Accurate recovery of the two linewidths hidden in laser beatnote statistics

Abstract

Photons from ultrastable lasers can remain coherent over distances approaching the Earth-Sun separation, enabling optical clocks projected to lose less than one second over the age of the Universe. Yet characterizing these photons poses an identifiability problem: a two-laser heterodyne measurement produces a single beatnote linewidth that conflates contributions from both lasers. For more than half a century, the standard solution has been the three-cornered-hat (TCH) method, which requires three independent ultrastable lasers. Here we derive the mathematical form and elucidate the physical origin of asymmetric beatnote-linewidth distributions arising from finite photon wave trains, a long-observed feature not captured by canonical Gaussian or Lorentzian statistics. This finding accurately recovers two linewidths hidden in laser beatnote statistics without a third laser. The framework consistently captures the observed coherence-length and coherence-time statistics of photons, while comparison with TCH measurements confirms the quantitative validity of the extracted individual linewidths across five independent ultrastable-laser datasets spanning nearly two orders of magnitude. Most notably, the method resolves the 7.8-mHz linewidth of a cryogenic silicon-cavity laser beating with a broader laser. This transformative function of beatnote-linewidth distributions, together with the resulting method, could fundamentally advance optical clocks and precision metrology.