In this work, we present a detailed study of the microwave excitation spectra of ultracold ²³Na⁴⁰K molecules, focusing on rotational transitions from the ground state (N = 0) to the first excited state (N = 1). By combining precise theoretical calculations with experimental measurements, we achieve an accurate calibration of these transitions, which enables quantum control techniques such as microwave shielding to suppress collisional losses and facilitate cooling toward quantum degeneracy.

Theoretically, a comprehensive Hamiltonian is employed to describe the complex internal structure, including rotational contribution, nuclear spin-rotation interaction, nuclear spin-spin interaction, nuclear electric quadrupole interactions, and the Zeeman effect under an external magnetic field. The Hamiltonian is diagonalized within an extended Hilbert space (36 and 108 hyperfine states for N = 0 and N = 1, respectively) to determine the eigenvalues, eigenstates, transition frequencies, and transition dipole moments.

Experimentally, ground-state molecules were prepared in selected hyperfine levels via Feshbach association followed by STIRAP (Stimulated Raman Adiabatic Passage). By scanning the microwave frequency around 5.643 GHz, loss spectroscopy was performed to obtain the excitation spectra. At a magnetic field of 70 G (1 G = 10^–4 T), the measured transition frequencies for the G₁ and G₂ states showed excellent agreement with theoretical predictions, enabling a definitive assignment of the hyperfine components within the (N = 1) rotational manifold. Furthermore, Rabi oscillations were measured at resonance to verify the calculated transition dipole moments via coherent population dynamics.

These findings provide a precise spectroscopic benchmark for the microwave control of ultracold molecules and lay the foundation for future research in quantum simulation and computation based on long-range dipolar interactions.