Simulating many-body physics with quantum nonlinear optics

The rapidly growing field of quantum information can benefit greatly from quantum nonlinear optics, which has the potential to generate highly correlated optical states with a sufficiently large interaction strength per photon. Such states play a crucial role in various quantum applications. While the traditional approach to generating correlated optical states involves controlled interactions between individual single photons through nonlinear mediums, a more efficient approach is to use the evolution of multiphotons in the highly nonlinear optical medium. To facilitate this approach, we propose a scheme that traces the time evolution of the photons encoded in Fock space to generate complex correlated states. Our approach mimics the dynamics of many-body systems with adjustable interaction strength, allowing us to simulate state transfer on a spin chain by tuning the interaction. We also investigate the feasibility of our scheme based on current technologies and explore the potential of quantum nonlinear optics in quantum simulation.