Nonlinear systems are important in many areas of modern science and technology. For example, nonlinearity plays an essential role in generating quantum mechanical states of both light and matter. As a result, there has been great interest in understanding the fundamental quantum nature of a variety of nonlinear effects. At the same time, there is currently a large gap between the classical and quantum understanding of nonlinear systems, with the classical understanding being far more developed. To close this gap, we introduce a general new theory which allows us to predict quantum effects in any nonlinear system purely in terms of its classical description. We demonstrate the predictions of our theory in experiments probing quantum fluctuations of intense femtosecond pulses propagating in an optical fiber undergoing soliton-fission supercontinuum generation, a process where broadband radiation is produced by a narrow-band input. Famously, this process is known to be highly noise-sensitive, leading to noisy outputs even from inputs with only quantum fluctuations. In contrast, our experiments uncovered a variety of previously hidden low-noise and noise-robust states arising from quantum correlations and entanglement, in agreement with the predictions of our theory. We also show how the theory points to new design concepts for controlling quantum noise in optics and beyond. We expect that our results will provide a template for discovering quantum effects in a wide variety of complex nonlinear systems.
