Optimized laser models with Heisenberg-limited coherence and sub-Poissonian beam photon statistics

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored within the laser, this being quadratically larger than the standard or Schawlow-Townes limit [Baker et al., Nat. Phys. 17, 179 (2021)]. Moreover, this was analytically proven to be the ultimate quantum limit (Heisenberg limit) scaling under defining conditions for CW lasers, plus a strong assumption about the properties of the output beam. In our related work [Ostrowski et al., Phys. Rev. Lett. 130, 183602 (2023)] we show that the latter can be replaced by a weaker assumption, which allows for highly sub-Poissonian output beams, without changing the upper bound scaling or its achievability. In this paper we provide details of the calculations given in our related paper and introduce three families of laser models which may be considered as generalizations of those presented in that work. Each of these families of laser models is parameterized by a real number, p, with p = 4 corresponding to the original models. The parameter space of these laser families is numerically investigated in detail, where we explore the influence of these parameters on both the coherence and photon statistics of the laser beams. Two distinct regimes for the coherence may be identified based on the choice of p, where for p > 3, each family of models exhibits Heisenberg-limited beam coherence, while for p < 3, the Heisenberg limit is no longer attained. Moreover, in the former regime, we derive formulas for the beam coherence of each of these three laser families which agree with the numerics. We find that the optimal parameter is in fact p approximate to 4.15, not p = 4.

Automated summary

Recently, a study has shown that a laser can produce a stationary beam with enhanced coherence by storing a higher number of excitations within the laser. This finding challenges the traditional limits of laser coherence and introduces new laser models with different parameterizations. The study also explores the influence of these parameters on the coherence and photon statistics of the laser beams, revealing distinct regimes based on the parameter values. The optimal parameter value is found to be approximately 4.15 instead of the conventional value of 4.