Studying Quasi-Parametric Amplifications: From Multiple PTPT -Symmetric Phase Transitions to Non-Hermitian Sensing

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