No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers

TL;DR

This paper proves that achieving Heisenberg-limited laser coherence does not conflict with having sub-Poissonian photon statistics, showing both can be maximized simultaneously.

Contribution

The authors extend the proof of the Heisenberg limit to laser coherence without requiring Poissonian statistics, demonstrating a positive correlation between coherence and sub-Poissonianity.

Findings

Heisenberg limit scales with the fourth power of excitations

Maximum coherence occurs at minimal Mandel Q

Sub-Poissonianity enhances laser coherence

Abstract

The Heisenberg limit to laser coherence $\mathfrak{C}$ -- the number of photons in the maximally populated mode of the laser beam -- is the fourth power of the number of excitations inside the laser. We generalize the previous proof of this upper bound scaling by dropping the requirement that the beam photon statistics be Poissonian (i.e., Mandel's $Q=0$). We then show that the relation between $\mathfrak{C}$ and sub-Poissonianity ($Q<0$) is win-win, not a tradeoff. For both regular (non-Markovian) pumping with semi-unitary gain (which allows $Q\xrightarrow{}-1$), and random (Markovian) pumping with optimized gain, $\mathfrak{C}$ is maximized when $Q$ is minimized.