Controlling quasi-parametric amplifications: From multiple PT-symmetry phase transitions to non-Hermitian sensing

Quasi-parametric amplification (QPA) is a nonlinear interaction in which the idler wave is depleted through some loss mechanism. QPA plays an important role in signal amplification in ultrafast photonics and quantum light generation. The QPA process has a number of features characterized by the non-Hermitian parity-time ($\mathcal{PT}$) symmetry. In this report, we explore new interaction regimes and uncover multiple $\mathcal{PT}$-symmetry phase transitions in such QPA process where transitions are particularly sensitive to external parameters. In particular, we demonstrate the feasibility of detection of $10^{-11}$ inhomogeneities of the doped absorber, which is order of magnitude more sensitive than similar measurements performed in a linear absorption regime. In doing so, we reveal a family of $\mathcal{PT}$-symmetry phase transitions appearing in the QPA process and provide a novel nonlinear optical sensing mechanism for precise optical measurements.