A local oscillator's frequency drifts away from a stable quantum reference (e.g. an atomic or qubit transition) under thermal and electronic noise — a random walk in frequency.
A quantum frequency stabilizer periodically measures the error between the oscillator and the reference, then feeds a correction back into the oscillator's control input. This is a discrete-time servo loop:
- Drift/noise — how fast the free-running frequency wanders (Hz per √s, a random-walk diffusion rate).
- Feedback gain — the fraction of the measured error cancelled at each correction pulse. Too low and drift wins; too high and the loop overshoots and rings.
- Correction interval — how often the servo samples and corrects. Faster sampling tracks drift better but each measurement also injects its own quantum-limited noise.
Both traces share the same noise draws each frame, so the only difference between the red (free-running) and green (stabilized) lines is the feedback loop itself.