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Recently, a novel three-dimensional entangled state called tree-typeentanglement, which is likely to have applications for improving quantumcommunication security, was prepared via adiabatic passage by Song et al.[Phys. Rev. A 93, 062321 (2016)]. Here we propose two schemes for fastgenerations of tree-type three-dimensional entanglement among three spatiallyseparated atoms via shortcuts to adiabatic passage. With the help of quantumZeno dynamics, two kinds of different but equivalent methods, Lewis-Riesenfeldinvariants and transitionless quantum driving, are applied to constructshortcuts to adiabatic passage. The comparisons between the two methods arediscussed. The strict numerical simulations show that the tree-typethree-dimensional entangled states can be fast prepared with quite highfidelities and the two schemes are both robust against the variations in theparameters, atomic spontaneous emissions and the cavity-fiber photon leakages.

Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving