In 1974 Stephen Hawking make a prediction that hints a connection between quantum mechanics, general relativity and thermodynamics. A prediction that was apparently doom to never be tested until a theoretical analogue proposed by Bill Unruh in 1980 connected Hawking's prediction with moving media. In recent years, laboratory analogues of the event horizon are getting closer to test one of the most elusive effects in Physics: Hawking radiation. What if we could recreate some aspects of these astrophysical objects in the laboratory? This is the field known as analogue gravity.

The nonlinear propagation of light in media has been a topic of research since the 1980s through the numerical simulation of the non-linear Schrödinger equation (NLSE. On the other hand, thanks to the development of photonic crystal fibers (PCs), ultra-short pulses have become a commonplace in optics labs, these pulses contain only few optical cycles and therefore its theoretical and numerical modeling is still a challenge due to highly nonlinear effects present in them, causing effects such as: soliton pulse formation, optical four-wave mixing and supercontinuum generation.

Nonlinear quantum optics stands as one of the most dynamic and promising frontiers in modern physics, uniting the fundamental principles of quantum mechanics with the rich phenomena of nonlinear optics. This interdisciplinary field has undergone rapid expansion in recent decades, propelled by breakthroughs in laser technology and the development of advanced optical materials. In our work, we explore novel effects that deviate from the conventional phase-matching conditions, instead satisfying a more flexible criterion we refer to as resonant condition.

Quantum simulation has emerged as a powerful paradigm to explore complex quantum systems that are otherwise intractable with classical computational tools: Instead of solving the problem directly, they replicate the behavior of the target system using a well-controlled quantum platform. Within this framework, optics plays a central role. Photonic systems provide exceptional control, coherence, and scalability, making them ideal candidates for quantum simulations. Using light, we can engineer synthetic Hamiltonians, simulate relativistic phenomena, and study the dynamics of entanglement and decoherence in real time. Optical quantum simulations are not only a means to understand nature, but a stepping stone toward the next generation of quantum devices.