Unidirectional flow of quantum noise through non-reciprocity

Quantum noise often dominates the dynamics in quantum optical systems, limiting their practical applications and making its control essential. In this work, we demonstrate that non-reciprocity enables a unidirectional flow of noise from the non-equilibrium steady states of nonlinear driven-dissipative systems. Specifically, in lattices with open boundary conditions, this unidirectional flow results from the non-Hermitian skin effect (NHSE) for quantum noise, even when the nonlinear mean-field does not exhibit this effect. We show that this mechanism offers a robust method for isolating parts of the system from degradation caused by excess noise injection. Additionally, we uncover novel topological transitions mediated by nonlinearity and demonstrate that the quantum noise sources inherent to non-Hermitian non-reciprocity can imprint themselves onto the quantum correlations of the driven system. Our approach establishes a novel link between non-Hermitian topology and nonlinear many-body systems, potentially leading to topological descriptions of interacting states of light.