The Heisenberg Limit to Laser Coherence

To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser, it can be quantified by the number C, the number of photons emitted consecutively into the beam with roughly the same phase. For 60 years, C was thought to be on the order of the square of the photon number in the laser itself, O(μ²), for an ideal laser. Here, assuming nothing about the laser operation except that its inputs have negligible coherence, but making standard assumptions on the ideality of the laser beam, we prove that the ultimate (or Heisenberg) limit is C = O(μ⁴). The quantum measurement theory of heterodyne measurements and canonical phase measurements are central to this proof. Moreover, we find a laser model that can achieve this scaling, and show that, in principle, it could be realised with familiar physical couplings in cavity QED or circuit QED. This work has been published in Nature Physics (2020). DOI: 10.1038/s41567-020-01049-3