The Heisenberg limit for laser coherence

Quantum optical coherence can be quantified only by accounting for both the particle- and wave-nature of light. For an ideal laser beam1-3, the coherence can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, C I, can be much larger than the number of photons in the laser itself, mu. The limit for an ideal laser was thought to be of order mu(2) (refs. (4,5)). Here, assuming only that a laser produces a beam with properties close to those of an ideal laser beam and that it has no external sources of coherence, we derive an upper bound on C I, which is of order mu(4). Moreover, using the matrix product states method(6), we find a model that achieves this scaling and show that it could, in principle, be realized using circuit quantum electrodynamics(7). Thus, C I of order mu(2) is only a standard quantum limit; the ultimate quantum limit-or Heisenberg limit-is quadratically better.

Automated summary

Research shows that for an ideal laser beam, coherence can be roughly considered as the number of photons emitted consecutively with the same phase. Using the matrix product states method, a model achieving this scaling is found, indicating it could be realized using circuit quantum electrodynamics.