Roadmap to vortex nucleation below the critical rotation frequency in a dipolar Bose-Einstein condensate

The formation of quantized vortices above a certain critical trap rotation frequency serves as a hallmark signature of superfluidity. Based on the beyond mean-field framework, crucial for the formation of exotic supersolid and droplet states, we investigate dynamical protocols for vortex nucleation in the superfluid and supersolid states of a dipolar Bose-Einstein condensate (BEC) at a trap rotation frequency lower than the conventional critical rotation frequency. We find that the critical rotation frequency depends not only on the dipole-dipole interaction strength, but also on the polarization direction of the external magnetic field. Interestingly, in the superfluid state, the critical rotation frequency increases with the tilt angle of the magnetic field, whereas in the supersolid state, increasing the tilt angle lowers the critical threshold. Leveraging these characteristics of dipolar BECs, along with the robustness of vortices with respect to changes in the polarization direction and $s$-wave scattering length, we demonstrate three dynamical protocols for vortex nucleation, even when rotating below the critical rotation frequency, viz., (i) varying the $s$-wave scattering length, (ii) changing the polarizing angle, and (iii) successive modulation of both the scattering length and polarizing angle. These dynamical vortex seeding protocols could serve as important benchmarks for future experimental studies.