We report on recent progress regarding the theoretical treatment of doubly-excited Rydberg states of atoms with two valence electrons. Building upon state-of-the-art techniques, we demonstrate that an approach based on configuration interaction with exterior complex scaling (CI-ECS) is capable of describing high Rydberg states (n∼100) and does not rely on the assumptions of R-matrix multichannel quantum-defect theory. We show that CI-ECS allows the simultaneous, accurate treatment of a range of doubly-excited Rydberg states broader than previously possible. The implementation of the method with numerical basis functions is explained in detail. As an example, CI-ECS calculations of the doubly-excited states of Mg and Sr are presented, and excellent agreement is found with available experimental data. The CI-ECS method opens new perspectives for studying collective two-electron dynamics in doubly-excited Rydberg states of alkaline-earth metal atoms, and is also of interest for the field of Rydberg-based quantum simulation.We report on recent progress regarding the theoretical treatment of doubly-excited Rydberg states of atoms with two valence electrons. Building upon state-of-the-art techniques, we demonstrate that an approach based on configuration interaction with exterior complex scaling (CI-ECS) is capable of describing high Rydberg states (n∼100) and does not rely on the assumptions of R-matrix multichannel quantum-defect theory. We show that CI-ECS allows the simultaneous, accurate treatment of a range of doubly-excited Rydberg states broader than previously possible. The implementation of the method with numerical basis functions is explained in detail. As an example, CI-ECS calculations of the doubly-excited states of Mg and Sr are presented, and excellent agreement is found with available experimental data. The CI-ECS method opens new perspectives for studying collective two-electron dynamics in doubly-excited Rydberg states of alkaline-earth metal atoms, and is also of interest for the field of Rydberg-based quantum simulation.

Molecular PhysicsDec 18, 20208 citations

Information and entanglement measures applied to the analysis of complexity in doubly excited states of helium

J. P. Restrepo Cuartas, José Luis Sanz‐Vicario

Shannon entropy and Fisher information calculated from one-particle density distributions and von Neumann and linear entropies (the latter two as measures of entanglement) computed from the reduced one-particle density matrix are analyzed for the $^{1,3}S^{e},\phantom{\rule{4pt}{0ex}}^{1,3}P^{o}$ , and $^{1,3}D^{e}$ Rydberg series of He doubly excited states below the second ionization threshold. In contrast with the Shannon entropy, we find that both the Fisher information and entanglement measures are able to discriminate low-energy resonances pertaining to different $_{2}(K,T)_{{n}_{2}}^{A}$ series according to the Herrick-Sinano\ifmmode \breve{g}\else \u{g}\fi{}lu-Lin classification. Contrary to bound states, which show a clear and unique asymptotic value for both Fisher information and entanglement measures in their Rydberg series $1sn\ensuremath{\ell}$ for $n\ensuremath{\rightarrow}\ensuremath{\infty}$ (which implies a loss of spatial entanglement), the variety of behaviors and asymptotic values of entanglement above the noninteracting limit value in the Rydberg series of doubly excited states $_{2}(K,T)_{{n}_{2}}^{A}$ indicates a signature of the intrinsic complexity and remnant entanglement in these high-lying resonances even with infinite excitation ${n}_{2}\ensuremath{\rightarrow}\ensuremath{\infty}$, for which all known attempts of resonance classifications fail in helium.Shannon entropy and Fisher information calculated from one-particle density distributions and von Neumann and linear entropies (the latter two as measures of entanglement) computed from the reduced one-particle density matrix are analyzed for the $^{1,3}S^{e},\phantom{\rule{4pt}{0ex}}^{1,3}P^{o}$, and $^{1,3}D^{e}$ Rydberg series of He doubly excited states below the second ionization threshold. In contrast with the Shannon entropy, we find that both the Fisher information and entanglement measures are able to discriminate low-energy resonances pertaining to different $_{2}(K,T)_{{n}_{2}}^{A}$ series according to the Herrick-Sinano\ifmmode \breve{g}\else \u{g}\fi{}lu-Lin classification. Contrary to bound states, which show a clear and unique asymptotic value for both Fisher information and entanglement measures in their Rydberg series $1sn\ensuremath{\ell}$ for $n\ensuremath{\rightarrow}\ensuremath{\infty}$ (which implies a loss of spatial entanglement), the variety of behaviors and asymptotic values of entanglement above the noninteracting limit value in the Rydberg series of doubly excited states $_{2}(K,T)_{{n}_{2}}^{A}$ indicates a signature of the intrinsic complexity and remnant entanglement in these high-lying resonances even with infinite excitation ${n}_{2}\ensuremath{\rightarrow}\ensuremath{\infty}$, for which all known attempts of resonance classifications fail in helium.

Physical Review AMay 1, 201536 citations

Quantum entanglement of helium atom in high-lying Rydberg states

Li-Guang Jiao, Y. K. Ho

Bulletin of the American Physical SocietyJun 9, 20150 citations

Entanglement in helium atom confined in an impenetrable cavity

Przemysław Kościk, Jayanta K. Saha

The European Physical Journal DNov 1, 201516 citations

^{1,3}S^{e},\phantom{\rule{4pt}{0ex}}^{1,3}P^{o}

, and

^{1,3}D^{e}

Rydberg series of He doubly excited states below the second ionization threshold. In contrast with the Shannon entropy, we find that both the Fisher information and entanglement measures are able to discriminate low-energy resonances pertaining to different

_{2}(K,T)_{{n}_{2}}^{A}

series according to the Herrick-Sinano\ifmmode \breve{g}\else \u{g}\fi{}lu-Lin classification. Contrary to bound states, which show a clear and unique asymptotic value for both Fisher information and entanglement measures in their Rydberg series $1sn\ensuremath{\ell}$ for $n\ensuremath{\rightarrow}\ensuremath{\infty}$ (which implies a loss of spatial entanglement), the variety of behaviors and asymptotic values of entanglement above the noninteracting limit value in the Rydberg series of doubly excited states

_{2}(K,T)_{{n}_{2}}^{A}

indicates a signature of the intrinsic complexity and remnant entanglement in these high-lying resonances even with infinite excitation ${n}_{2}\ensuremath{\rightarrow}\ensuremath{\infty}$, for which all known attempts of resonance classifications fail in helium.