Abstract
We consider a nanostructure of two coupled ring waveguides with constant linear gain and nonlinear absorption - the system that can be implemented in various settings including polariton condensates, optical waveguides or atomic Bose-Einstein condensates. It is found that, depending on the parameters, this simple configuration allows for observing several complex nonlinear phenomena, which include spontaneous symmetry breaking, modulational instability leading to generation of stable circular flows with various vorticities, stable inhomogeneous states with interesting structure of currents flowing between rings, as well as dynamical regimes having signatures of chaotic behavior.
Highlights
Ring-shaped structures are a natural framework for studying diverse phenomena in both optics and physics of degenerate quantum gases
The Kerr nonlinearity is introduced by the intensity-dependent refractive index of the medium and in the mean-field theory of condensates it appears due to two-body interactions
The Gross-Pitaevskii equation (GPE) describing atomic Bose-Einstein condensates (BECs) is conservative and they retain a number of integrals of motion and support families of nonlinear modes characterized by the dependence of the chemical potential on the total number of atoms
Summary
In this work we reported very rich behaviors of a simple system consisting of two identical ring-shaped nonlinear waveguides in the presence of the linear gain and nonlinear dissipation. We have identified stable and unstable solutions. The former ones appear either symmetric or represent different types of the symmetry breaking, which can be expressed either in nonzero transversal currents (asymmetric solutions) or in inhomogeneous density distributions along the waveguides. Unstable solutions, being initially perturbed, can manifest different dynamics which ends up either in one of the stable state (homogeneous, vortex, asymmetric, or inhomogeneous) or display chaotic-like behavior
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