Quantum entanglement in plasma-embedded helium atom
Yen-Chang Lin1,2*, Te-Kuei Fang3, Yew Kam Ho1
1Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
2Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, New Taipei, Taiwan
3Department of Physics, Fu Jen Catholic University, New Taipei, Taiwan
* presenting author:Yen-Chang Lin, email:linyc@pub.iams.sinica.edu.tw
Entanglement is fundamental property in quantum physics, and it plays an important role in studies of quantum gravity [1], quantum teleportation [2], and quantum computation [3]. When measuring entanglement in a system consists of two electrons, this bipartite system must be treated as a whole, and it cannot be considered as two independent particles. Measuring one of the two electrons will change the behavior of the other electron. The electron-electron orbital correlation is related to quantum entanglement. How to quantify entanglement is an active research topic in recent years. The linear entropy (SL=Tr(ρA)) and von Neumann entropy (SvN=-Tr(ρAlog2 ρA)) have been used to quantify entanglement, with ρA being the one-particle reduced density matrix, and ρA=Tr(ρAB)=ρB. Our previous studies were concentrated on bound states [4] and on resonance states of free helium atom. In the present work, the atom is embedded in weakly coupled Debye plasmas, in which the pure Coulomb potential between two charged particles for free atoms is replaced by a screened Coulomb (Yukawa-type) potential. The Hamiltonian for helium in Debye plasmas, with energy expressed in atomic units, is
H=-(▽1)²/2-(▽2)²/2-Zexp(-μr1)/r1-Zexp(-μr2)/r2+exp(-μr12)/r12.
And
exp(-μr12)/r12(m=0 to ∞)(2m+1)Km+½(μr>)Im+½(μr<)Pm(cosθ12)/√(r>r<).
Here, μ=1/D is screening parameter with D being the Debye length, which is a function of temperature and charge density of the plasma. The K and I are modified Bessel functions of first and second kind, respectively. From such calculations, accurate wave functions and energies can be obtained, and they can then be used in entropy calculations. At the meeting we will show our results on interplay between entanglement, strength of the screening effects, and structures for the plasma-embedded helium atom.

This work was supported by the Ministry of Science and Technology in Taiwan.

References
[1] D. V. Fursaev, Phys. Rev. D 73, 124025 (2006).
[2] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information
(Cambridge University Press, Cambridge, 2000).
[3] M.-J. Zhao, S.-M. Fei,. and X. Li-Jost, Phys. Rev. A 85, 054301 (2012).
[4] Y. C. Lin, C. Y. Lin and Y. K. Ho, Phys. Rev. A 87, 022316 (2013).


Keywords: Debye plasmas, Entanglement, von Neumann entropy, linear entropy, Helium atom