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arXiv:1401.7070 · Physical Review A

Effect of loss on photon-pair generation in nonlinear waveguide arrays

Diana A. Antonosyan, Alexander S. Solntsev, Andrey A. Sukhorukov

Published Oct 21, 2014• 32 citations
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Abstract

We describe theoretically the process of spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schr\"odinger-type equations for the biphoton wave function and the wave function of one photon when the other photon in a pair is lost. We demonstrate effects arising from loss-affected interference between the generated photon pairs and show that nonlinear waveguide arrays can serve as a robust loss-tolerant integrated platform for the generation of entangled photon states with nonclassical spatial correlations.

DOI
10.1103/physreva.90.043845

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We describe theoretically the process of spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schr"odinger-type equations for the biphoton wave function and the wave function of one photon when the other photon in a pair is lost. We demonstrate effects arising from loss-affected interference between the generated photon pairs and show that nonlinear waveguide arrays can serve as a robust loss-tolerant integrated platform for the generation of entangled photon states with nonclassical spatial correlations.
Integrated nonlinear waveguide structures enable generation of quantum entangled photons. We describe theoretically the effects of spatially inhomogeneous loss on the creation of photon pairs through spontaneous parametric down-conversion in quadratically nonlinear directional couplers, where photons experience effective parity-time (PT) symmetric potential due to the presence of optical loss in one of the waveguides. We show that for losses below the PT-breaking threshold, the quantum photon states can be flexibly tuned similarly to conservative couplers, whereas for stronger losses, the correlations between two waveguide modes are suppressed. We also formulate a quantum-classical correspondence with sum-frequency generation for fast evaluation of device performance. These results can be applied for the design of quantum plasmonic circuits.
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We predict that all-optically-reconfigurable generation of photon pairs with tailored spatial entanglement can be realized via spontaneous parametric down conversion in integrated nonlinear coupled waveguides. The required elements of the output quantum wave function are directly mapped from the amplitudes and phases of the classical laser pump inputs in each waveguide. This is achieved through special nonuniform domain poling, which locally inverts the sign of quadratic nonlinear susceptibility and accordingly shapes the interference of biphoton quantum states generated along the waveguides. We demonstrate a device configuration for the generation of any linear combination of two-photon Bell states.
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.
We establish theoretically and demonstrate experimentally that photon-pair generation through spontaneous parametric down-conversion in a nonlinear waveguide with scattering or material losses can be effectively emulated by classical laser light propagation through a specially designed linear waveguide circuit. This platform can represent arbitrary photon and pump losses, with a potential for the emulation of non-Markovian decay. We characterize the photon-pair correlation spectrum and observe its characteristic transformation from the well-known sinc-shape in lossless waveguides towards a Lorentzian shape in the presence of photon loss.
We analyze the process of photon-pair generation with simultaneous quantum walks in a quadratic nonlinear waveguide array. We demonstrate that the spontaneous parametric down-conversion in the array allows for creating quantum states with strongly pronounced spatial correlations, which are qualitatively different from those possible in bulk crystals or through quantum walks in linear waveguide arrays. Most importantly, the photon correlations can be controlled entirely classically by varying the spatial profile of the pump beam or the phase-matching conditions.