Position-Squared Coupling in a Tunable Photonic Crystal Optomechanical Cavity

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 g[over ˜]^{′}/2π=245 Hz is inferred between the optical supermodes and the fundamental in-plane mechanical resonance of the structure at ω_{m}/2π=8.7 MHz, which in displacement units corresponds to a coupling coefficient of g^{′}/2π=1 THz/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 g[over ˜]^{′}/2π=46 Hz