Anderson Localization of Quantum Noise

Anderson localization is the absence of diffusion in disordered media, illustrating how disorder can suppress transport in quantum systems. Here, we show that an analogous phenomenon can arise for quantum noise in nonlinear driven-dissipative systems. We study a one-dimensional chain of Kerr resonators with detuning and drive disorder and analyze the linearized fluctuations around steady-state solutions. As disorder strength increases, the noise covariance matrix and mode-resolved inverse participation ratios reveal exponentially localized noise modes. Such noise localization persists across a wide range of system parameters, irrespective of whether disorder is applied to detuning or drive. Our findings offer new possibilities for designing nonequilibrium quantum optical systems, where disorder, typically viewed as detrimental, can be exploited as a resource to enhance stability and suppress noise propagation.