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Quantum Information and Measurement (QIM)

Super-resonant parametric generation and golden ratio entanglement in hexagonally poled nonlinear crystals

A. Gatti, Ottavia Jedrkiewicz, E. Brambilla, Katia Gallo

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We analyze the twin beam radiation generated by parametric down-conversion in a hexagonally-poled photonic crystal representing an interesting monolithic source of path-entangled photonic states. We highlight a super-resonance condition associated with a four-mode entanglement state.
DOI
10.1364/qim.2019.f5a.14

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This work analyzes 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 four-mode entanglement, dominated by the golden ratio of the segment $\ensuremath{\phi}=(1+\sqrt{5})/2$. A maximal coherence between the two nonlinear processes is established here, 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.
Summary form only given. The efficiency and engineering capabilities afforded by parametric processes in second-order [χ(2)] nonlinear media have tremendously benefitted from periodic poling technologies in ferroelectric materials such as LiNbO3, nowadays routinely exploited in optical parametric generators, amplifiers and oscillators, as well as high brightness sources of entangled photons [1, 2]. Nonlinear photonic crystals (NPCs) implemented by periodic poling, have also attracted a great deal of attention, since they provide additional degrees of freedom to coherently shape the angular and spectral response of parametric devices [3-4]. Following the first demonstration of coherently coupled twin-beam optical parametric generation (OPG) in a χ(2)NPC [4], a number of studies investigated their potential for classical and quantum applications [5-6].Here we demonstrate twin beam OPG in a hexagonally poled LiTaO3 NPC pumped at 527 nm and generating signal and idlers in the near-infrared (λS~800 nm) and telecom (λI~1550nm) ranges. We perform a complete spectral and angular mapping of its OPG response for different pump pulse energies (10 - 100μJ) and incidence angles (-2.5 to 2.5°), finding very good agreement between predictions (Fig. 1b-c) and experiments
We study the quantum state of twin photons generated by parametric down-conversion in a two-dimensional nonlinear photonic crystal, driven by a dual pump beam. The interplay between the grating of the ${\ensuremath{\chi}}^{(2)}$ nonlinear response and the transverse spatial modulation of the pump opens a rich scenario of possibilities for controlling the quantum state. We focus on a spatial resonance condition between the pump and the nonlinear grating, where a quadripartite entangled state is generated in proper light modes. The device is shown to implement the mixing of a pair of independent two-mode squeezed states onto four separate spatial modes, without the need of any external beam-splitter. Remarkably, both the squeezing parameters and the mixing coefficients can be reconfigured by modulating the relative phase and intensity of the two pumps, enabling thus the generation of a variety of quantum states in a single device.
We propose a two-dimensional ${\ensuremath{\chi}}^{(2)}$ nonlinear photonic crystal capable of satisfying quasi-phase-matching conditions for two or three parametric down-conversions simultaneously. Seeded by a two-mode coherent state, this crystal can produce two-, three-, four-, or five-photon path-entangled states, provided the corresponding number photons are produced, i.e., in a postselection-free way. In particular, up to five-photon NOON state can be generated, which enables phase supersensitive measurements at the Heisenberg limit. The concurrent multiple quasi-phase-matchings provided by the nonlinear photonic crystal open up a way to integrated quantum light sources.