Quantum Optical Rogue Waves
The origin of rogue waves is still not understood, even if they appear in many diverse fields of science and life, from water waves to stock markets. This situation has led to an ever-growing interest in the scientific community. Seemingly, quantum nonlinear optics has gained a great interest in the last decades, but a complete and profound theoretical model of light propagation through nonlinear media at few photon regime is still missing.
From the quantization of Maxwell¿s equations, we can derive a description of electromagnetic field both in homogeneous and in inhomogeneous nonlinear dielectric. By phase-space methods we can map our quantum model to a system of stochastic partial differential equations, where the non-deterministic part represents the quantum noise due to the Heisenberg principle. This route leads to a new approach to the theoretical investigation of quantum nonlinear optical phenomena: the classical numerical studies become quantum by adding stochastic noise in propagation.
In the specific case of third order nonlinearity, that is, the Kerr effect, we can model several light dynamics, such as the generation of quantum solitons, shock waves, modulation instability, and also rogue waves. Classically, rogue waves are giant perturbations that form out of noise, reach enormous amplitudes and rapidly decay. The role of quantum noise at low photon number in optical rogue wave generation is completely unknown.
This research project aims at theoretically analyzing the way quantum noise contributes to the development of optical extreme events in wave propagation through nonlinear media at a quantum regime. To reach the scope, we plan to exploit the proper model of the quantum noise and to simulate quantum rogue waves in third-order-nonlinear dielectrics. Studying quantum optical rogue waves in nonlinear media is a very new frontier, which can open new routes both in fundamental and in applied physics.