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arXiv:quant-ph/0110032

Comment on relationship between atomic squeezed and entangled states

Arup Banerjee

Published Oct 5, 2001• 1 citation
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Abstract

The ability of parameter recently proposed by Sorensen et al. (Nature, 409, 63 (2001)) to characterize entanglement or inseparability is investigated for a system of two two-level atoms interacting with a single mode of radiation field. For comparison we employ the necessary and sufficient criterion of Peres and Horodecki for inseparability of bipartite states. We show that for diagonal atomic density matrix the parameter of Sorensen et al. fails to show entangled nature of collective atomic state whereas same state is inseparable in accordance with Peres-Horodecki criterion.

DOI
10.48550/arxiv.quant-ph/0110032

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The ability of parameter recently proposed by Sorensen et al. (Nature, 409, 63 (2001)) to characterize entanglement or inseparability is investigated for a system of two two-level atoms interacting with a single mode of radiation field. For comparison we employ the necessary and sufficient criterion of Peres and Horodecki for inseparability of bipartite states. We show that for diagonal atomic density matrix the parameter of Sorensen et al. fails to show entangled nature of collective atomic state whereas same state is inseparable in accordance with Peres-Horodecki criterion.
We investigate the efficiency of inseparability criteria in detecting the entanglement properties of two-mode non-Gaussian states of the electromagnetic field. We focus our study on the relevant class of two-mode squeezed number states. These states combine the entangling capability of two-mode squeezers with the non-Gaussian character (nonclassicality) of number states. They allow for some exact analytical treatments, and include as a particular case the two-mode Gaussian squeezed vacuum. We show that the generalized PPT criterion recently proposed by Shchukin and Vogel, based on higher order statistical moments, is very efficient in detecting the entanglement for this class of non-Gaussian states.
Entanglement properties of two-mode squeezed coherent states in the radiation field are investigated according to the entanglement criterion [Phys. Rev. Lett. 84 (2000) 2722]. The dependence of entanglement on squeeze angle and squeeze parameter is discussed. It shows that the system evolves into entangled states and entanglement does not increase persistently with the increase of squeeze angle and squeeze parameter. There only exists a certain squeeze angle in which the entanglement exists continuously.
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of inseparability with light are not uncommon, but such demonstrations in physically well-separated massive systems, such as distinct gases of atoms, are new and present significant challenges and opportunities. Rigorous theoretical criteria are needed for demonstrating that given data are sufficient to confirm entanglement. Such criteria for experimental data have been derived for the case of continuous-variable systems obeying the Heisenberg-Weyl (position-momentum) commutator. To address the question of experimental verification more generally, we develop a sufficiency criterion for arbitrary states of two arbitrary systems. When applied to the recent study by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 (2001)] of spin-state entanglement of two separate, macroscopic samples of atoms, our criterion confirms the presence of spin entanglement.
Considering the propagation of a two-mode optical field that is initially in a squeezed vacuum state in a thermal environment, we obtain an intuitive expression for inseparability condition of the two-mode mixed state which is given in the coherent state representation. This condition shows that the two modes have quantum entanglement if and only if the coefficient of the correlation term between the two modes is larger than that of the off-diagonal term of each mode in the density matrix. We find that even if the quantum channel is dynamically coupled to the thermal environment, the fidelity for teleporting coherent states larger than 1/2 is still the criterion for quantum teleportation. We also show that the entanglement, squeezing and quantum teleportation conditions are always consistent with each other.