Single-site dissipation stabilizes a superconducting nonequilibrium steady state in a strongly correlated system

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 $η$-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 $η$-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 $% η$-pseudospin coherence and suppress ODLRO. These findings open up a disorder-tolerant pathway for stabilizing superconducting order as a non-thermal attractor through minimal local quantum-jump control.

💡 Research Summary

This paper addresses the longstanding question of whether a macroscopic, strongly‑correlated quantum phase such as superconductivity can be stabilized using only a minimal, strictly local dissipative resource. The authors focus on the particle‑hole symmetric Hubbard model, a paradigmatic strongly‑interacting lattice system that possesses an exact η‑pairing SU(2) pseudospin symmetry. In equilibrium, η‑pairing states are high‑energy excitations and are thermodynamically unstable, but they are ideal candidates for non‑equilibrium steady states (NESS) when appropriate dynamical symmetries are engineered.

The core idea is to apply a rotated quantum‑jump operator on a single lattice site. The jump operator is a locally transformed η‑pair lowering operator, \