Three-mode optomechanical system for angular velocity detection<xref rid="cpb_27_8_084203_fn1" ref-type="fn">*</xref><fn id="cpb_27_8_084203_fn1"><label>*</label><p>Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0301200), the National Basic Research Program of China (Grant No. 2014CB921403), the Science Challenge Project of China (Grant No. TZ2017003), and the National Natural Science Foundation of China (Grant Nos. 11774024, 11534002, and U1530401).</p></fn>

Three-mode optomechanical system for angular velocity detection**

Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0301200), the National Basic Research Program of China (Grant No. 2014CB921403), the Science Challenge Project of China (Grant No. TZ2017003), and the National Natural Science Foundation of China (Grant Nos. 11774024, 11534002, and U1530401).

Li Kai, Davuluri Sankar, Li Yong^†

(color online) (a) The minimum detectable angular velocity in Eq. (41). (b) The corresponding transmission coefficient σ(ω_y) versus Δ for different values of ω_x. (c) Simulation of the condition given in Eq. (35) with ω = ω_y for different ω_x. (d) The ratio of S_add(ω_y) in Eq. (32) to S_xx(ω_y) in Eq. (33) as a function of ω_x and Ω with fixed Δ = 0 and T = 300 K. The other parameters are:^[40]m = 6.9 × 10⁻⁴ kg, ω_y/2π = 84.8 Hz, γ_x/2π = γ_y/2π = 1.9 × 10⁻³ Hz, κ/2π = 4 × 10⁶ Hz, and g/2π = 1.46 × 10¹⁷ Hz/m. The effective optomechanical coupling strength is taken as G/2π = 2.19 × 10²² Hz/m (with the corresponding ). For these parameters, the optimal value of Ω_noise(ω_y)/2π = 9.5 × 10⁻⁴ Hz, also see the vertical line in panel (c).