Probing intensity noise in ultrafast pulses using the dispersive Fourier transform augmented by quantum sensitivity analysis

To reach the next frontier in multimode nonlinear optics, it is crucial to better understand the classical and quantum phenomena of systems with many interacting degrees of freedom -- both how they emerge and how they can be tailored to emerging applications, from multimode quantum light generation to optical computing. Soliton fission and Raman scattering comprise two such phenomena that are ideal testbeds for exploring multimode nonlinear optics, especially power-dependent physics. To fully capture the complexity of such processes, an experimental measurement technique capable of measuring shot-to-shot pulse variations is necessary. The dispersive Fourier transform (DFT) is the ideal technique to achieve this goal, using chromatic dispersion to temporally stretch an ultrafast pulse and map its spectrum onto a measurable temporal waveform. Here, we apply DFT to explore the power-dependent mean field and noise properties of soliton fission and Raman scattering. To explain quantum noise properties, the traditional approach is to perform several hundred stochastic simulations for computing statistics. In our work, we apply quantum sensitivity analysis (QSA) to compute the noise in any output observable based on fluctuations in the input pulse, all using a single backwards differentiation step. We find that the combination of DFT and QSA provides a powerful framework for understanding the quantum and classical properties of soliton fission and Raman scattering, and can be generalized to other multimode nonlinear phenomena.