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Biphoton generation in quadratic waveguide arrays: A classical optical simulation

Markus Gräfe, Alexander S. Solntsev, Robert Keil, Andrey A. Sukhorukov, Matthias Heinrich, Andreas Tünnermann, Stefan Nolte, Alexander Szameit, Yuri S. Kivshar

Published Aug 16, 2016• 29 citations
OpenAlex

Abstract

∗ both authors contributed equally Quantum entanglement, the non-separability of a multipartite wave function, became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demon-strated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. With the discovery of spontaneous parametric down-conversion (SPDC) in nonlinear crystals, an efficient source for entangled photon pairs, so-called biphotons, be-came available. It has recently been shown that SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional spatial dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional (1D) arrays can be simulated through classical optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-type inequality. PACS numbers: 42.50.-p, 42.82.Et, 42.65.Lm

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∗ both authors contributed equally Quantum entanglement, the non-separability of a multipartite wave function, became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demon-strated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. With the discovery of spontaneous parametric down-conversion (SPDC) in nonlinear crystals, an efficient source for entangled photon pairs, so-called biphotons, be-came available. It has recently been shown that SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional spatial dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional (1D) arrays can be simulated through classical optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-type inequality. PACS numbers: 42.50.-p, 42.82.Et, 42.65.Lm
Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.
This work reveals that linear propagation of classical light beams can be used to simulate the nonlinear effect of SPDC leading to photon pair generation and quantum random walks of the generated biphotons. In particular, the authors demonstrate that the quantum correlations of biphotons generated in a quadratically nonlinear 1D waveguide array can be mapped onto a linear beam propagation in specially designed 2D array of coupled optical waveguides. This analogy enables us to simulate, with classical light, the quantum coincidence counts for biphotons including the regime of breaking a 1D Bell like inequality as indicated by positve values of the non-classicality.
Arrays of coupled optical waveguides provide a flexible platform for manipulation of optical beams and pulses. Recently, the propagation of non-classical light in waveguide arrays has shown a surging attention. It was shown that quantum walks of correlated photon pairs realized through propagation in waveguide arrays can lead to nontrivial quantum correlations at the array output. However, all currently used schemes for quantum walks utilise correlated photon pairs generated externally to the array. Here, we propose and demonstrate numerically a novel scheme enabling simultaneous generation of correlated photon pair through spontaneous parametric downconversion (SPDC) and quantum walks inside a single photonic element an array of quadratic nonlinear waveguides. This scheme avoids entirely the need for complex interfaces between the different photonic elements and enables novel ways for control of the quantum correlations.
The generation of multi-photon quantum states in integrated waveguiding structures provides a route to the creation of quantum optical chips. In particular, the simultaneous generation of photons through spontaneous parametric down-conversion (SPDC) and their quantum walks in nonlinear waveguide arrays (WGAs) can be used to produce strongly spatially entangled biphoton states [1] with applications for quantum search algorithms [2]. Whereas up to now only arrays of single-mode nonlinear waveguides have been considered for SPDC, in general the waveguides may support several guided modes, which were demonstrated to strongly affect nonlinear wave mixing in the classical regime [3]. Here we show that using higher order modes for SPDC has a significant influence on the generated two-photon states and gives additional means to control them. In particular, we employ the symmetry of the modes to engineer effectively nonlocal photon pair generation by SPDC.