Generation of entangled photon states in nonlinear nanostructures and metamaterials

Entangled photon states are promising for quantum computing, cryptography and metrology. While room temperature quantum interference of light on a chip has been recently demonstrated, the light generation still relied on external bulk nonlinear crystals [1]. The practical development of compact and robust nonlinear quantum circuits calls for a versatile toolbox which can fully describe the generation and detection of entangled photons and plasmons. Here, we present theoretical and experimental results on entangled photon pair generation and sum-frequency generation in complex nonlinear nanostructures.\\ \\We formulate a general theoretical framework of integrated paired photon-plasmon generation through spontaneous wave mixing in nonlinear plasmonic and metamaterial nanostructures, rigorously accounting for material dispersion and losses in the quantum regime through the electromagnetic Green function [2]. As a specific application of our approach we design nonlinear metal/ dielectric plasmonic structures and predict photon-plasmon correlations with 70\% internal heralding quantum efficiency. We reveal a novel mechanism of generation enhancement in a multi-layered metal-dielectric metamaterial, originating from the broadband phase synchronism at the topological transition to the hyperbolic dispersion regime. Next, we prove a general quantum-classical reciprocity relation between the spontaneous parametric down-conversion (SPDC) in an arbitrary nonlinear structure and the reverse sum frequency generation process. We formulate a quantum process tomography protocol to determine a biphoton state produced via SPDC by using only classical measurements. The classical reconstruction of amplitude and phase of biphoton wavefunction has been experimentally verified in a multi-channel integrated nonlinear waveguide array [3].\\ \\$[1]$ J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317 (2014).\newline [2] A. N. Poddubny, I.V. Iorsh, and A.A. Sukhorukov, Phys. Rev. Lett. 117, 123901 (2016).\newline [3] F. Lenzini, A.N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A.A. Sukhorukov, and M. Lobino, in preparation (2017).