Nonlinear optical analogues of quantum phase transitions in a squeezing-enhanced LMG model

Abstract: We investigate nonlinear optical analogues of quantum phase transitions within a squeezing-enhanced generalized Lipkin-Meshkov-Glick (LMG) model, focusing on excited-state quantum phase transitions in optical fibers with tetragonal symmetry. Our analysis reveals a novel squeezing effect that induces classical bifurcations in polarization dynamics, even without a linear rotor-like term. By mapping the nonlinear polarization dynamics to the generalized LMG model, we establish a direct correspondence between optical bifurcations and quantum critical phenomena, uncovering geometric gauge structures akin to Berry-like phases. These findings highlight the interplay between classical and quantum behaviors in optical systems, offering a versatile platform for studying quantum many-body physics with applications in quantum metrology and simulation.