Higher-order dark solitons and control dynamics in microcavity polariton condensates

Dark solitons carrying quantized phase information have inspired great interest in different nonlinear systems. A dark soliton in one dimension can be stabilized in microcavity polariton condensates as a confinement is imposed on it to prevent its decay. Such a confinement can be realized by optical methods, i.e., by using optically induced potential traps. Under nonresonant excitation with spatially periodically modulated optical beams, we numerically demonstrate that, besides fundamental dark solitons, higher-order dark solitons with multiple density minima and $\ensuremath{\pi}$-phase jumps can also stably survive in the potential (pump) valleys. Simultaneously exciting several orders of dark soliton states by properly choosing the lattice constant of the optical pump gives rise to dark oscillators. In some cases, the stably trapped dark solitons in adjacent pump valleys squeeze the condensate density between them and generate another type of density dip in the pump peak area. Surprisingly, such a density dip supports another stable dark soliton with a larger size that is essentially composed of two dark solitons, and the two $\ensuremath{\pi}$-phase jumps enable efficient optical control of dark solitons.