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

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 $Q\to -1$), and random (Markovian) pumping with optimized gain, $\mathfrak{C}$ is maximized when $Q$ is minimized.

This is a companion letter to the manuscript entitled "Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics", arxiv:2208.14082. 6 pages, 2 figures

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• Quantum noise and its evasion in feedback oscillators
• Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics