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arXiv:1412.3186 · Optics Letters

Effect of scattering loss on connections between classical and quantum processes in second-order nonlinear waveguides

L. G. Helt, Michael J. Steel

Published Mar 27, 2015• 27 citations
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Abstract

We show that a useful connection exists between spontaneous parametric downconversion (SPDC) and sum frequency generation in nonlinear optical waveguides with arbitrary scattering loss, while the same does not hold true for SPDC and difference frequency generation. This result refines the relationship between these quantum and classical second-order nonlinear optical processes in waveguides, and identifies the most accurate characterization of a waveguide's quantum performance in the presence of loss based solely on classical measurements.

DOI
10.1364/ol.40.001460

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We show that a useful connection exists between spontaneous parametric downconversion (SPDC) and sum frequency generation in nonlinear optical waveguides with arbitrary scattering loss, while the same does not hold true for SPDC and difference frequency generation. This result refines the relationship between these quantum and classical second-order nonlinear optical processes in waveguides, and identifies the most accurate characterization of a waveguide's quantum performance in the presence of loss based solely on classical measurements.
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 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.
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.
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function.\n\nIn the limit of a low probability of pair production, photon pair production fficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical “seed” field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless enerated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption\nor free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis.\n\nBiphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This further allows estimation of the suitability of their associated photon pairs for various quantum information processing applications. As an alternative to dispersion engineering a channel waveguide photon pair source, it is calculated that microring resonators can very naturally produce nearly spectrally uncorrelated photon pairs, which behave very much like idealized single-mode photons and are thus useful for applications involving the interference of photons from multiple sources.