Nonlinear optical realization of non-integrable phases accompanying quantum phase transitions

TL;DR

This paper demonstrates a feasible nonlinear optical setup to observe non-integrable phases, like the Hannay angle, associated with quantum phase transitions, using anisotropic fibers and nano-crystals.

Contribution

It introduces a novel optical method to simulate non-integrable phases linked to quantum phase transitions through nonlinear polarization control.

Findings

Nonlinear polarization in fibers can simulate quantum phases.

Adiabatic tuning of susceptibilities induces Hannay angle accumulation.

Experimental feasibility via nano-crystal deposition is discussed.

Abstract

In this work, we propose an experimentally feasible nonlinear optical realization of a type of non-integrable phase found in interacting quantum systems at quantum phase transitions. We show that an exotic term in the dynamical equation governs the nonlinear polarization of the optical field along an anisotropic low-birefringence fiber with tetragonal symmetry. Intriguingly, by adiabatically tuning nonlinear susceptibilities along the fibers, the Stokes vector on the Poincar\'e sphere accumulates a non-integrable phase called the Hannay angle, which shares the same geometric gauge structure as that associated with quantum phase transitions. Experimental realization via adiabatically depositing nano-crystals along the fibers is discussed.