Solitons in $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling and critical nonlinearity

Abstract

We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light propagation in a dual-core waveguide with skewed coupling between the cores. Stability regions for the solitons are identified in the system's parameter space. They include the main semi-infinite gap, and an additional finite $\text{annex gap}$. Stability boundaries are identified by means of simulations of the perturbed evolution, which agree with results produced by the linear-stability analysis for small perturbations. Distinct evolution scenarios are identified for unstable solitons. Generally, they suffer blowup or decay, while weakly unstable solitons transform into breathers. Due to a regularizing effect of SOC, stationary solitons are also found beyond the exceptional point, at which the $\mathcal{P}\mathcal{T}$ symmetry breaks down, but they are unstable. Interactions between adjacent solitons are explored too, featuring rebound or merger followed by blowup. Slowly moving (tilted) solitons develop weak oscillations, while fast ones are completely unstable. Also considered is the reduced diffractionless system, which creates only unstable solitons.

To be published in Commun. Nonlin. Sci. and Num. Sim

References in corpus (12)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• The creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space
• Collapse of spin-orbit coupled Bose-Einstein condensates
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
• Solitons in PT-symmetric ladders of optical waveguides
• Stabilization of one-dimensional Townes solitons by spin-orbit coupling in a dual-core system
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management