Navigating entanglement via Ruderman-Kittel-Kasuya-Yosida exchange: oscillatory, boundary-residing, pulsed, and damping-stabilized trajectories.

Entanglement dynamics are fundamental to quantum technologies, yet controlling their temporal evolution in a reversible and stable manner remains challenging. We propose a solid-state framework based on the Ruderman-Kittel-Kasuya-Yosida interaction, realizable in gate-defined quantum dots or suspended structures, in which two spin qubits couple to a central spin qudit that mediates an effective, time-dependent exchange. The dynamics are governed by an exchange-time integral that unifies interaction strength and physical time into a single scalar control variable, enabling time-reversible and cyclic navigation of the Hilbert space. Crucially, we show that out-of-phase modulation grants access to higher entanglement subspaces, while introducing damping to the exchange modulation achieves stabilized trajectories that drive the system toward stationary entanglement values. This framework provides a systematic route for shaping entanglement dynamics, particularly in the near-boundary regime, using exchange control alone, overcoming the limitations of monotonic evolution and offering practical strategies for entanglement stabilization in realistic solid-state architectures, with direct relevance to quantum metrology and environment-assisted entanglement engineering.