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

View Article: PubMed Central - PubMed

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.

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The fidelity for the LRI method versus (a) tf/g−1 with ε = 0.177 and (b) ε with tf = 80/g, respectively; (c) the three dimensional image of the fidelity for the LRI method versus tf/g−1 and ε.
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f2: The fidelity for the LRI method versus (a) tf/g−1 with ε = 0.177 and (b) ε with tf = 80/g, respectively; (c) the three dimensional image of the fidelity for the LRI method versus tf/g−1 and ε.

Mentions: Firstly, to determine the parameters of the LRI method, we plot the fidelity versus the operation time tf and ε in Fig. 2, where /Φ(tf)〉 is the state at the time t = tf of the whole system governed by the total Hamiltonian Htotal in Eq. (10). In Fig. 2(a), we plot the relation between the fidelity and the operation time tf with ε = 0.177 which is determined in Eq. (28). And we can see that in a very short operation time tf = 80/g the fidelity is already almost unity: F(tf = 80/g) = 0.996. From Fig. 2(b), we can find that under tf = 80/g when ε = 0.177 the fidelity is highest. Thus we can choose tf = 80/g and ε = 0.177 as the parameters of the LRI method in the following discussion. Furthermore, in order to consider the joint effects of tf and ε on the fidelity we plot the three dimensional image of the fidelity versus tf/g−1 and ε in Fig. 2(c). From the three dimensional image, it is clear that the effects of tf and ε on the fidelity are not dependent on each other.


Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving
The fidelity for the LRI method versus (a) tf/g−1 with ε = 0.177 and (b) ε with tf = 80/g, respectively; (c) the three dimensional image of the fidelity for the LRI method versus tf/g−1 and ε.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036061&req=5

f2: The fidelity for the LRI method versus (a) tf/g−1 with ε = 0.177 and (b) ε with tf = 80/g, respectively; (c) the three dimensional image of the fidelity for the LRI method versus tf/g−1 and ε.
Mentions: Firstly, to determine the parameters of the LRI method, we plot the fidelity versus the operation time tf and ε in Fig. 2, where /Φ(tf)〉 is the state at the time t = tf of the whole system governed by the total Hamiltonian Htotal in Eq. (10). In Fig. 2(a), we plot the relation between the fidelity and the operation time tf with ε = 0.177 which is determined in Eq. (28). And we can see that in a very short operation time tf = 80/g the fidelity is already almost unity: F(tf = 80/g) = 0.996. From Fig. 2(b), we can find that under tf = 80/g when ε = 0.177 the fidelity is highest. Thus we can choose tf = 80/g and ε = 0.177 as the parameters of the LRI method in the following discussion. Furthermore, in order to consider the joint effects of tf and ε on the fidelity we plot the three dimensional image of the fidelity versus tf/g−1 and ε in Fig. 2(c). From the three dimensional image, it is clear that the effects of tf and ε on the fidelity are not dependent on each other.

View Article: PubMed Central - PubMed

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.

No MeSH data available.