## 4 Radiation Pressure-Driven PhC Cavity Sensors
### Sensing Applications Based on Radiation Pressure  
#### 4.2.1 Displacement Sensing  
Highly sensitive displacement detection lays the technical foundation for other sensing applications because variations of other physical parameters can be converted to the movement of an on-chip component. Optomechanical photonic cavities are excellent for displacement sensing due to the strong interaction between the mechanical resonator and photonic cavity. However, displacement sensing based on optical cavities is technically limited by fundamental quantum shot noise on the photodetector [110]. The level of quantum shot noise decreases as the square-root of input light power. As the optical intensity further increases, the shot noise arising from optical cavity can lead to an oscillating optical force on the mechanical object, eventually causing the fluctuation of displacement. In the position measurement, standard quantum limit (SQL) provides a comparison scale to evaluate whether the measurement imprecision of displacement is sufficient to distinguish the zero-point fluctuation (ZPF) of mechanical resonator At the SQL, the backaction noise \(S_{xx}^{SQL}\) induced by optical force is equal to the imprecision shot noise \(S_{xx}^{ZPF}\) caused by displacement fluctuation [20,111]. In this critical condition, SQL is equal to the ZPF of mechanical motion given as \(x_{SQL}=\sqrt{\hbar/2m\Omega_{m}}\). At the resonance, SQL is also defined by \(S_{xx}^{SQL}=\hbar/\left(m\Omega_{m}\Gamma_{m}\right)\), which corresponds to a quarter of mechanical quantum noise energy. To overcome this limit, displacement detection below SQL can theoretically be achieved by applying squeezed light for input laser, and this technological breakthrough has been experimentally  
Figure 14: Schematic illustrating optical spring sensing mechanism [108]: (**a**) optical transmission spectrum; (**b**,**c**) mechanical spectra shift due to the applied tiny perturbation. demonstrated in a gravitational wave measurement [112]. In the zipper-cavity experiment shown in Figure 15a, the in-plane differential mechanical motion induced by radiation-pressure, modifying the gap between nanobeams, strongly modulated optical frequency with an optomechanical coupling rate of \(g_{0}/2\pi=1\) MHz. A level of \(4.5\pm 0.5\%\) squeezing with a bandwidth of a few MHz at the mechanical frequency of \(\Omega_{m}=28\) MHz was experimentally obtained. Radiation-pressure backaction fluctuation was greatly inhibited and affected by the motion of mechanical resonator, which demonstrated a fundamentally quantum aspect of displacement measurement. Another adiabatic tapered waveguide-PhC cavity scheme was developed into an on-chip optomechanical device [61], as shown in Figure 15b. Note that a mounted fiber tip well-aligned with a coupled waveguide could realize a coupling efficiency of 52% at the resonance wavelength. The measured imprecision noise floor at the fundamental in-plane mechanical mode of 3.3 MHz revealed a factor of 2.8 above SQL for continuous displacement sensing. The mechanical resonator with an effective mass of 15 pg was equal to a zero-point amplitude reaching up to \(x_{ZPF}=13\) fm. In addition, several technical conditions of high Q-factor and mechanical frequency, as well as cryogenic operation (10 K), were essential to restrain the effect of thermal noise. Future improvements could exploit alternative photonic material platforms for higher Q-factors, such as diamond [113; 114] or silicon carbide [115; 116]. Nonlinear optomechanics occurs when the optical cavity frequency couples into the square of mechanical displacement in the radiation pressure interaction, which have been exploited in the realization of motion measurements.