Creation of high-dimensional entanglement of polar molecules via optimal control fields

Quantum entanglement in high-dimensional Hilbert space offers broad prospects for quantum information science. Polar molecules have a rich internal structure and long coherence time, serving as an attractive candidate for quantum information processing. In this paper, we propose a theoretical scheme for creating high-dimensional entangled states based on ultracold SrO molecules. Qudits are encoded in the pendular states induced by an external electric field and coupled by the dipole-dipole interaction. With the assistance of optimal control theory, a series of optimal microwave fields is designed for the generation of an entangled qutrit-qubit state, qutrit-qutrit state, and ququart-ququart state through numerical iterations. We detail the relation of the fidelity and entanglement of the systemic final states with the number of iteration steps after the control fields are applied and analyze the population dynamics of the field-driven wave functions during time evolution. Moreover, three coupled SrO molecules arranged in an equilateral triangle configuration are employed as pendular qubits, and the trimolecular W and Greenberger-Horne-Zeilinger states are realized with high fidelities by optimal control. The specific molecule and experimental parameters used in our theoretical studies are chosen for computational convenience, but we include a discussion of how our results can be applied to realistic situations as well. In principle, our results could be extended to a situation with more pendular qudits, providing a significant step toward the achievement of high-dimensional quantum information processing with arrays of polar molecules.