Characterization of heterodyne optical phase locking for relative laser frequency noise suppression in differential measurement

Laser frequency noise is particularly challenging to mitigate in low Fourier frequency measurement. For differential measurement schemes using heterodyne optical phase-locked loops, this noise can be common-mode suppressed in the final readout while maintaining a flexible frequency offset and a large frequency-shift dynamic range. We demonstrate simultaneous optical phase-locked loops using digital servo systems, with up to 300 MHz offset frequency range, 250 dB open-loop gain at 0.1 Hz, and control timescales suitable for low-frequency measurement. We also detail a four-laser differential measurement intended for use in a precision measurement device that uses optical phase-locked loops, suppressing relative free-running noise to reach below 0.1 / at 0.1 Hz in the measurement readout.