This study presents a method for deterministically preparing high-dimensional Greenberger-Horne-Zeilinger (GHZ) states using a neutral atom platform combined with quantum reservoir engineering. The approach leverages the advantages of neutral atoms in a modified unconventional Rydberg pumping mechanism, along with controlled dissipation, to achieve a three-dimensional GHZ state with fidelity exceeding 99% through multiple pump and dissipation cycles. This method offers a feasible path for experimentally preparing high-dimensional GHZ states in Rydberg atom systems, enhancing quantum information processing capabilities. High-dimensional quantum entanglement, characterized by complex correlations among entangled particles, is crucial for quantum information processing. It has applications in quantum computing, quantum simulation, quantum key distribution, and quantum communications. However, generating high-dimensional GHZ states in linear optical systems has been challenging due to low success probabilities and non-deterministic outcomes. This study addresses these challenges by utilizing neutral atoms, which provide a controlled environment for trapping, cooling, and manipulating atoms, converting decoherence factors into valuable resources. The neutral atom system uses hyperfine ground states of Rubidium and Cesium to encode qudits, enabling the expansion of qudit dimensionality. By engineering pairwise additive interactions between excited Rydberg states, entangling operations can be facilitated, simplifying the scaling of quantum systems. The study demonstrates the preparation of a three-dimensional GHZ state through a series of coherent operations and dissipative processes, showing that the fidelity of the target state increases with the number of cycles. The experimental setup involves three Rubidium atoms confined in an equilateral triangle, with specific hyperfine ground states used to encode the qutrits. The study shows that the method is robust against variations in initial states and is resilient to fluctuations in atomic spacing and timing errors. The approach also mitigates the impact of the Doppler effect, allowing for higher fidelity in the target state through increased cycles. The study highlights the potential of neutral atom platforms for high-dimensional quantum information processing, offering a promising avenue for future research and development in quantum technologies.This study presents a method for deterministically preparing high-dimensional Greenberger-Horne-Zeilinger (GHZ) states using a neutral atom platform combined with quantum reservoir engineering. The approach leverages the advantages of neutral atoms in a modified unconventional Rydberg pumping mechanism, along with controlled dissipation, to achieve a three-dimensional GHZ state with fidelity exceeding 99% through multiple pump and dissipation cycles. This method offers a feasible path for experimentally preparing high-dimensional GHZ states in Rydberg atom systems, enhancing quantum information processing capabilities. High-dimensional quantum entanglement, characterized by complex correlations among entangled particles, is crucial for quantum information processing. It has applications in quantum computing, quantum simulation, quantum key distribution, and quantum communications. However, generating high-dimensional GHZ states in linear optical systems has been challenging due to low success probabilities and non-deterministic outcomes. This study addresses these challenges by utilizing neutral atoms, which provide a controlled environment for trapping, cooling, and manipulating atoms, converting decoherence factors into valuable resources. The neutral atom system uses hyperfine ground states of Rubidium and Cesium to encode qudits, enabling the expansion of qudit dimensionality. By engineering pairwise additive interactions between excited Rydberg states, entangling operations can be facilitated, simplifying the scaling of quantum systems. The study demonstrates the preparation of a three-dimensional GHZ state through a series of coherent operations and dissipative processes, showing that the fidelity of the target state increases with the number of cycles. The experimental setup involves three Rubidium atoms confined in an equilateral triangle, with specific hyperfine ground states used to encode the qutrits. The study shows that the method is robust against variations in initial states and is resilient to fluctuations in atomic spacing and timing errors. The approach also mitigates the impact of the Doppler effect, allowing for higher fidelity in the target state through increased cycles. The study highlights the potential of neutral atom platforms for high-dimensional quantum information processing, offering a promising avenue for future research and development in quantum technologies.