Enhanced optomechanical readout using optical coalescence

We present a scheme to strongly enhance the readout sensitivity of the squared displacement of a mobile scatterer placed in a Fabry-Pérot cavity. We investigate the largely unexplored regime of cavity electrodynamics in which a highly reflective element positioned between the end mirrors of a symmetric Fabry-Pérot resonator strongly modifies the cavity response function, such that two longitudinal modes with different spatial parity are brought close to frequency degeneracy and interfere in the cavity output field. In the case of a movable middle reflector we show that the interference in this generic “optical coalescence” phenomenon gives rise to an enhanced frequency shift of the peaks of the cavity transmission that can be exploited in optomechanics.

Figure 1

(a) Optical cavity with a middle reflector of polarizability ${\zeta }_{\mathrm{m}}$, accommodating odd (red, full line), even (blue, dashed line) modes that couple to outside “left” and “right” modes. (b) Cavity transmission spectra over three free spectral ranges, illustrating the strong shift of the odd resonances toward the even ones as the reflectivity is increased. (c) Transmission spectra (solid black curves) for increasing $\left|{\zeta }_{\mathrm{m}}\right|$. The dashed curves denote the “bare” resonances. “Mode-pulling” effects can be seen by comparing the positions of these resonances and the peaks of the transmission. At coalescence (${\zeta }_{\mathrm{m}}^{*}$ is defined in the text) one finds a single peak with close to unity transmission over an increased bandwidth. Past this point the maximum transmission is reduced below unity.

Figure 2

The resonant transmission as a function of the membrane position $x$. We use $\zeta =-10$ and ${\zeta }_{\mathrm{m}}=-0.5$ (blue, dashed line), $-5$ (red, full line), and $-50$ (black, dotted line). The data points show the numerically calculated transmission, and the solid curves $T_{\mathrm{res}}\left(x\right)$.

Figure 3

Mode-pulling behavior of adjacent cavity modes ($\zeta =-10$, ${\zeta }_{\mathrm{m}}=-196.6$). Shown are two adjacent resonances as a function of middle-mirror displacement about the center of the cavity. For perfect cavity mirrors, i.e., zero linewidth, one obtains the resonances shown by the dotted curves. Imperfect cavity mirrors cause an interference effect that pulls adjacent modes closer together (solid curves), resulting in a sharper avoided crossing, and enhanced quadratic optomechanical coupling.