High-dimensional quantum systems offer advantages in verifying quantum theories, improving quantum computing error resilience, and enhancing quantum communication capacity and robustness. Optical photons are ideal for high-dimensional encoding, with various degrees of freedom utilized, including path, orbital angular momentum, frequency, spatial, and temporal modes. Frequency encoding is particularly promising for on-chip implementation because it avoids complex components such as long delay lines and highly multimodal waveguides. Previous work has generated biphoton QFCs on integrated platforms using spontaneous four-wave mixing, but these typically use discrete components, limiting scalability and efficiency. Second-order nonlinearity offers significantly higher power efficiency. This research demonstrates on-chip parallel processing of QFCs using an integrated aluminum nitride (AlN) platform. Near-identical spectral distribution QFCs are simultaneously generated using cavity-enhanced parametric down-conversion in a Sagnac configuration. Parallel quantum interference of different frequency modes is achieved using an integrated phase shifter and beamsplitter, enabling deterministic separation of photon pairs without spectral filtering, and demonstrating a high-dimensional Hong-Ou-Mandel effect.

The literature review extensively cites previous research on high-dimensional quantum entanglement using various degrees of freedom. It highlights the advantages of frequency encoding for on-chip integration, referencing several papers that demonstrate QFC generation using spontaneous four-wave mixing on integrated platforms and their applications in quantum communication and coherent superposition. However, it points out the limitations of these approaches, including the use of discrete components that hinder scalability and the lower efficiency compared to second-order nonlinearity.

The researchers utilized an integrated AlN platform for on-chip generation and manipulation of QFCs. A continuous-wave pump laser around 775 nm is split and coupled into a ring cavity in clockwise and counter-clockwise directions. The AlN's χ(2) nonlinearity enables efficient parametric down-conversion within the cavity, generating photon pairs in multiple cavity resonances, forming QFCs. The Sagnac configuration ensures near-identical spectral distribution in both directions, crucial for high-visibility interference. An on-chip phase shifter controls the relative phase between the QFCs. A balanced multimode interferometer combines the QFCs, and superconducting nanowire single-photon detectors (SNSPDs) detect the photons after filtering. Measurements include characterization of single-photon spectra, frequency correlation, self-correlation in the time domain (Hanbury-Brown-Twiss setup), and parallel quantum interference. Classical interference patterns from a Mach-Zehnder interferometer served as a reference. The Hong-Ou-Mandel effect was demonstrated by introducing a tunable optical delay line and polarization controller, with programmable filters selecting specific frequency modes. The fabrication process involved MOCVD growth of the AlN wafer, electron-beam lithography, reactive ion etching, PECVD deposition of SiO2, and photolithography for electrode definition.

The study successfully generated QFCs with near-identical spectral distributions using a Sagnac configuration and cavity-enhanced parametric down-conversion. High interference visibility (93.8 ± 0.51%) was maintained across all frequency modes with the same circuit settings, demonstrating the ability for on-chip QFC reconfiguration. The high-dimensional Hong-Ou-Mandel effect was observed, confirming the deterministic separation of photon pairs without spectral filtering. The Schmidt number, a measure of the entanglement dimension, scaled linearly with the number of resonance pairs. The self-correlation measurements using a Hanbury-Brown-Twiss setup also confirmed the multi-resonance property of the generated QFCs. The parallel processing capability was shown by the consistent interference patterns across different frequency modes, even when multiple modes were selected simultaneously. The researchers achieved coincidence-to-accidental ratios above 25 dB for all resonance pairs and a Hong-Ou-Mandel visibility of 89.6 ± 2.5% for a single degenerate mode and observed fast oscillations in the coincidence counts when multiple resonance pairs were included, consistent with the theoretical predictions.

The results address the research question by demonstrating the feasibility of on-chip parallel processing of QFCs, paving the way for scalable and efficient quantum information processing. The high visibility and deterministic photon separation significantly enhance the potential for practical applications. The use of AlN, with its strong second-order nonlinearity, makes this platform promising for future advancements, particularly in coherent frequency operations on the chip itself, unlike previous work that relied on free-space or fiber-based components. The ability to control and manipulate multiple frequency modes simultaneously opens doors for more complex quantum algorithms and protocols.

This work successfully demonstrated parallel processing of QFCs on an integrated AlN platform. The use of a Sagnac configuration and cavity-enhanced parametric down-conversion led to indistinguishable QFCs and high-visibility quantum interference across various frequency modes. The deterministic photon separation without spectral filtering enabled the observation of a high-dimensional Hong-Ou-Mandel effect. This research represents a significant advancement in high-dimensional quantum photonics and opens exciting avenues for integrated photonic quantum information processing. Future work could focus on expanding the path dimensions by incorporating multiple ring cavities, utilizing techniques like post-fabrication tuning and quantum frequency conversion to manage spectral overlap.

The current implementation is limited to two QFCs due to the Sagnac configuration. Expanding the path dimension would require integrating multiple ring cavities, which presents challenges in terms of fabrication and spectral management. While the Hong-Ou-Mandel experiment demonstrated intra-pair coherence, further investigation using active methods is needed to fully characterize the inter-pair coherence and entanglement in the frequency domain. The study assumes the coherent superposition of photon pairs in different resonances.