Clarifying the essential mechanism of lattice formation in BECs can significantly contribute to these disciplines. Vortex lattice phenomena observed in rotating Bose–Einstein condensates (BECs) have garnered attention in many fields related to condensed matter physics.
In conclusion, we successfully developed a new SPH scheme for the simulations of vortex lattice formation in rotating BECs. These results demonstrate our approach at a certain degree of accuracy. We confirmed that each branch point of the phase of wavefunctions corresponds to each vortex. Consequently, it was confirmed that the simulation began with the periodic oscillation of the condensate, which attenuated and maintained a stable rotation with slanted elliptical shapes however, the surface was excited to be unstable and generated ripples, which grew into vortices and then penetrated inside the condensate, forming a lattice.
The geometric patterns of formed lattices were successfully reproduced for several cases, for example, the hexagonal lattice observed in the experiments of rotating BECs. We performed simulations of a rotating Bose gas trapped in a harmonic potential, showing results that qualitatively agreed with previously reported experiments and simulations. We adopt the fourth-order Runge–Kutta method for time evolution. Specifically, the Gross–Pitaevskii equation was described as a complex representation to obtain a pair of time-dependent equations, which were then solved simultaneously following discretization based on SPH particle approximation. This study proposed a new numerical scheme for vortex lattice formation in a rotating Bose–Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit real-time integration scheme.
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