Noise-enhanced temporal boundary states in non-Hermitian systems
Time-periodic modulation introduces a synthetic degree of freedom to manipulate topological phases. This synthetic dimension can trigger a phase transition that localizes a boundary state at the temporal interface. Noise is widely deemed a fundamental threat to topological protection, universally anticipated to weaken or even destroy topological states. Here, we introduce periodically repeated temporal noise and fully random temporal noise into a 2D periodically driven non-Hermitian system. Paradoxically, under ensemble averaging, such temporal noise drives an exponential enhancement of the response intensity at the temporal interface. An averaged superoperator analysis shows that the noiseless band structure is preserved under both types of noise. Yet the noise increases the growth rate of growing modes while suppressing the decay rate of decaying ones. Finally, we experimentally realize the noise-enhanced temporal boundary state in a robotic metamaterial network. This finding establishes temporal noise as a constructive ingredient, enabling the unambiguous emergence of topological states and conferring exceptional robustness upon topological devices.