Entanglement Entropy for Doubly Excited Resonance States in He
Chien-Hao Lin1*, Yew Kam Ho1
1Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
* presenting author:林建豪, email:b99202042@ntu.edu.tw
Studies of quantum entanglement play an important role in research areas such as quantum teleportation, quantum cryptography, and quantum information sciences. Research on quantum entanglement has recently extended to atomic systems such as two-electron model atoms and natural real atoms (see [1-3], and references therein). In our previous works, we have investigated entanglement measures in natural atomic systems that involve two highly correlated indistinguishable spin-1/2 fermions (electrons). Linear entropy and von Neumann entropy were calculated as spatial (electron-electron orbital) entanglement measures for ground and singly excited bound states in two-electron atomic systems, such as the helium atom (He), the hydrogen and positronium negative ions (H- and Ps-) [1-5]. These entanglement entropies are practical and quantitative measures of the amount for entanglement. In our present work, we stretch out our research and carry out an investigation on entanglement in doubly excited resonance states of helium. Since the resonance states are lying in the scattering continuum, their energies are no longer bound by the variational theorem; we apply the complex scaling method [6] to solve the complex energy pole with which the resonance energy and resonance width are deduced. Hylleraas-type wave functions are used to consider correlation effects. Once the wave function for a doubly excited state is obtained, we apply the Schmidt-Slater decomposition method [4-5] to calculate the linear entropy and von Neumann entropy for the resonance states. At this meeting, we will report our results for the doubly excited 2s2, 2s3s, 2p2, 3s2, and 3p2 1Se resonance states in the helium atom.
Our work has been supported by the Ministry of Science and Technology of Taiwan.

[1] Y.-C. Lin, C.-Y. Lin, and Y. K. Ho, Phys. Rev. A 87, 022316 (2013).
[2] Y.-C. Lin and Y. K. Ho, Can, J. Phys. (2014), accepted.
[3] C. H. Lin, Y.-C. Lin, and Y. K. Ho, Few-Body Syst. 54, 2147 (2013).
[4] C. H. Lin and Y. K. Ho, Few-Body Syst. 55, 1141 (2014).
[5] C. H. Lin and Y. K. Ho, Phys. Lett. A 378, 2861 (2014).
[6] Y. K. Ho, Phys. Rept. 99, 1 (1983).

Keywords: resonance state, entanglement measures, linear entropy, von Neumann entropy, complex scaling method