Study of quantum turbulence by vortex-antivortex dynamics in dipolar BECs

We investigate vortex nucleation and dynamics in a dipolar Bose-Einstein condensate stirred by a rotating Gaussian obstacle. Two stirring protocols are compared: continuous stirring with constant amplitude (Case 1), and obstacle removal at $t=15$ ms with linear amplitude ramp-down (Case 2). In both cases, a smooth angular velocity ramp ($t_{\text{acc}}=3$ ms) suppresses spurious phonon excitations. The first vortex pairs exit the obstacle at $t\sim 3$ ms, and by $t\sim 8$ - $10$ ms the individual vortices and antivortices are fully resolved in the phase maps. Case 1 yields a vortex population that grows up to $t\sim 40$ ms and then roughly saturates, while Case 2 yields a population that peaks around $t\sim 15$ - $25$ ms and then decreases. Remarkably, both protocols lead to local triangular-like ordering in selected regions of the condensate by $t\sim 50$ ms, exhibiting clear dipolar signatures: elliptical distortion and elongated vortex cores along the polarization axis. The mixed vortex-antivortex population remains stable up to $100$ ms with no observable annihilation, indicating that dipolar interactions strongly suppress vortex decay. Kinetic energy decomposition confirms that incompressible (vortex) energy dominates at late times. These results establish a controlled platform for vortex studies in dipolar superfluids and provide benchmarks for future experiments on quantum turbulence with long-range anisotropic interactions.