The Entropy Flow of a Laser Beam

TL;DR

The paper addresses the entropy of a phase-diffused laser beam, showing that even an ideal laser (with phase diffusion at rate $ell$) is in a mixed state and possesses a well-defined entropy flow. By modeling the beam as a wandering-phase coherent state and employing Renyi-2 entropy, the author derives an explicit formula for the entropy flow: $\dot{S}_2 = k_B \sqrt{\dot{N} \ell}$. The key methodological steps involve a two-copy Feynman-Kac approach that maps the problem to a 1D Schrödinger-type operator and yields the ground-state eigenvalue $\lambda_0 = \sqrt{\dot{N} \ell}$ in the high-coherence limit. The result highlights a fundamental difference between laser light and thermal radiation, offering new insights into irreversibility in optical systems and potential connections to clock physics.

Abstract

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 $\dot{S} = \sqrt{\dot{N}\ell}$, 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.