Kardar-Parisi-Zhang universality in the linewidth of non-equilibrium 1D quasi-condensates

TL;DR

This paper explores how the emission linewidth of a 1D non-equilibrium condensate scales with system size, revealing a transition from laser-like behavior to Kardar-Parisi-Zhang universality in larger systems, with implications for experimental studies.

Contribution

It demonstrates the finite-size scaling of linewidth governed by KPZ physics and introduces a configuration with open boundaries for experimental investigation.

Findings

Linewidth follows Schawlow-Townes scaling in small systems

Large systems exhibit KPZ universality in linewidth scaling

Open boundary conditions support uniform steady-states for experiments

Abstract

We investigate the finite-size origin of the emission linewidth of a spatially-extended, one-dimensional non-equilibrium condensate. We show that the well-known Schawlow-Townes scaling of laser theory, possibly including the Henry broadening factor, only holds for small system sizes, while in larger systems the linewidth displays a novel scaling determined by Kardar-Parisi-Zhang physics. This is shown to lead to an opposite dependence of the linewidth on the optical nonlinearity in the two cases. We then study how sub-universal properties of the phase dynamics such as the higher moments of the phase-phase correlator are affected by the finite size and discuss the relation between the field coherence and the exponential of the phase-phase correlator. We finally identify a configuration with enhanced open boundary conditions, which supports a spatially uniform steady-state and facilitates experimental studies of the linewidth scaling.