Dissipative Nonlinear Thouless Pumping of Temporal Solitons

The interplay between topology and soliton is a central topic in nonlinear topological physics. So far, most studies have been confined to conservative settings. Here, we explore Thouless pumping of dissipative temporal solitons in a nonconservative one-dimensional optical system with gain and spectral filtering, described by the paradigmatic complex Ginzburg–Landau equation. Two dissipatively induced nonlinear topological phase transitions are identified. First, when varying dissipative parameters across a threshold the soliton transitions from being trapped in time to quantized drifting. This quantized temporal drift remains robust, even as the system evolves from a single-soliton state into a multi-soliton state. Second, a dynamically emergent phase transition is found: the soliton is arrested until a critical point of its evolution, where a transition to topological drift occurs. Both phenomena uniquely arise from the dynamical interplay of dissipation, nonlinearity, and topology.