The Entropy Flow of a Laser Beam

A laser beam is often modelled by a pure coherent state. In fact its state is mixed, even if it has coherent-state photon-number statistics (Poissonian), because the phase must vary. We consider such an ideal laser beam, with phase diffusion rate $\ell$, equal to its (Lorentzian) spectral width. We show that the beam entropy is extensive, with an entropy flow of $\dot{S} = k_B \sqrt{\dot{N}\ell}$, where $\dot{N}$ is the number flow. We give an intuitive explanation for this remarkably simple result, and compare it to a unidirectional thermal beam’s.

💡 Research Summary

The paper addresses a gap in the literature concerning the entropy of an ideal laser beam. While textbooks often model a laser output as a pure coherent state |α⟩ with a fixed phase, any realistic laser—even one limited only by quantum noise—exhibits phase diffusion. This diffusion, characterized by a rate ℓ equal to the full‑width‑half‑maximum (FWHM) of the Lorentzian spectrum, renders the beam a statistical mixture of coherent states with the same photon‑number distribution (Poissonian) but random phase.

The author models the beam as a continuous stream of infinitesimal temporal modes described by bosonic operators (\hat b(t)) satisfying (