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

The formation of quantized vortices in a superfluid 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 dynamic protocols for vortex nucleation in the superfluid and supersolid states of a dipolar Bose-Einstein condensate (BEC), at a significantly lower trap rotation frequency. We find that the critical rotation frequency of the trap varies with the dipole-dipole interaction strength and the polarization direction of the external magnetic field. Leveraging these characteristics of dipolar BECs, we demonstrate three dynamic 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 dynamic vortex seeding protocols could serve as important benchmarks for future experimental studies.