Spontaneous Symmetry Breaking In Nonlinear Binary Periodic Systems

TL;DR

This paper investigates spontaneous symmetry breaking in nonlinear periodic systems with symmetric double-well potentials, deriving analytical predictions for the critical power and confirming results through numerical simulations.

Contribution

It introduces an analytical model for SSB in 1D and 2D periodic systems with symmetric double-well units, highlighting the dependence on quasi-momentum.

Findings

Critical power for SSB decreases with increasing quasi-momentum.

Analytical predictions match numerical eigenmode analysis.

SSB threshold can approach zero at high quasi-momentum.

Abstract

Spontaneous symmetry breaking (SSB) occurs when modes of asymmetric profile appear in a symmetric, double-well potential, due to the nonlinearity of the potential exceeding a critical value. In this study, we examine SSB in a periodic potential where the unit cell itself is a symmetric double-well, in both one-dimensional and two-dimensional periodic systems. Using the tight-binding model, we derive the analytical form that predicts the critical power at which SSB occurs for both 1D and 2D systems. The results show that the critical power depends significantly on the quasi-momentum of the Bloch mode, and as the modulus of momentum increases, the SSB threshold decreases rapidly, potentially dropping to zero. These analytical findings are supported by numerical nonlinear eigenmode analysis and direct propagation simulations of Bloch modes.