Symmetry Breaking and Spatiotemporal Pattern Formation in Photonic Time Crystals

TL;DR

This paper investigates how nonlinear photonic media with time-varying properties can undergo phase transitions that break symmetries, leading to lattice-like patterns and modes similar to those in condensed matter physics, with implications for time crystal research.

Contribution

It introduces a novel analysis of symmetry breaking and pattern formation in 2+1D time-varying photonic media with Kerr nonlinearity, connecting to dissipative time crystals.

Findings

Symmetry breaking induces lattice-like wave patterns.

Emergence of Goldstone-like and Higgs-like modes.

Extension of analysis to 2+1 dimensions and connection to time crystals.

Abstract

In this work, we explore the dynamics of time varying photonic media with an optical Kerr nonlinearity and an associated phase transition. The interplay between a periodically modulated permittivity and the nonlinearity induces a continuous transition of electromagnetic waves to a state with broken spatial and time translation symmetries. This transition gives rise to a lattice-like wave pattern, in many ways similar to a spatial crystallization in solids. Symmetry breaking triggers the emergence of soft, Goldstone-like modes, which propagate as deformations of the lattice structure, as well as massive Higgs-like modes -- spatially uniform oscillations of the field amplitude. We extend the analysis of the non-equlibrium symmetry breaking to 2+1 dimensional time varying media and discuss pattern formation as well as the connection to discrete dissipative time crystals.