Microwave shielding has recently emerged as a powerful technique for suppressing inelastic collisions and enabling evaporative cooling of ultracold polar molecules. With appropriately applied microwave fields, a repulsive shielding barrier emerges at short range, which prevents molecules from reaching reactive collision distances. So far, both fermionic and bosonic molecular gases can be cooled below the degeneracy temperature through microwave shielding. Moreover, it offers a convenient method to tune molecular interaction. In addition to the microwave field, achieving effcient microwave shielding requires a strong bias magnetic field to define a quantization axis and to suppress processes that involve changes in the internal spin degrees of freedom. In current experimental setups, the polarization or spatial orientation of the microwave field is often not perfectly aligned with the magnetic field, which is referred to as mismatched fields, leaving an important gap between idealized theoretical treatments and practical experiments.
In this work, we theoretically investigate the impact of mismatches between microwave and magnetic fields on the shielding performance. By performing multi-channel scattering calculations together with adiabatic potential analyses for two colliding polar molecules, we systematically vary the mismatch angle and examine the resulting scattering rates. We demonstrate that the shielding effect is highly robust even under significant mismatches: the elastic scattering rate remains essentially unchanged, while the inelastic loss rate stays effciently suppressed to a level comparable to the perfectly aligned case. More importantly, we identify the underlying physical mechanism behind this robustness. We find that in a suffciently strong magnetic field, the projection of the molecular nuclear spin is hardly affected by the mismatch angle. As a result, the molecular state can be accurately approximated as a direct product of a rotational state and a fixed nuclear-spin projection state. This observation reveals that the primary role of the magnetic field is to lock the nuclear-spin projection of the molecule, which does not require precise alignment with the microwave field. Consequently, the microwave shielding effect for ultracold polar molecules is remarkably robust against mismatches between the microwave and magnetic fields.
Our findings also provide a natural explanation for experimental observations reported in earlier works: even a simple rigid-rotor model that completely ignores hyperfine structure can reproduce experimental results quantitatively, regardless of the mismatch. In typical ultracold molecule experiments, the microwave field often has a large ellipticity, which tends to obscure the subtle effects of field mismatches and hyperfine details. Under such conditions, treating the molecule as a structureless rigid rotor becomes fully adequate.