Control of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Dy</mml:mi><mml:mprescripts /><mml:none /><mml:mn>164</mml:mn></mml:mmultiscripts></mml:math> Bose-Einstein condensate phases and dynamics with dipolar anisotropy

We investigate the quench dynamics of quasi-one and two dimensional dipolar Bose-Einstein condensates (dBEC) $^{164}$Dy atoms under influence a fast rotating magnetic field. The field thus controls both magnitude sign potential. account for quantum fluctuations, critical to formation exotic droplet supersolid phases in extended Gross-Pitaevskii formalism, which includes so-called Lee-Huang-Yang (LHY) correction. An analytical variational ansatz allows us obtain phase diagrams superfluid phases. crossover from single arrays is probed with particle number interaction. strength tuned by subsequent effects on boundaries. Following interaction quenches across aforementioned phases, we monitor dynamical clusters or lattices. include losses due three-body recombination over regime, where rate coefficient scales fourth power scattering length ($a_s$) dipole ($a_{dd}$). For fixed values dimensionless parameter, $\epsilon_{dd} = a_{dd}/a_s$, tuning anisotropy leads an enhancement lifetimes.