Nonlinear-optical realization of nonintegrable phases accompanying quantum phase transitions

In this work, we propose an experimentally feasible nonlinear optical platform to realize nonintegrable geometric phases that emerge in interacting quantum systems undergoing quantum phase transitions. Specifically, we demonstrate that an exotic nonlinear term in the dynamical equations governs the polarization evolution of the optical field propagating along an anisotropic low-birefringence fiber with tetragonal symmetry. Intriguingly, by adiabatically tuning the nonlinear susceptibilities along the fiber, the Stokes vector on the Poincar\'e sphere accumulates a nonintegrable phase known as the Hannay angle---the classical counterpart to the Berry phase---which exhibits the same geometric gauge structure, including conic singularities in parameter space, as those associated with quantum phase transitions in systems like Bose-Einstein condensates. We further discuss a practical experimental implementation through the adiabatic deposition of nanocrystals along the fiber to control these susceptibilities, highlighting assumptions such as negligible losses and low birefringence for realistic fiber lengths.