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arXiv:2608.26499

Real-Space Analysis of Two-Photon Polarization States in Type-II SPDC for High-Purity Polarization Entanglement

Koji Taninaka, Takashi Kakue, Ken Morita

quant-phphysics.opticsSubmitted Aug 27, 2026• Announced Aug 28, 2026• 0 citations
arXivHTMLPDF

Abstract

Spontaneous parametric down-conversion (SPDC) is one of the most widely used sources of polarization-entangled photon pairs, and understanding the generated biphoton state is essential for realizing high-brightness and high-purity entangled-photon sources. In particular, Type-II SPDC produces a biphoton wavefunction with a complex coupling between the spatial and polarization degrees of freedom owing to birefringence. In this study, we calculate the real-space distribution of the two-photon polarization state from the biphoton wavefunction of Type-II SPDC generated in a \b{eta}-barium borate (BBO) crystal. By identifying the spatial correlation direction between polarization and real-space coordinates, we designed aperture shapes that restrict the collection along this correlation direction. Through both numerical simulations and experiments, we demonstrate that such correlation-aligned apertures simultaneously achieve higher entanglement purity and improved photon collection efficiency. These results establish a practical design principle for optimizing aperture geometries based on the real-space biphoton wavefunction, providing a new approach to realizing high-purity and high-brightness SPDC entangled-photon sources.

Comments
12 pages, 5 figures

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Spontaneous parametric down-conversion (SPDC) is one of the most widely used sources of polarization-entangled photon pairs, and understanding the generated biphoton state is essential for realizing high-brightness and high-purity entangled-photon sources. In particular, Type-II SPDC produces a biphoton wavefunction with a complex coupling between the spatial and polarization degrees of freedom owing to birefringence. In this study, we calculate the real-space distribution of the two-photon polarization state from the biphoton wavefunction of Type-II SPDC generated in a \b{eta}-barium borate (BBO) crystal. By identifying the spatial correlation direction between polarization and real-space coordinates, we designed aperture shapes that restrict the collection along this correlation direction. Through both numerical simulations and experiments, we demonstrate that such correlation-aligned apertures simultaneously achieve higher entanglement purity and improved photon collection efficiency. These results establish a practical design principle for optimizing aperture geometries based on the real-space biphoton wavefunction, providing a new approach to realizing high-purity and high-brightness SPDC entangled-photon sources.
Summary form only given. By far the most efficient source of two-particle entangled state is spontaneous parametric downconversion (SPDC). Especially, cw laser pumped type-II SPDC has been widely treated as a good source of entangled photon pairs, since one can easily prepare a polarization Bell state. However, femtosecond pulse pumped type-II SPDC shows poor quantum interference visibility when a thick crystal is used. To restore the visibility, one has to use narrow-band spectral filters at the expense of available photon flux. We demonstrate a scheme for high-visibility two-photon interference with thick (3.4 mm.) type-II BaB/sub 2/O/sub 4/ (BBO) crystals in femtosecond pulse pumped SPDC. Polarization Bell states can be prepared using this method without spectral and amplitude post-selection.
We construct a compact polarization-entangled photon source using type-II degenerate spontaneous parametric down-conversion (SPDC) in beta-barium borate (BBO) crystal pumped by a 405 nm violet laser diode. In order to compensate the spatial displacement and the temporal delay due to the birefringence and dispersion effect of signal and idler photons, we make the down-converted photon pairs pass through a half wave plate and an additional BBO crystal with the half thickness of the original one. This improves the visibility of two-photon interference by eliminating the distinguishability of the paired photons. We measure the polarization correlations by two adjustable polarization analyzers in two conjugate bases, H/V and +45°/-45°, respectively. The polarization analyzer consists of a polarization beam splitter cube preceded by a rotatable half wave plate. When rotating one of the half wave plates and keeping the other one at fixed angle, we obtain the expected sin2 dependence of the coincidence counts. The highly visible sinusoidal coincidence indicates the violation of the Bell inequality and demonstrates the high quality of the polarization-entangled photon source. This compact polarization-entangled photon source is easily configurable and robust to demonstrate optical quantum information processing.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
Entanglement generated by Spontaneous Parametric Down Conversion (SPDC) involves multiple, often mutually correlated degrees of freedom. These degrees of freedom are often treated independently, overlooking the intrinsic correlation between them. We focus on the spatial spectral correlations that, if left uncontrolled, introduce distinguishability and reduce coherence, undermining applications such as high-dimensional OAM encoding. We analyze the spatio spectral structure of the biphoton and identify source configurations enabling a strong reduction of such correlations. We then quantify how spatial spectral coupling degrades OAM spatial purity, mapping high-purity regions as functions of OAM order, crystal length, and pump/collection waists. The resulting design parameters enable engineering bright, high purity OAM entangled sources, reducing the need for loss-introducing filtering and therefore supporting scalable high-dimensional photonic quantum technologies.
Spontaneous parametric down-conversion (SPDC) is a reliable and robust source of photons for quantum information applications. For applications that involve operations such as entanglement swapping or single-photon heralding, two-photon states are required to be factorable (uncorrelated) in their spectral and spatial degrees of freedom. We report the design and experimental characterization of an SPDC source that has been optimized for high spectral and spatial purity. The source is pumped by the 776 nm output of a mode-locked Ti:Sapphire laser and consists of a periodically-poled Potassium Titanyl Phosphate (PPKTP) crystal phase-matched for collinear type-II SPDC. The dispersive properties of PPKTP at these wavelengths is such that it is possible to minimize the spectral entanglement by matching the widths of the pump to the spectral phase-matching function. The spatial entanglement is minimized through careful control of the pump focus, yielding nearly single-mode emission. An advantage of this approach is that the emission rate into the collection modes is very high, resulting in a very bright SPDC source. We also report a scheme that employs the output of collinear sources such as these to produce polarization-entangled photon pairs. The scheme, which requires only simple polarization elements, can be scaled to N-photon GHZ states.
Spontaneous Parametric Down-Conversion (SPDC) is key to generating broadband spectrally entangled photons for quantum optical spectroscopy. Here we use a common-path birefringent interferometer to experimentally map the spatial-spectral distribution of SPDC in Type I and II β-barium borate crystals using hyperspectral k-space imaging. Under broadband pulsed pumping, we observe strong spatial variations in the spectra, with distinct features for each phase-matching type. Simulations based on biphoton amplitudes and phase-matching conditions qualitatively match our results. This spatial-spectral mapping enables control over biphoton entanglement entropy, paving the way for optimized quantum light sources for material spectroscopy.