Solid-state spin qubits based on color centers in wide-bandgap semiconductors are a promising platform for quantum networks, information processing, and sensing due to their robust spin-optical properties and long coherence times. Silicon carbide (SiC) stands out as a wafer-scalable material with established isotopic engineering and CMOS compatibility, paving the way for scalable systems. Significant progress with SiC spin qubits includes demonstrations of millisecond spin coherence times at room temperature, high-fidelity spin and optical control, coherent spin-photon interfaces, entanglement with nuclear spin registers, and single-shot charge readout. Integration of negatively charged silicon vacancy centers (Vs−) into nanophotonic waveguides and resonators, compatible with SiC-on-insulator processing, further advances scalability. The cubic lattice site Vs− (V2 in 4H-SiC) is a strong contender for quantum applications due to its potential for dense integration. However, a complete understanding of its intrinsic spin-optical dynamics is crucial for optimizing cavity-emitter coupling and spin/optical properties, and for developing realistic quantum network applications. This paper focuses on the V2 center in 4H-SiC, which has a larger zero-field splitting (ZFS) in the ground state than the hexagonal-site V1 center, leading to faster ground-state spin manipulation and higher state fidelities. The research comprehensively reveals the internal spin dynamics of the V2 center through theoretical characterization of its electronic structure, confirmed by experimental investigations of spin-selective excited state lifetimes, ground state spin initialization, and the dynamics within metastable state manifolds.

Previous studies have explored the potential of silicon vacancy centers in silicon carbide for quantum applications. However, a complete understanding of the spin-optical dynamics of the V2 center in 4H-SiC, crucial for optimizing device performance and enabling scalable quantum networks, has been lacking. Existing work on V1 centers in 4H-SiC has provided insights into spin-dependent excited-state lifetimes and intersystem crossing. However, the V2 center, with its larger zero-field splitting, presents unique dynamics that have not been fully characterized. The theoretical work by Soykal et al. provided a group theoretical framework for understanding the electronic structure, but experimental data were lacking to validate and fully elucidate the intricate spin-optical dynamics. Dong et al. explored the intersystem crossing, but crucial details regarding specific doublet states and mechanisms such as the pseudo-Jahn-Teller effect and deshelving remained unresolved. This research builds upon previous findings, providing the critical experimental data necessary to complete the picture of V2 center behavior, addressing the limitations of prior studies and offering a comprehensive model for practical quantum applications.

The research employed a combination of theoretical modeling and experimental techniques. The theoretical characterization of the V2 center's electronic structure utilized a group theoretical framework based on multi-particle symmetry-adapted total wavefunctions constructed from single-electron molecular orbitals (MOs) and linear combinations of localized many-body sp³ orbitals. This allowed for the identification of spin-dependent radiative and non-radiative transition rates and provided insights into the intersystem crossing (ISC) mechanisms, including spin-orbit coupling, dynamic pseudo-Jahn-Teller effects, and optical deshelving. Experimental investigations involved measurements of spin-selective excited-state lifetimes using resonant and off-resonant laser excitation and fluorescence decay analysis. Spin-dependent measurements were performed to probe the intricate dynamics within the metastable state manifolds, using techniques such as spin manipulation combined with delayed pulse measurements. These measurements enabled the determination of all spin-dependent radiative and non-radiative transition rates. A six-level rate model was developed to effectively capture the observed dynamics, incorporating the power-dependent deshelving mechanism. A parameter optimization algorithm was used to fit the theoretical model to the experimental data, refining the values of the transition rates. Finally, protocols for generating time-bin entangled multi-photon Greenberger-Horne-Zeilinger (GHZ) and cluster states were developed using the obtained transition rates, considering various sources of error, and assessing the required Purcell enhancement factors for different photon numbers.

The research revealed a comprehensive understanding of the internal spin dynamics of the V2 center in 4H-SiC. Key findings include: 1. **Detailed Electronic Fine Structure:** A detailed electronic fine structure model of the V2 center was developed and validated experimentally, incorporating the crucial intersystem crossing and deshelving processes. This model accounts for multiple metastable states and their interactions. 2. **Spin-Selective Transition Rates:** All spin-dependent radiative and non-radiative transition rates were experimentally determined for the first time. The excited-state lifetimes were found to be significantly different for different spin sublevels (6.1 ns for O1 and 11.3 ns for O2 transitions), indicating a slower intersystem crossing for the ±3/2 spin sublevels. 3. **Intersystem Crossing Mechanism:** The ISC mechanism was elucidated, involving transitions from the excited spin-quartet state to higher metastable spin-doublet states, mediated by spin-orbit and electron-phonon interactions. The pseudo-Jahn-Teller effect and a deshelving mechanism were identified as significant contributors. 4. **Power-Dependent Deshelving:** A novel deshelving mechanism was discovered, where optical excitation promotes an electron from a lower to a higher-lying metastable state. This mechanism is power-dependent and affects the overall lifetime of the metastable states. 5. **High-Fidelity Spin Initialization:** High-fidelity spin initialization (≥95%) was achieved experimentally using both resonant and off-resonant laser excitation techniques. 6. **Entangled Multi-Photon State Generation:** A protocol for generating time-bin entangled multi-photon GHZ and cluster states was proposed and analyzed. The analysis indicates that the generation of up to three-photon GHZ or cluster states is readily achievable with current nanophotonic technology.

The comprehensive determination of the intrinsic spin dynamics of the V2 center in 4H-SiC directly addresses the need for detailed knowledge to optimize the performance of this promising qubit platform. The identification of all relevant transition rates, including the novel deshelving mechanism, provides crucial insights for engineering efficient quantum devices. The experimental validation of the theoretical model strengthens the reliability of the findings and allows for accurate predictions of the V2 center's behavior under various conditions. The proposed protocol for generating entangled multi-photon states showcases the potential of this system for scalable quantum networks and quantum computing. The observed differences between the V1 and V2 centers highlight the importance of considering specific lattice site characteristics when designing quantum technologies. The high quantum efficiency of the O2 transition, coupled with the proposed protocol, suggests promising avenues for realizing advanced quantum network applications. The high-fidelity spin initialization methods developed here pave the way for reliable and robust operation of V2-based devices.

This research provides a comprehensive understanding of the intrinsic spin-optical dynamics of the V2 center in 4H-SiC, a crucial step towards realizing scalable integrated quantum photonics. All relevant spin-selective radiative and non-radiative decay rates have been experimentally determined and incorporated into a detailed model. This has enabled the proposal and analysis of a realistic protocol for generating time-bin entangled multi-photon GHZ and cluster states. The findings demonstrate the feasibility of using the V2 center for the creation of multi-photon entangled states using currently available technology, paving the way for future development of scalable quantum networks and other quantum applications. Future work could focus on further optimizing these processes, for example through phonon or strain engineering to enhance the system's coherence and branching ratio.

The experiments were conducted at cryogenic temperatures (5.5 K). While the V2 center exhibits millisecond coherence times at room temperature, the performance of the proposed entangled state generation protocols at higher temperatures would require further investigation. The theoretical model and simulations, while providing excellent fits to the experimental data, may not perfectly capture all the complexities of the system, such as the effects of various noise sources and environmental fluctuations. The fidelity of the proposed multi-photon entangled state generation protocol is limited by various imperfections, including excitation errors and branching errors. While the analysis shows that up to three-photon entangled states are feasible, achieving higher photon numbers would require further improvements in nanophotonic resonator technology.