The Goldstone mode of planar optical parametric oscillators

TL;DR

This paper investigates the Goldstone mode in driven-dissipative planar optical parametric oscillators, highlighting its overdamped nature and how symmetry breaking affects its dispersion, with predictions for semiconductor cavities.

Contribution

It introduces an experimental approach to probe the Goldstone mode in non-equilibrium systems and analyzes the effects of symmetry breaking on its properties.

Findings

Goldstone mode is overdamped with linewidth approaching zero at long wavelengths.

Breaking U(1) symmetry opens a gap and broadens the probe response.

Quantitative predictions for semiconductor cavities in strong coupling regime.

Abstract

We propose an experimental setup to probe the low-lying excitation modes of a parametrically oscillating planar cavity, in particular the soft Goldstone mode which appears as a consequence of the spontaneously broken U(1) symmetry of signal/idler phase rotations. Differently from the case of thermodynamical equilibrium, the Goldstone mode of such a driven-dissipative system is an overdamped mode, whose linewidth goes to zero in the long-wavelength limit. When the phase of the signal/idler emission is pinned by an additional laser beam in the vicinity of the signal emission, the U(1) symmetry is explicitely broken and a gap opens in the Goldstone mode dispersion. This results in a dramatic broadening of the response to the probe. Quantitative predictions are given for the case of semiconductor planar cavities in the strong exciton-photon coupling regime.