Can superconducting order be engineered as a robust attractor of open-system dynamics in strongly correlated systems? We demonstrate this possibility by proposing a minimal dissipation-engineering protocol for the particle-hole symmetric Hubbard model. By applying a rotated quantum jump operator, specifically a locally transformed $\eta$-pair lowering operator, on a single lattice site only, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) exhibiting macroscopic $\eta$-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization stands in stark contrast to schemes reliant on spatially extensive reservoirs: Here, a single local dissipative seed suffices to establish long-range coherence across the entire interacting lattice system. We elucidate the underlying mechanism via three core features: Local dark-state selection, the controlled elimination of off-manifold excursions induced by hopping, and a Liouvillian invariant-subspace structure that yields an attractive fixed point with a finite dissipative gap. Furthermore, we systematically classify the stability of this NESS with respect to static disorder, and identify a wide regime in which the superconducting attractor remains robust against Hamiltonian perturbations that preserve the effective subspace structure. We also pinpoint specific perturbations that directly cause dephasing of the $\eta$-pseudospin coherence and suppress ODLRO. These findings open up a disorder-tolerant pathway for stabilizing superconducting order as a nonthermal attractor through minimal local quantum-jump control.

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• Cold atoms & matter waves
• Open quantum systems
• Open quantum systems & decoherence
• PT-symmetric quantum mechanics
• Non-Hermitian systems
• Nonequilibrium systems
• Quantum many-body systems
• Strongly correlated systems
• Dynamic critical phenomena