Golden Ratio entanglement in hexagonally poled nonlinear crystals

TL;DR

This paper investigates the quantum entanglement properties of twin photons and beams generated in hexagonally poled nonlinear crystals, revealing a unique resonance condition linked to the Golden Ratio and Fibonacci sequence.

Contribution

It demonstrates the emergence of Golden Ratio entanglement in a hexagonally poled crystal, connecting nonlinear optics with mathematical constants and sequences.

Findings

Tripartite entangled state at coexistence points of two nonlinear processes

Transition to 4-mode entanglement dominated by the Golden Ratio

Maximal coherence achieved through angle tuning and resonance conditions

Abstract

This work analyses the quantum state of twin photons and twin beams generated by parametric-down conversion in a hexagonally poled photonic crystal,characterized by the simultaneous presence of two nonlinear processes sustained by two vectors of the reciprocal lattice. In those special points of the fluorescence spectrum where the two processes coexist,we show that a tripartite entangled state is realized, equivalent to a single parametric process followed by a beam-splitter. By proper angle tuning a peculiar resonance condition is reached, with a transition to a 4-mode entanglement, dominated by the Golden Ratio of the segment $\phi= (1+\sqrt 5)/2$. A maximal coherence between the two nonlinear processes is here estabilished, as the overall process is shown to be equivalent to two independent parametric processes followed by a beam-splitter. We offer an interpretation of the occurrence of the golden ratio in this system based on an analogy between the evolution of the light modes and the Fibonacci sequence.