Topological resilience of optical skyrmions in local decoherence

The topologically protected configuration embedded in skyrmions has prompted some investigations into their fundamental properties and versatile applications, sparking interest and guiding ongoing development. The topological protection associated with skyrmions was initially observed in systems with interactions. It is widely believed that skyrmions are stable, yet relevant confirmation and empirical research remain limited. A pertinent question is whether skyrmion configurations formed by a single classical beam with two coupled degrees of freedom also exhibit topological stability. In this study, we affirm this hypothesis by investigating the effects of local decoherence. We analytically and numerically demonstrate the topological resilience of skyrmions and the occurrence of transition points of skyrmion numbers in local decoherence across three typical decoherence channels. On the other hand, we show that these qualities are independent of the initial state. From the numerical results, we find that inhomogeneous but continuous decoherence channels also have the same behaviors and maintain the topological stability of skyrmions as homogeneous decoherence channels do. These properties of skyrmions contribute to further applications in various areas, including communication and imaging.