The physical analogy between nonlinear optical dynamics and quantum mechanical systems, receiving growing attention in recent years, often leads to discoveries of new phenomena and solutions to existing challenges in nonlinear optical systems, not to mention the excitement scientists feel when unifying topics that were seemingly unrelated. More specifically, the coupled nonlinear interaction between two classical or quantum waves with non-degenerate frequencies, with one or more co-existing classical pump waves, is analogous to a coupled quantum two-state system. The two systems also share a common problem: the varying dispersion in optical nonlinear interaction, a universal obstacle in broadband optical frequency conversion, is analogous to the ensemble inhomogeneity in quantum two-state systems, which is preventing full population transition in resonance. Fortunately, the latter system has a well-established solution: rapid adiabatic passage, which can achieve full-population inversion despite the ensemble impurity. Thus motivated, an exciting research concept to overcome such challenge was examined in the recent decade: rapid adiabatic passage (RAP) in optical three-wave mixing (TWM). Realized through a slow dispersion sweep in quadratic electric susceptibility $\chi^{(2)}$ nonlinear media, RAP in TWM has demonstrated spectacular capability of reaching over 90% adiabatic inversion of photon population over octave-spanning pulses, while also achieving phase and amplitude shaping over the entire bandwidth. Such exquisite concept, if achievable in cubic electric susceptibility $\chi^{(3)}$ nonlinear media, can not only greatly expand the selection of nonlinear platforms for broadband frequency conversion, but solve challenges in many crucial applications of $\chi^{(3)}$ nonlinear process. The works of my PhD are thus motivated to probe into the theory, numerical study, experimental observation, and many future possibilities of RAP in optical four-wave mixing (FWM). The story of this thesis, same as most scientific discoveries and technological inventions, were born from a simple question: is RAP possible in optical FWM? From there, we first derive the coupled two-level system equations from nonlinear Schr"{o}dinger equations for optical FWM. Delicate, yet fundamental findings can be discovered for the concept even from its skeleton form. Meanwhile, realistic numerical simulations were crafted as comprehensively as possible to model the feasibility of our theory. We then thoroughly examine potential platforms, ranging from low-energy step-index fibers to high-flux hollow core fiber. Results indicate that, due to its fundamental nature, RAP in optical FWM can be realized in essentially all cubic nonlinear platforms. Next, we experimentally demonstrate this concept using a highly-nonlinear photonic crystal fiber. Our proof-of-concept experiment is the first observation of RAP in optical FWM, with results closely follow our theoretical and numerical predictions. Lastly, we summarize some interesting yet unpublished investigations on potential platforms, which reveal promising applications and sometimes even new physics.