=2.7$ mN (blue curves), $s_{m1}=2.7$ mN and $s_{m2}=0$ (red curves), and $s_{m1}=s_{m2}=0$ (black curves); and (c) $s_{m1}=5.7$ mN and $s_{m2}=0$ (red curves), and $s_{m1}=s_{m2}=5.7$ mN and ${\varphi }_{m2}=\pi /2$ (black curves).

Figure 4

The real part of the anti-Stokes field as a function of normalized probe detuning for different values of phase ${\varphi }_{m1}$. (a) ${\varphi }_{m1}=3\pi /2$. (b) ${\varphi }_{m1}=\pi /2$. (c) ${\varphi }_{m1}=0$. (d) ${\varphi }_{m1}=\pi$.

Figure 5

Fano resonance in the real part of the anti-Stokes field as a function of normalized probe detuning for $s_{m1}=4.6$ mN and (a) ${\varphi }_{m1}=3\pi /2$ and (b) ${\varphi }_{m1}=\pi /2$.

Figure 6

The real part of the anti-Stokes field as a function of normalized probe detuning $({\omega }_{\mathrm{pr}}-{\omega }_0)/\mathrm{\Omega }$ for $s_{m1}=5.2$ mN, ${\varphi }_{m1}=3\pi /2$ and $s_{m2}=18$ mN, ${\varphi }_{m2}=\pi$ (blue curve), $s_{m1}=2.6$ mN, ${\varphi }_{m1}=3\pi /2$ and $s_{m2}=9$ mN, ${\varphi }_{m2}=\pi$ (red curve); and $s_{m1}=0$, ${\varphi }_{m1}=3\pi /2$ and $s_{m2}=0$, ${\varphi }_{m2}=\pi$ (black curve).

Figure 7

Double Fano resonance in the real part of the antiStokes field as a function of normalized probe detuning for $s_{m1}=8$ mN, ${\omega }_{m1}=0.8\mathrm{\Omega }$, $s_{m2}=12$ mN, ${\omega }_{m2}=1.2\mathrm{\Omega }$, and ${\varphi }_{m1}={\varphi }_{m2}=0$ (red dashed curve); and ${\varphi }_{m1}=0$ and ${\varphi }_{m2}=\pi$ (black solid curve).

Figure 8

Real part of anti-Stokes field vs normalized probe detuning for $s_{m1}=s_{m2}=9$ mN, ${\varphi }_{m1}={\varphi }_{m2}=\pi$ (blue curve); $s_{m1}=14$ mN, ${\varphi }_{m1}=\pi$, $s_{m2}=6$ mN, ${\varphi }_{m2}=0$ (red curve); $s_{m1}=s_{m2}=9$ mN, ${\varphi }_{m1}=\pi$, ${\varphi }_{m2}=0$ (black curve).