This study proposes a method to deterministically generate high-dimensional Greenberger-Horne-Zeilinger (GHZ) states using a neutral atom platform and quantum reservoir engineering. By leveraging the modified unconventional Rydberg pumping mechanism and controlled dissipation, the researchers achieve a three-dimensional GHZ state with a fidelity exceeding 99% through multiple pump and dissipation cycles. This approach overcomes the limitations of linear optical systems and superconducting qubits, which often suffer from decoherence and non-deterministic preparation. The experimental setup involves confining three $^{87}$Rb atoms in an equilateral triangle using optical tweezers and manipulating their hyperfine ground states. The modified Rydberg pumping mechanism and controlled dissipation techniques ensure the stabilization of the system within the desired GHZ state, demonstrating the feasibility of deterministic high-dimensional GHZ state preparation in Rydberg atom systems. This advancement has significant implications for quantum information processing, offering enhanced security, increased capacity, and stronger violations of Bell-type inequalities.This study proposes a method to deterministically generate high-dimensional Greenberger-Horne-Zeilinger (GHZ) states using a neutral atom platform and quantum reservoir engineering. By leveraging the modified unconventional Rydberg pumping mechanism and controlled dissipation, the researchers achieve a three-dimensional GHZ state with a fidelity exceeding 99% through multiple pump and dissipation cycles. This approach overcomes the limitations of linear optical systems and superconducting qubits, which often suffer from decoherence and non-deterministic preparation. The experimental setup involves confining three $^{87}$Rb atoms in an equilateral triangle using optical tweezers and manipulating their hyperfine ground states. The modified Rydberg pumping mechanism and controlled dissipation techniques ensure the stabilization of the system within the desired GHZ state, demonstrating the feasibility of deterministic high-dimensional GHZ state preparation in Rydberg atom systems. This advancement has significant implications for quantum information processing, offering enhanced security, increased capacity, and stronger violations of Bell-type inequalities.