A robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates

We present a robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (BEC). Using the rotating Lagrangian coordinates transform (Bao et al., 2013), we reformulate the original coupled Gross-Pitaevskii equations (CGPE) into new equations where the rotating term vanishes and the potential becomes time-dependent. A time-splitting Fourier pseudospectral method is proposed to numerically solve the new equations where the nonlocal Dipole-Dipole Interactions (DDI) are computed by a newly-developed Gaussian-sum (GauSum) solver (Exl et al., 2016) which helps achieve spectral accuracy in space within O(NlogN) operations (N is the total number of grid points). The new method is spectrally accurate in space and second order accurate in time - these accuracies are confirmed numerically. Dynamical properties of some physical quantities, including the total mass, energy, center of mass and angular momentum expectation, are presented and confirmed numerically. Interesting dynamical phenomena that are peculiar to the rotating two-component dipolar BECs, such as dynamics of center of mass, quantized vortex lattices dynamics and the collapse dynamics in 3D, are presented.