Routes to chaos and generation of cnoidal wave envelopes in exciton-polariton microcavities

We show the presence of intermittent chaos as a function of the variation of the chemical potential during the condensation of exciton-polaritons using the bifurcation diagram and the Lyapunov Exponent. We then show the possibility of controlling the chaos in the homogeneous solution by the variation of the chemical potential when the pump increases. The influence of the chemical potential is demonstrated in stationary state by studying stability using the Routh-Hurwitz criterion. We also prove the existence of cnoidal waves and through phase portraits, their stabilities in propagation are established using the notion of symmetry. For this, we use a dissipative Gross-Pitaevskii equation for the polariton field, coupled to a reservoir dynamics equation, commonly used to describe polariton condensates under non-resonant pumping.

Automated summary

We demonstrate the presence of intermittent chaos during the condensation of exciton-polaritons by analyzing bifurcation diagrams and Lyapunov Exponents. Furthermore, we investigate the possibility of controlling chaos in the homogeneous solution by varying the chemical potential as the pump increases. The influence of the chemical potential in the stationary state is examined through stability analysis using the Routh-Hurwitz criterion. Additionally, we establish the existence of cnoidal waves and their stability in propagation through phase portraits and the concept of symmetry.