[Paper Review] Engineered optical nonlinearity for a quantum light source

Agata M. Brańczyk, Alessandro Fedrizzi+2 more|Queensland's institutional digital repository (The University of Queensland)|May 18, 2010

Photonic and Optical Devices3 citations

TL;DR

This paper proposes engineering the nonlinearity profile of periodically poled KTP crystals to shape the joint spectral amplitude of photon pairs from spontaneous parametric downconversion, achieving a Gaussian phase-matching function without altering phase-matching conditions. The method enables high-purity, spectrally uncorrelated single photons by eliminating sinc-function side lobes through tailored nonlinearity, confirmed via two-photon interference and numerical simulations showing separable joint spectral amplitudes.

ABSTRACT

Single-photon pairs created in the nonlinear process of spontaneous parametric downconversion form the backbone of fundamental and applied experimental quantum information science. Many applications benefit from careful spectral shaping of the single-photon wave-packets. In this paper we tailor the joint spectral wave-function of downconverted photons by modulating the nonlinearity of a poled crystal without affecting the phase-matching conditions. We designed a crystal with a 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.

Motivation & Objective

• To overcome spectral correlations in heralded single-photon sources caused by sinc-shaped phase-matching functions in standard periodically poled crystals.
• To eliminate the need for spectral filtering in generating high-purity single photons by shaping the joint spectral amplitude at the source.
• To demonstrate a method for creating separable, spectrally pure single-photon states using tailored nonlinearity profiles in quasi-phase-matched crystals.
• To validate the approach experimentally through two-photon interference and numerically via joint spectral amplitude engineering.

Proposed method

• Designing a crystal with a non-uniform, approximately Gaussian nonlinearity profile by using higher-order poling to vary effective nonlinearity across discrete sections.
• Using the Fourier transform of the nonlinearity profile χ(z) to shape the phase-matching function Φ(ωi, ωs), aiming for a Gaussian form ΦG(ΔkL/2) = exp(−γ(ΔkL/2)²).
• Implementing a monochromatic pump with frequency μp to isolate the joint spectral amplitude as f(ωi, ωs) ∝ α(ωi+ωs)Φ(ωi, ωs), with α being a delta function.
• Achieving the desired nonlinearity through discrete domain poling with varying poling orders m and duty cycles, approximating a continuous Gaussian profile.
• Verifying the method by comparing the resulting phase-matching function to ideal Gaussian and standard sinc functions using both basic and detailed models.
• Combining group velocity matching with engineered nonlinearity to produce a separable joint spectral amplitude, enabling pure single-photon states without filtering.

Experimental results

Research questions

• RQ1 Can the phase-matching function of a periodically poled crystal be engineered to have a Gaussian shape by modulating the nonlinearity profile without changing the poling period?
• RQ2 Does a Gaussian phase-matching function eliminate spectral side lobes and thus reduce spectral correlations in photon pairs?
• RQ3 Can the joint spectral amplitude be made separable through nonlinearity engineering, enabling high-purity heralded single photons?
• RQ4 To what extent does the discrete approximation of a continuous Gaussian nonlinearity profile affect the resulting phase-matching function?
• RQ5 Can the method be extended to generate other shaped phase-matching functions, such as triangular or top-hat profiles?

Key findings

• A custom-poled KTP crystal with a non-uniform nonlinearity profile successfully produced a phase-matching function closely matching the target Gaussian shape, as confirmed by comparison with theoretical and standard ppKTP results.
• The joint spectral amplitude became separable, f(ωi, ωs) = g(ωi)h(ωs), due to the rotational symmetry of the two-dimensional Gaussian, enabling spectrally uncorrelated photons.
• Numerical simulations showed that the engineered crystal design achieved a joint spectral amplitude with no side lobes, unlike standard ppKTP crystals with sinc-shaped PMFs.
• Two-photon interference experiments confirmed the success of wave-packet shaping, demonstrating high-visibility interference consistent with the designed spectral profile.
• The method enables the generation of high-purity single photons without spectral filtering, as the side lobes that necessitate filtering are eliminated by the Gaussian PMF.
• The approach is extendable to other shaped phase-matching functions, such as triangular and top-hat profiles, by tailoring the nonlinearity profile accordingly.