Quantum criticality in photorefractive optics: vortices in laser beams and antiferromagnets

摘要

We study vortex patterns in a prototype nonlinear optical system:counterpropagating laser beams in a photorefractive crystal, with or withoutthe background photonic lattice. The vortices are effectively planar anddescribed by the winding number and the "flavor" index, stemming from the factthat we have two parallel beams propagating in opposite directions. The problemis amenable to the methods of statistical field theory and generalizes theBerezinsky-Kosterlitz-Thouless transition of the XY model to the "two-flavor"case. In addition to the familiar conductor and insulator phases, we also havethe perfect conductor (vortex proliferation in both beams/"flavors") and thefrustrated insulator (energy costs of vortex proliferation and vortexannihilation balance each other). In the presence of disorder in the backgroundlattice, a novel phase appears which shows long-range correlations and absenceof long-range order, thus being analogous to spin glasses. An important benefitof this approach is that qualitative behavior of patterns can be known withoutintensive numerical work over large areas of the parameter space. Moregenerally, we would like to draw attention to connections between the(classical) pattern-forming systems in photorefractive optics and the methodsof (quantum) condensed matter and field theory: on one hand, we use thefield-theoretical methods (renormalization group, replica formalism) to analyzethe patterns; on the other hand, the observed phases are analogous to thoseseen in magnetic systems, and make photorefractive optics a fruitful testingground for condensed matter systems. As an example, we map our system to adoped $O(3)$ antiferromagnet with $\mathbb{Z}_2$ defects, which has the samestructure of the phase diagram.