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arXiv:2602.00452

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

X. Z. Zhang

quant-phcond-mat.str-elSubmitted Jan 31, 2026• Announced Feb 3, 2026• 0 citations
v1 · Jan 31, 2026v2 · Feb 5, 2026
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Abstract

Can superconducting order be made a robust attractor of open-system dynamics in strongly correlated lattices? We demonstrate that it can by proposing a minimal dissipation-engineering protocol for the particle--hole symmetric Hubbard model. By applying a rotated quantum jump operator, a locally transformed $η$-pair lowering operator, on as little as a single lattice site, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) with macroscopic $η$-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization contrasts with schemes requiring spatially extensive reservoirs: here, a strictly local dissipative seed suffices to establish coherence across the interacting system. We elucidate the mechanism via local dark-state selection, 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 classify the stability of this NESS against static disorder, identifying a broad regime where the superconducting attractor is resilient to Hamiltonian perturbations that leave the effective subspace structure intact, while pinpointing specific perturbations that directly dephase the $η$-pseudospin coherence and suppress ODLRO. Our results establish a disorder-tolerant route to stabilizing superconducting order as a non-thermal attractor via minimal local quantum-jump control.

Comments
15 pages, 11 figures

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Can superconducting order be made a robust attractor of open-system dynamics in strongly correlated lattices? We demonstrate that it can by proposing a minimal dissipation-engineering protocol for the particle--hole symmetric Hubbard model. By applying a rotated quantum jump operator, a locally transformed ηηη-pair lowering operator, on as little as a single lattice site, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) with macroscopic ηηη-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization contrasts with schemes requiring spatially extensive reservoirs: here, a strictly local dissipative seed suffices to establish coherence across the interacting system. We elucidate the mechanism via local dark-state selection, 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 classify the stability of this NESS against static disorder, identifying a broad regime where the superconducting attractor is resilient to Hamiltonian perturbations that leave the effective subspace structure intact, while pinpointing specific perturbations that directly dephase the ηηη-pseudospin coherence and suppress ODLRO. Our results establish a disorder-tolerant route to stabilizing superconducting order as a non-thermal attractor via minimal local quantum-jump control.
The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard model in the context of $\ensuremath{\eta}$ symmetry. We show that the non-Hermitian Hubbard Hamiltonian can respect a full real spectrum even if a local non-Hermitian impurity is applied to. The balance between dissipation of single fermion and on-site pair fluctuation results in a highest-order coalescing state with off-diagonal long-range order (ODLRO). Based on the characteristic of high-order EP, the critical non-Hermitian Hubbard model allows the generation of such a steady superconducting-like state through the time evolution from an arbitrary initial state, including the vacuum state. Remarkably, this dynamic scheme is insensitive to the on-site interaction and entirely independent of the locations of particle dissipation and pair fluctuation. Our results lay the groundwork for the dynamical generation of a steady ODLRO state through the critical non-Hermitian strongly correlated system.
Dissipation is usually regarded as a source of decoherence that suppresses quantum interference and localization. Here we show that suitably engineered dissipation can instead be used to select localized or extended states in a strictly non-disordered one-dimensional lattice. The underlying clean lattice has spatially inhomogeneous hopping and supports both extended bulk states and localized boundary states, including an algebraically localized bound state in the continuum. We introduce a nonlocal bond jump operator with a tunable relative phase and show that this phase selectively favors eigenstates with different spatial phase correlations. As a result, the long-time density matrix can be steered toward sectors dominated by localized or extended Hamiltonian eigenstates without changing any Hamiltonian parameter. The microscopic origin of the selection is quantified by the fraction of site pairs separated by a distance lll that are phase matched with the dissipative channel. We further characterize the dissipative quench through the quantum fidelity and show that the selected character of the steady state can persist after the dissipation is removed. Our results establish phase-selective bond dissipation as a route to controllable state preparation and transport manipulation in non-disordered lattices.
The dynamics described by the non-Hermitian Hamiltonian typically capture the short-term behavior of open quantum systems before quantum jumps occur. In contrast, the long-term dynamics, characterized by the Lindblad master equation, drive the system towards a nonequilibrium steady state (NESS), which is an eigenstate with zero energy of the Liouvillian superoperator, denoted as L\mathcal{L}L. Conventionally, these two types of evolutions exhibit distinct dynamical behaviors. However, in this study we challenge this common belief and demonstrate that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The criticality of the system arises from the exceptional point of the effective non-Hermitian Hamiltonian. Additionally, the NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. We apply this finding to a series of critical open quantum systems and show that a local dissipation channel can induce collective alignment of all spins in the same direction. This direction can be well controlled by modulating the quantum jump operator. The corresponding NESS is a product state and maintains long-time coherence, facilitating quantum control in open many-body systems. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.
A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.
We propose a Josephson diode mechanism in which nonreciprocity arises not from a conventional asymmetric Andreev spectrum but from nonequilibrium occupation of the current-carrying states engineered by attached reservoirs. We realize this mechanism in a double-quantum-dot junction, where a phase-textured nonlocal reservoir acts as a quantum Zeno selector: rapid dissipation freezes out the bright state directly coupled to the jump operator LLL, while preserving an orthogonal dark Andreev channel whose supercurrent remains comparable to that of the lossless junction. In the infinite-gap limit, the steady-state current factorizes as Iss=IAPγI_{\rm ss}=I_A P_γIss​=IA​Pγ​, so that even when the Andreev current IAI_AIA​ is strictly reciprocal, the phase asymmetry of PγP_γPγ​ alone can produce a Josephson diode effect through reservoir engineering. We further show that local Coulomb repulsion can drive the system toward a nearly ideal diode regime via a dark-pair resonance. Using Keldysh-Lindblad calculations, we demonstrate that our results remain robust for realistic junctions with a finite superconducting gap and dissipation.
Abstract In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry—an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.