Liquid crystal enabled nonlinear optics and quantum optics

Liquid crystals (LCs), due to their intrinsic optical anisotropy and strong response to external stimuli, have emerged as a critical bridge between classical optics and quantum photonics. Initially recognized for their transformative impact on display technologies, LCs have garnered increasing attention in recent years within the fields of nonlinear optics (NLO) and quantum optics, driven by their advantages such as electrically tunable birefringence, reconfigurable molecular alignment, and compatibility with compact photonic architectures. This review provides a comprehensive overview of the latest advancements in LC-enabled linear, nonlinear, and quantum optical systems. We begin by discussing the fundamental optical properties and phase states of LCs. Building upon this, we focus on the emerging field of ferroelectric nematic LCs (FNLCs), which, owing to their spontaneous polarization and unique molecular alignment control, demonstrate significantly enhanced second-order nonlinear effects. Helical derivatives of FNLCs further enhance polarization control, giving rise to new concepts in nonlinear geometric phase. Additionally, this paper highlights the applications of FNLCs in quantum photonics, including entangled photon generation and polarization state manipulation. These innovations overcome the limitations of time-reversal symmetry inherent in traditional systems, offering promising opportunities for unidirectional quantum communication, secure quantum networks, and high-fidelity quantum state manipulation. Finally, we discuss the challenges currently facing this field and explore future prospects for FNLCs in interdisciplinary domains such as linear photonics, NLO, and quantum engineering.