Intensity-Difference Squeezing in a Fiber Nonlinear Interferometer: Theoretical Optimization and Experimental Realization

Nonlinear interferometers offer a robust platform for quantum sensing beyond the standard quantum limit. Specifically, the generation of high-quality intensity-difference-squeezed (IDS) states provides a distinct advantage by circumventing the need for complex phase-coherent local oscillators. However, practical imperfections such as asymmetric inter-stage transmission and unbalanced detection losses severely degrade the generation of these states. In this work, we analyze IDS state generation within fiber nonlinear interferometers utilizing cascaded parametric amplifiers. Using a single-mode theoretical framework and experimental demonstration, we derive an optimal electronic gain ratio for differential detection to compensate for asymmetric detection-induced noise mismatches, extending achievable squeezing into the high-gain regime. We further analyze system tolerance to inter-stage losses and path delays. Experiments demonstrate that while higher initial parametric gain improves quantum correlations, it amplifies intensity noise and accelerates gain saturation, resulting in optimal squeezing at balanced low-gain configurations. These findings establish a robust framework for the design and optimization of all-fiber quantum sensors.