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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 TQD method versus (a) Δ/g with tf = 80/g and (b) tf/g−1 with Δ = 6 g, respectively; (c) the three dimensional image of the fidelity for the TQD method versus Δ/g and tf/g−1.
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f4: The fidelity for the TQD method versus (a) Δ/g with tf = 80/g and (b) tf/g−1 with Δ = 6 g, respectively; (c) the three dimensional image of the fidelity for the TQD method versus Δ/g and tf/g−1.

Mentions: Based on the correlation in Eq. (35), the Rabi frequencies of the TQD method can be figured out. As an illustration, we plot the fidelity versus the detuning Δ and tf in Fig. 4, where /Φ(tf)〉 is the state at the time t = tf of the whole system governed by the total Hamiltonian in Eq. (31). To compare with each other effectively, we choose the same operation time tf = 80/g in the TQD method as that in the LRI method. From Fig. 4(a), we can find that under tf = 80/g when Δ = 6 g the fidelity is highest. Besides, we can see that the fidelity is almost unity: F(tf = 80/g) = 0.996 at the point tf = 80/g from Fig. 4(b). Thus we choose tf = 80/g and Δ = 6 g as the parameters of the TQD method in the following discussion. Similar to the LRI method, in order to consider the joint effects of tf and Δ on the fidelity we plot the three dimensional image of the fidelity versus tf/g−1 and Δ/g in Fig. 4(c). However, from Fig. 4(c), we are not able to judge whether the effects of tf and Δ on the fidelity are dependent or not dependent on each other. We will make a detailed discussion about the joint effects of tf and Δ on the fidelity later in the last subsection.


Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving
The fidelity for the TQD method versus (a) Δ/g with tf = 80/g and (b) tf/g−1 with Δ = 6 g, respectively; (c) the three dimensional image of the fidelity for the TQD method versus Δ/g and tf/g−1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: The fidelity for the TQD method versus (a) Δ/g with tf = 80/g and (b) tf/g−1 with Δ = 6 g, respectively; (c) the three dimensional image of the fidelity for the TQD method versus Δ/g and tf/g−1.
Mentions: Based on the correlation in Eq. (35), the Rabi frequencies of the TQD method can be figured out. As an illustration, we plot the fidelity versus the detuning Δ and tf in Fig. 4, where /Φ(tf)〉 is the state at the time t = tf of the whole system governed by the total Hamiltonian in Eq. (31). To compare with each other effectively, we choose the same operation time tf = 80/g in the TQD method as that in the LRI method. From Fig. 4(a), we can find that under tf = 80/g when Δ = 6 g the fidelity is highest. Besides, we can see that the fidelity is almost unity: F(tf = 80/g) = 0.996 at the point tf = 80/g from Fig. 4(b). Thus we choose tf = 80/g and Δ = 6 g as the parameters of the TQD method in the following discussion. Similar to the LRI method, in order to consider the joint effects of tf and Δ on the fidelity we plot the three dimensional image of the fidelity versus tf/g−1 and Δ/g in Fig. 4(c). However, from Fig. 4(c), we are not able to judge whether the effects of tf and Δ on the fidelity are dependent or not dependent on each other. We will make a detailed discussion about the joint effects of tf and Δ on the fidelity later in the last subsection.

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.