Excitation transfer and many-body dark states in waveguide quantum electrodynamics

In one-dimensional waveguide quantum electrodynamics systems, quantum emitters interact through infinite-range, dispersive, and dissipative dipole-dipole interactions mediated by guided photonic modes. These interactions give rise to long-range periodic behavior and rich many-body physics absent in free space. In this work, we construct a set of symmetrized multi-excitation dark states and derive analytic expressions for their time-evolution projections. This framework captures the essential dynamics of excitation transport and storage while significantly reducing computational complexity compared to full quantum simulations. Our analysis reveals a fundamental bound on energy redistribution governed by the structure of dark states and collective dissipation, and discovers that optimal excitation transfer between emitter ensembles converges toward an initial pumped fraction of $N_\text{p}/N \approx 0.55$ for large system sizes. We further examine the robustness of this mechanism under realistic imperfections, including positional disorder, nonradiative decay, and dephasing. These results highlight the role of many-body dark states in enabling efficient and controllable energy transfer, offering new insights into dissipative many-body dynamics in integrated quantum platforms.