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

Quantum Physics