Abstract

We present the design, fabrication, and characterization of a planar silicon photonic crystal cavity in which large position-squared optomechanical coupling is realized. The device consists of a double-slotted photonic crystal structure in which motion of a central beam mode couples to two high-$Q$ optical modes localized around each slot. Electrostatic tuning of the structure is used to controllably hybridize the optical modes into supermodes that couple in a quadratic fashion to the motion of the beam. From independent measurements of the anticrossing of the optical modes and of the dynamic optical spring effect, a position-squared vacuum coupling rate as large as ${\tilde{g}}^{\prime }$$/2\pi =245\mathrm{Hz}$ is inferred between the optical supermodes and the fundamental in-plane mechanical resonance of the structure at ${\omega }_m/2\pi =8.7\mathrm{MHz}$, which in displacement units corresponds to a coupling coefficient of $g^{\prime }/2\pi =1\mathrm{THz}/{\mathrm{nm}}^2$. For larger supermode splittings, selective excitation of the individual optical supermodes is used to demonstrate optical trapping of the mechanical resonator with measured ${\tilde{g}}^{\prime }/2\pi =46\mathrm{Hz}$.