# Editorial Board Members' Collection Series: Nonlinear Photonics
## 2 An Overview of the Articles in This Special Issue  
Systems that utilize quantum information resources generally take advantage of coherent macroscopic superposition and/or entanglement, both of which are generically found in states supported by nonlinear systems. However, optical nonlinearities are typically weak for closed systems. With the advent of epsilon-near-zero materials and polariton-enhanced scattering, commonly facilitated by electronically induced transparency, large effective nonlinearities become increasingly realistic as well. When realized in a high-Q optical resonator, strong optical nonlinearities with relatively long evolution time and low loss facilitate deterministic quantum optical state engineering. We note that in a material with second- and third-order nonlinearities comparable in strength at optical frequencies, the interaction between field states is strongly photon-number-dependent. With this in mind, in reference [4], a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions is proposed. A class of nonlinear optical resonators is individuated, which can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon-number-dependent frequency matching, inducing photon-number-selective interactions. With a high-amplitude coherent pump, the number-selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing. The requisite material properties to build the device and highlight the remaining material degrees of freedom, which offer flexible material design, are also reported. Recurrent neural networks (RNNs) are promising methods for the classification of anomalous diffusion trajectories, identifying temporal dependencies and sequential patterns, which are essential for characterizing anomalous diffusion processes. The integration of statistical methods with RNNs has enabled the development of robust frameworks that can detect and predict the occurrence of anomalous diffusion, even in the presence of significant noise. By leveraging these techniques, reference [5] aims to improve accuracy for identifying diffusion types without the need for extensive preprocessing or noise filtering. Therefore, it contributes to the broader application of a combination of higher-order statistics and artificial intelligence in analyzing and predicting phenomena within stochastic and noisy environments. In reference [5], feature extraction through parametric and non-parametric spectral analysis methods is explored to decode anomalously diffusing trajectories, achieving reduced computational costs compared with other approaches that require additional data or prior training. The proposed methods deliver accurate results, even with short trajectories and in the presence of noise. A soliton molecule consists of two or more solitons, and these solitons have fixed phase differences and temporal pulse intervals between adjacent solitons. Soliton molecules can be efficiently generated in fiber laser oscillators through increasing pump power or decreasing saturable power/energy of intra-cavity saturable absorbers. The possible experimental realization techniques of soliton molecules with chirped Gaussian pulses are the constructions of passively mode-locked fiber lasers, accompanied by intra-cavity management of pump power, group-velocity dispersion, saturable absorbers, and so on. In reference [6], the extra-cavity modulation of a soliton molecule with a chirped Gaussian pulse shape is developed in a 1 \(\upmu\)m optical fiber system. The optical fiber modulation system can efficiently modulate temporal and frequency properties of optical soliton molecules and their orthogonal components. Different soliton parameters in orthogonal polarizations are applied to achieve controllable optical solitons' output with specific properties in the time/frequency domain.