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.
n the last decades, how and why RWs form attracted large interest in the most diverse fields of physics. At the same time, the need of understanding the effects of nonlinearities for beam at low photon number regime pushed physicists to better develop the theory of quantum nonlinear optics. However, both for RWs and for quantum nonlinear optics a thorough theoretical model is still missing. If we consider the most natural merge of these two topics, that is, the study of quantum optical RWs in a Kerr medium, we immediately understand that we are facing a completely new argument of fundamental relevance. The generation of quantum RWs is an untouched and open problem, and developing its theoretical structure could allow us to answer many fundamental questions about the effects of nonlinearity at low photon number regime, or the way this nonlinearity affects the formation of quantum RWs. The same is valid for quantum noise: we could comprehend if it can generate quantum RWs by itself and how quantum noise and nonlinearity interact with each other.
In order to answer to all this open questions, this project aims at establishing a new direction for the understanding of optical quantum RWs, putting together concepts of quantum optics, statistical mechanics, nonlinear wave theory and stochastic simulations into a unique, thorough model.
At high photon number, optical RWs are giant perturbations that form out of noise, reach enormous amplitudes and rapidly decay back into noise. At low photon number, we want to understand if quantum noise can have a role in RW generation, and how much it is relevant. This could open new routes not only in optics, but in modelling extreme events at quantum level in general.
Our challenge is to exploit the proper model of the quantum noise and to simulate quantum RWs in third-order-nonlinear dielectrics. Our key innovation here is the rigorous model of quantum noise by adopting modern approaches of nonlinear quantum optics, such as phase-space methods. This methodology enables to simulate a fully quantum evolution and hence will enable to determine the best strategy for the generation of RWs in a well established and complete theoretical description.
Noise and disorder are generally considered as those generating mechanisms giving stochastic properties and unpredictability to extreme wave events. The idea that quantum noise can be used to generate or enhance optical RWs at low photon number regime represents a complete innovation. The engineering of structural properties of the wave-supporting medium to foster the formation of high-intensity spots may find application in photonic devices and quantum technologies, where the enhancement of light-matter interaction in desired position is a crucial requirement for spectroscopy, energy storage, nanoscale functionalities and quantum information.