Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schr\"odinger equation with focusing saturable nonlinearity and PT-symmetric potential

TL;DR

This paper investigates spontaneous symmetry breaking, ghost states, and soliton dynamics in the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential, revealing novel phenomena unique to fractional media.

Contribution

It introduces the first analysis of symmetry breaking and ghost states in fractional media with PT-symmetry, including bifurcation behavior and stability properties.

Findings

Fundamental solitons bifurcate into asymmetric ghost states with complex conjugate propagation constants.

Symmetry breaking depends on fractional Lévý index and nonlinear parameters.

Stable soliton excitations and collision phenomena are characterized in the fractional PT-symmetric system.

Abstract

We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schr\"odinger (FNLS) equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole (antisymmetry) and tripole solitons are also studied numerically. Moreover, we analyze the influences of fractional L\'evy index and saturable nonlinear parameters on the symmetry breaking of solitons in detail. And the stability of fundamental soliton, asymmetric, dipole and tripole solitons are explored via the linear stability analysis and direct propagations. Moreover, we explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons. Meanwhile, we find the stable excitations from the fractional diffraction with saturation nonlinearity to integer-order diffraction with Kerr nonlinearity via the adiabatic excitations of parameters. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related physical experiments in the fractional media with PT-symmetric potentials.