Rotating dipole and quadrupole quantum droplets in binary Bose-Einstein condensates

Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and vortex QDs with vorticity $S=1$ (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescent-like components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with $S=2$. Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand, and VQDs on the other.