Optically Levitated Rotor Gyroscope

Angular momentum H resists reorientation (gyroscopic stabilization); the optical trap supplies a restoring torque k; the resulting deflection vector α = (α_x, α_y) reads out the input rate vector Ω. Steady state: α = (H/k)·Ω. Normalized units (I_t=1).

Readout α_x vs. input Ω_x

α_x — noisy readout Ω_x × (H/k) — true rate, scaled

Deflection plane (α_x, α_y)

trajectory (last 5 s) current readout |readout| reference circle

Spin frequency f (H ∝ f)

f — spin frequency (saturates at τ₀/γ)

Input

Constant rate |Ω| 0.100 Sine amplitude 0.100 Sine frequency (Hz) 0.50 Direction θ (deg) 0 Sim speed 2.00×

Noise & damping

σ_A readout noise 0.0100 σ_T spin torque noise 0.0010 c rotational damping 0.20

Live state

spin f—

H = f (norm.)—

α_x readout—

α_y readout—

Ω true—

Ω est = (k·α)/H—

scale factor H/k—

ARW (rate)—

bias instability—