Abstract
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. Here we propose two schemes for fast generating 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.
Highlights
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 Here we propose two schemes for fast generating tree-type three-dimensional entanglement among three spatially separated atoms via shortcuts to adiabatic passage
Based on a set of cavity QED parameters g = 2π × 750 MHz, γ = 2π × 3.5 MHz and κ = 2π × 2.62 MHz, which are achieved in recent experiments[58,59,60], we can obtain the very high fidelities FLRI = 0.984 and FTQD = 0.990 corresponding to the Lewis-Riesenfeld invariants (LRI) method and the transitionless quantum driving (TQD) method respectively, which show our schemes for generating tree-type three-dimensional entangled states both are feasible in the experiment
We have proposed two schemes to speed up the generations of the tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving
Summary
Where Htotal is the total Hamiltonian of the whole system, Hal (Hacf) is the interaction between the atoms and the classical laser fields (the cavity-fiber system), v1(2),L(R) is the coupling strength between the modes of the cavity[1,2]. In order to construct a shortcut by the LRI method for fast generating of tree-type three-dimensional entanglement, we are supposed to chase down the Hermitian invariant operator I(t) satisfying i ∂tI (t) = [H0(t), I (t)]. For the appropriate Rabi frequencies and the fidelity F = 1, we can choose arctan 2 = 2π, sin ε i.e. the transformation Ψ1 → ΨLRI is achieved and we have constructed a shortcut by the LRI method to speed up the generation of the tree-type three-dimensional entanglement. The fast generation of tree-type three-dimensional entanglement, φ19 + φ20 ) is the tree-type three-dimensional entanglement generated by the TQD method
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