Fano resonances and their control in optomechanics

The Fano line profiles, originally discovered in the context of photoionization, have been found to occur in a large class of systems such as resonators, metamaterials, and plasmonics. We demonstrate the existence of such resonances in cavity optomechanics by identifying the interfering contributions to the fields generated at anti-Stokes and Stokes frequencies. Unlike the atomic systems, the optomechanical systems provide great flexibility as the width of the resonance is controlled by the coupling field. We further show how the double cavities coupled by a single optomechanical mirror can lead to the splitting of the Fano resonance and how the second cavity can be used to tune the Fano resonances. The Fano resonances are quite sensitive to the decay parameters associated with cavities and the mechanical mirror. Such resonances can be studied by both pump probe experiments as well as the spectrum of the quantum fluctuations in the output fields.

Figure 1

(a) Schematic of OMS and (b) photon-phonon interaction.

Figure 2

Schematic double-cavity OMS.

Figure 3

Schematic illustration of frequencies used in obtaining Fano line shapes. Fano asymmetry parameter $q$ is defined in terms of detuning $q=-{\Omega }_1/{\kappa }_1$. The effective damping is defined by ${\Gamma }_1=G_1^2/\left[{\kappa }_1(1+q^2)\right]$.

Figure 4

The anti-Stokes field ${\mathcal{E}}_{1\mathrm{AS}}$ (a) and the Stokes field ${\mathcal{E}}_{1\mathrm{S}}$ (b) as a function of frequency of the probe laser input ${\omega }_p$ for the OMS in Fig. 1a. The black dotted, blue dashed, and red solid curves are corresponding to ${\Omega }_1=0$, ${\Omega }_1=0.5{\kappa }_1$ and ${\Omega }_1={\kappa }_1$, respectively.

Figure 5

The anti-Stokes fields ${\mathcal{E}}_{1\mathrm{AS}}$ in cavity 1 (a) and in cavity 2 (b) as a function of frequency of the probe laser input in a double-cavity OMS. The thin black, blue dashed, and red solid curves are corresponding to different coupling strength of cavity 2 that $G_2/{\kappa }_1=0$, $0.15$ and $0.3$, respectively. We set ${\Omega }_2=0.1{\kappa }_1$ and ${\kappa }_2=0.05{\kappa }_1$.

Figure 6

The anti-Stokes field (a) and Stokes field (b) in cavity 1 as a function of frequency of the probe laser input in a double-cavity OMS. The solid curves: double-cavity OMS with $G_2=0.02{\kappa }_1$ shows the emergence of a the second Fano resonance, compared to the dashed curve: single-cavity OMS. The inset in (a) shows the full profile in a large scale. We set ${\Omega }_2=-0.05{\kappa }_1$ and ${\kappa }_2=0.5{\gamma }_m=0.005{\kappa }_1$.

Figure 7

Schematic double-cavity OMS. Here ${\mathcal{E}}_{ci}$ are coherent fields and $a_{i\mathrm{in}}$ are the quantum vacuum fields. $\xi$ is the Brownian noise.

Figure 8

The spectra of the quadratures for the cavity fields and output fields for both single-cavity OMSs (solid curves) and double-cavity OMSs (dashed curves). The parameters used are the same to Fig. 3.