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Temperature-stress phase-matching tuning in BBO crystals for high-efficiency quantum radiometric calibration

Lei Wang, Yun Zhang, Sa Hao, Sheng Zheng, 夏茂鹏, Xiaobing Zheng

Published Aug 4, 2026• 1 citation

Abstract

Entangled photon pairs generated via spontaneous parametric down-conversion (SPDC) in beta-barium borate (BBO) crystals are fundamental to the realization of anchor-free quantum metrology and spaceborne radiometric standards. High-precision calibration strictly necessitates rigorous spectral and spatial matching of these entangled photons. However, the spatial distribution of entangled photons exhibits a profound dependence on the phase-matching angle. Due to the combined effects of crystal fabrication tolerances, environmental perturbations, and the extremely low intensity of entangled signals (∼pW level), conventional mono-dimensional angle tuning struggles to balance the conflicting requirements of spectral bandwidth and spatial distribution matching. To address this bottleneck, a synergistic tuning strategy integrating angle, temperature, and stress is proposed in this work. A multi-channel, high-precision temperature control system based on series-connected thermoelectric coolers (TECs) was developed, achieving a control precision superior to 0.01 ℃ at a setpoint of 50 ℃. By combining theoretical derivations with thermo-structural coupled simulations, the tuning regularities of temperature (30–70 ℃) and stress on the photon output angle were quantitatively characterized. Experimental measurements on the multi-channel BBO crystal configuration (comprising eight crystals) achieved a maximum tuning range (Δ θ OA ) of 2.941° and identified a non-destructive stress threshold of 312.5 N. This work elucidates the intrinsic mechanisms of temperature and stress in BBO phase-matching, providing critical engineering methodologies and theoretical underpinnings for enhancing quantum calibration accuracy while offering a paradigm for the multi-dimensional tuning of nonlinear optical crystals.

DOI: 10.1364/oe.604548

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Entangled photon pairs generated via spontaneous parametric down-conversion (SPDC) in beta-barium borate (BBO) crystals are fundamental to the realization of anchor-free quantum metrology and spaceborne radiometric standards. High-precision calibration strictly necessitates rigorous spectral and spatial matching of these entangled photons. However, the spatial distribution of entangled photons exhibits a profound dependence on the phase-matching angle. Due to the combined effects of crystal fabrication tolerances, environmental perturbations, and the extremely low intensity of entangled signals (∼pW level), conventional mono-dimensional angle tuning struggles to balance the conflicting requirements of spectral bandwidth and spatial distribution matching. To address this bottleneck, a synergistic tuning strategy integrating angle, temperature, and stress is proposed in this work. A multi-channel, high-precision temperature control system based on series-connected thermoelectric coolers (TECs) was developed, achieving a control precision superior to 0.01 ℃ at a setpoint of 50 ℃. By combining theoretical derivations with thermo-structural coupled simulations, the tuning regularities of temperature (30–70 ℃) and stress on the photon output angle were quantitatively characterized. Experimental measurements on the multi-channel BBO crystal configuration (comprising eight crystals) achieved a maximum tuning range (Δ θ OA ) of 2.941° and identified a non-destructive stress threshold of 312.5 N. This work elucidates the intrinsic mechanisms of temperature and stress in BBO phase-matching, providing critical engineering methodologies and theoretical underpinnings for enhancing quantum calibration accuracy while offering a paradigm for the multi-dimensional tuning of nonlinear optical crystals.

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.

There are two general methods in radiometric calibration of detectors, one is based on radiation sources and the other based on detectors. Because the two methods need to establish a primary standard of high precision and a transfer chain, precision of the standard will be reduced by extension of the chain. A new calibration method of detectors can be realized by using correlated photons generated in spontaneous parametric down-conversion (SPDC) effect of nonlinear crystal, without needing transfer chain. Using 351.1-nm output of a tunable laser to pump 'beta'-barium borate (BBO) crystal, an absolute calibration experimental system of single photon detectors based on correlated photons is performed. The quantum efficiency of photomultiplier (PMT) at 702.2 nm is measured by the setup. Advantages of this method over traditional methods are also pointed out by comparison.

Spontaneous Parametric Down-Conversion (SPDC) is key to generating broadband spectrally entangled photons for quantum optical spectroscopy. Here we use a a common-path birefringent interferometer to experimentally map the spatial-spectral mode structure of SPDC in Type I and II

\beta

-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.

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.

We propose a protocol for probing mechanically induced stochastic phase-matching fluctuations in spontaneous parametric downconversion (SPDC) by Hong-Ou-Mandel (HOM) interferometry. The analysis is formulated for collinear type-II SPDC in β-barium borate (BBO). We distinguish the ideal white-jerk limit from the experimentally relevant finite-bandwidth regime. In the ideal limit, the incremental phase variance generated during a photon transit scales as L5; however, for a 5-mm BBO crystal, the transit time is only about 29 ps, so a piezoelectric mechanical drive is quasi-static on this time scale and the L5 law is not assumed as a direct experimental signature. Instead, the measured acceleration power spectral density and the mechanical transfer function are used to calculate the finite-bandwidth phase fluctuations. The connection to HOM visibility is derived through the biphoton joint spectral amplitude: stochastic phase mismatch modifies the phase-matching function, and the ensemble-averaged spectral-exchange overlap determines the coincidence dip. A frequency-independent common phase cancels from this overlap and therefore does not reduce HOM visibility. The resulting formulation provides a directly testable route for phase-stability metrology without requiring the experimentally inaccessible white-noise approximation.