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Optics Express

Domain engineering algorithm for practical and effective photon sources

Jean-Luc Tambasco, Andreas Boes, L. G. Helt, Michael J. Steel, Arnan Mitchell

Published Aug 16, 2016• 52 citations
Publisher

Abstract

We introduce a method for shaping the spectral response of nonlinear light sources by tailoring the quasi-phase matching. Our algorithm relies on engineering the poling to accurately trace a generated target signal field amplitude to determine the desired nonlinearity profile. The proposed poling algorithm results in a poling pattern that is more robust to manufacture, as all domain inversions are of equal width. The poling pattern is verified using a nonlinear beam propagation method simulation. This approach is applied to achieve Gaussian-shaped phase matching along a potassium titanyl phosphate (KTP) crystal in order to generate pure heralded single photons of spectral purity ~0.996-this is highly desirable for heralded single photon quantum optics.

DOI
10.1364/oe.24.019616

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arXiv:1005.3086•Optics Express•Dec 20, 2010•141 citations
We introduce a method for shaping the spectral response of nonlinear light sources by tailoring the quasi-phase matching. Our algorithm relies on engineering the poling to accurately trace a generated target signal field amplitude to determine the desired nonlinearity profile. The proposed poling algorithm results in a poling pattern that is more robust to manufacture, as all domain inversions are of equal width. The poling pattern is verified using a nonlinear beam propagation method simulation. This approach is applied to achieve Gaussian-shaped phase matching along a potassium titanyl phosphate (KTP) crystal in order to generate pure heralded single photons of spectral purity ~0.996-this is highly desirable for heralded single photon quantum optics.
We demonstrate Gaussian-shaped phase matching of a periodically-poled potassium titanyl phosphate (PPKTP) crystal by imposing a custom duty-cycle pattern on its grating structure while keeping the grating period fixed. The PPKTP's phase-matching characteristics are verified through optical difference-frequency generation measurements, showing good agreement with expected values based on our design parameters. Our theoretical analysis predicts that under extended phase-matching conditions the custom-poled PPKTP crystal is capable of generating heralded single photons with a spectral purity of 97%, and can reach as high as 99.5% with gentle spectral filtering, something that is highly desirable for photonic quantum information processing applications.
Summary form only given. Parametric downconversion (PDC) allows the generation of highly coherent, spectrally pure single photons for quantum photonics. In a typical heralded PDC source, the signal photon emerges in a spectrally mixed state due to strong (anti)correlation in the joint spectrum of PDC photon pairs.One method for reducing spectral correlations is spectral filtering, but this compromises the heralding efficiency and the brightness of the source. A more sophisticated method for increasing the heralded photon purity is group-velocity matching, which works by erasing part of the timing information between the pump and PDC photons. What group-velocity matching cannot address, however, are the remaining correlations in the joint spectrum that come from the sinc-shaped phase-matching function (PMF) typical to standard PDC crystals. Further source engineering is therefore required to remove these correlations. Several studies have introduced domain-engineering techniques for shaping the phase matching function (PMF) in periodically poled crystals to improve single photon purities [1-4]. We present a new technique for tailoring crystal nonlinearities which combines the advantages of a deterministic method for domain engineering [4] and an annealing method developed for classical applications in higher-harmonic generation [5]. In our method, we first choose each domain orientation such that the generated field amplitude along the crystal matches the target field amplitude obtained by integrating the desired nonlinearity profile. Using a one-block structure instead of a two-blocks structure (as in [4]) results in a higher flexibility of the algorithm in tracking the target function and yields to more accurate results. We then use an annealing algorithm to slightly vary the width of each domain, further improving the effective PMF. Our technique outperforms its predecessors, particularly for short crystals, leading to high single photon purities, as shown in Fig.1. We experimentally characterise our method through a high-precision measurement of multiphoton interference between two heralded photons generated by two independent sources.We also notice that by considering a complex target field amplitude function it is possible to generalise the algorithm in [5] to any constant domain width (not necessarily equal to the coherence length), leading to a better approximation of the desired phase matching function, especially in the very short crystal regime. Moreover, tracking both the real and imaginary components of the target function allows us to approximate more exotic cases such as chirped nonlinearity profiles. Since scalable quantum photonics will require integrated architectures in which nonlinear processes are typically employed for single-photon generation, it will be interesting to explore new techniques similar to in-fibre Bragg grating structures which might yield quasi-periodic four-wave mixing and apply our algorithm to these new platforms.
Heralded single-photon sources are a fundamental building block for optical quantum technologies. These sources need to be unfiltered and integrated to have good scalability and avoid unnecessary losses. To attain this goal, it is necessary to control the effective nonlinearity seen by the fields as they mix and propagate in a waveguide source. In this paper, we introduce a method to design nonlinear waveguides with arbitrarily shaped effective nonlinearity profiles. The method takes advantage of the fact that the second-order nonlinear response is a tensor quantity and thus the local effective nonlinearity of a material depends on the propagation direction of the fields participating in the interaction. Thus, by locally changing the propagation direction of the fields we can modulate the wave-mixing process. Our method allows for the waveguide fabrication process to be significantly simplified. The material structure of the waveguide is made by a single crystal, no longer needing oriented patterning or periodic poling. We use our method to design waveguides with a nonlinearity profile that is Gaussian in the propagation length, allowing the generation of perfectly pure heralded single photons.
Photonic quantum technology relies on efficient sources of coherent single photons, the ideal carriers of quantum information. Heralded single photons from parametric down-conversion can approximate on-demand single photons to a desired degree, with high spectral purities achieved through group-velocity matching and tailored crystal nonlinearities. Here we propose crystal-nonlinearity-engineering techniques with sub-coherence-length domains. We first introduce a combination of two existing methods: a deterministic approach with coherence-length domains and probabilistic domain-width annealing. We then show how the same deterministic domain-flip approach can be implemented with sub-coherence-length domains. Both of these complementary techniques create highly pure photons, outperforming previous methods, in particular for short nonlinear crystals matched to femtosecond lasers.
Many applications in optical quantum information processing benefit from careful spectral shaping of single-photon wave-packets. In this paper we tailor the joint spectral wave-function of photons created in parametric downconversion by engineering the nonlinearity profile of a poled crystal. We designed a crystal with an approximately Gaussian nonlinearity profile and confirmed successful wave-packet shaping by two-photon interference experiments. We numerically show how our method can be applied for attaining one of the currently most important goals of single-photon quantum optics, the creation of pure single photons without spectral correlations.