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Theory of scattering loss during spontaneous parametric downconversion in waveguides

L. G. Helt, John E. Sipe, M. J. Seel

Published Jan 1, 2014• 1 citation
Publisher

Abstract

We consider simultaneous SPDC and scattering loss in waveguides by coupling waveguide modes to a reservoir. We calculate that a reduction in pair generation efficiency can be accompanied by an increase in heralded photon purity.
DOI
10.1364/cleo_qels.2014.fw3a.5

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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 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.
The generation of high purity single photons and entangled photon pairs is a crucial first step in many quantum optics experiments, including those that require quantum teleportation [1], entanglement swapping [2], and the generation of multi-photon entanglement [3]. The most widely used and established approach for creating photon pairs is spontaneous parametric down conversion (SPDC) - where pump photons undergo a non-linear optical process to create a down-converted photon pair [4]. Traditionally, the generation of high-purity heralded single photons required severe spectral filtering, introducing additional loss. However, through careful engineering of spectral correlations of the down-converted photon pairs one can circumvent the need for filtering and avoid the accompanying reduction in heralding efficiency.
Recently, we verified that spontaneous parametric down conversion (SPDC) is enhanced in a waveguide, in agreement with theory showing an inverse dependence on mode confinement [1]. Here we investigate highly-confined nanophotonic waveguides designed to maximize the SPDC rate. A theory modified to include highly-confined waveguides is used to calculate the spectral width and pair generation rates in a sample system. Pair generation rates exceeding 10(9)/sec/nm/mW are predicted for periodically-poled KTP (PPKTP) nanophotonic waveguides. This results in an enhancement of the downconverted signal power greater than 45x that of low-index-contrast PPKTP waveguides and greater than 6500x that of bulk PPKTP crystals.