Golden Ratio entanglement in hexagonally poled nonlinear crystals

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 $\varphi =(1+\sqrt{5})/2$. 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.

arXiv comment16 pages, 10 figures

References in corpus (6)

• Correlated imaging, quantum and classical
• Coherent imaging with pseudo-thermal incoherent light
• Compact engineering of path-entangled sources from a monolithic quadratic nonlinear photonic crystal
• Multi-photon, multi-mode polarization entanglement in parametric down-conversion
• Compact 2D Nonlinear Photonic Crystal Source of Beamlike Path Entangled Photons
• Space-time coupling in the up-conversion of broadband down-converted light

Cited by in corpus (5)

• Phase sensitivity of spatially broadband high-gain SU(1,1) interferometers
• Efficient parametric generation in a nonlinear photonic crystal pumped by a dual beam
• Hot-spots and gain enhancement in a doubly pumped parametric down-conversion process
• Engineering multipartite entangled states in doubly pumped parametric down-conversion processes
• Multipartite spatial entanglement generated by concurrent nonlinear processes