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Quantum entanglement by Spontaneous Parametric Down-Conversion (SPDC) and the probability of correlated behavior

Chur Chin

Published Apr 21, 2025• 0 citations
Publisher

Abstract

SPDC is a process commonly used in quantum optics to produce entangled photon pairs. It typically occurs in a nonlinear optical material (such as a beta barium borate (BBO) crystal), where a single high-energy photon (like a laser photon) interacts with the crystal and is down-converted into two lower-energy photons. These photons are often entangled in terms of properties like polarization, momentum, or phase.We also determine the probability of their entanglement and correlated behavior.

DOI
10.31219/osf.io/ft3qu_v1

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SPDC is a process commonly used in quantum optics to produce entangled photon pairs. It typically occurs in a nonlinear optical material (such as a beta barium borate (BBO) crystal), where a single high-energy photon (like a laser photon) interacts with the crystal and is down-converted into two lower-energy photons. These photons are often entangled in terms of properties like polarization, momentum, or phase.We also determine the probability of their entanglement and correlated behavior.
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.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)\chi^{(2)}χ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
The generation of entangled photon pairs through spontaneous parametric down conversion (SPDC) is widely used and considered one of the key entanglement generation techniques in quantum optics. The quality of the entanglement produced depends significantly on the physical properties of the nonlinear crystal employed in the SPDC process. In this study, we investigate the influence of the crystal parameters such as phase matching configurations on the degree of entanglement. Our results demonstrate the importance of crystal selection for achieving highly entangled photon sources, which are essential for applications in quantum communication and quantum information.
In recent years, the use of entangled photons in quantum spectroscopy has gained attention, offering new possibilities for studying materials. In this work, we present an entangled photon source developed for future applications in ultrafast quantum spec- troscopy, particularly in biological research. Entangled photons at visible wavelengths are generated using pulsed type-I spontaneous parametric down-conversion (SPDC) in a Beta-Barium Borate (BBO) crystal, pumped by a 1030 nm laser after third and fourth harmonic generation. Photon detection was performed with an intensified sCMOS cam- era, enabling observation and study of spatial and, after integration of a custom-built spectrograph, spatio-energetic correlations between photon pairs. We optimized detec- tion, imaging, and data processing methods. We believe that our results, combined with the improvements we propose, form a solid foundation for integrating entangled photon pairs into time-resolved optical spectroscopy.
The quantum entangled photon-pair source, as an essential component of optical quantum systems, holds great potential for applications such as quantum teleportation, quantum computing, and quantum imaging. The current workhorse technique for preparing photon pairs involves performing spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. However, the current power consumption and cost of preparing entangled photon-pair sources are relatively high, posing challenges to their integration and scalability. In this paper, we propose a low-power system model for the quantum entangled photon-pair source based on SPDC theory and phase matching technology. This model allows us to analyze the performance of each module and the influence of component characteristics on the overall system. In our experimental setup, we utilize a 5 mW laser diode and a typical type-II barium metaborate (BBO) crystal to prepare an entangled photon-pair source. The experimental results are in excellent agreement with the model, indicating a significant step towards achieving the goal of low-power and low-cost entangled photon-pair sources. This achievement not only contributes to the practical application of quantum entanglement lighting, but also paves the way for the widespread adoption of optical quantum systems in the future.