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Europhysics Letters (EPL)

Optical emulation of photon-pair generation in nonlinear lossy waveguides

Markus Gräfe, Diana A. Antonosyan, Alexander S. Solntsev, Andrey A. Sukhorukov, Alexander Szameit

Published Jun 1, 2017• 4 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/118/54001

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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 derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss.Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients.In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator, and we find that this density operator is naturally composed of two photon, one photon, and zero photon contributions.The biphoton probability density, or joint spectral intensity (JSI), associated with the two-photon contribution is determined not only by a phase matching term, but also by a loss matching term.The relative sizes of the loss coefficients within this term lead to three qualitatively different regimes of SPDC JSIs.If either the pump or generated photon loss is much higher than the other, the side lobes of the phase matching squared sinc function are washed out.On the other hand, if pump and generated photon loss are appropriately balanced, the lossy JSI is identical to the lossless JSI.Finally, if the generated photon loss is frequency dependent, the shape of the JSI can be altered more severely, potentially leading to generated photons that are less frequency correlated though also produced less efficiently when compared to photons generated in low-loss waveguides.
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.
Integrated optical circuits enable stable and scalable realization of quantum logic devices, which can form a basis for the mass production of photonic chips for quantum communications and computations. An important challenge is the integration of single-photon sources, which should provide on-chip generation and preparation of quantum photon states. Spontaneous parametric down-conversion (SPDC) provides an attractive solution for experimental generation of correlated and entangled photon pairs [1,2]. However, internal losses in the waveguides may still be present, affecting nontrivially the emerging photon state [3].
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.