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Molecular Physics

Theoretical approaches for doubly-excited Rydberg states in quasi-two-electron systems: two-electron dynamics far away from the nucleus

Matthieu Génévriez

Published Dec 18, 2020• 8 citations
Publisher

Abstract

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.

DOI
10.1080/00268976.2020.1861353

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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.
Abstract In this brief review, the opportunities that the alkaline-earth elements offer for studying new aspects of Rydberg physics are discussed. For example, the bosonic alkaline-earth isotopes have zero nuclear spin which eliminates many of the complexities present in alkali Rydberg atoms, permitting simpler and more direct comparison between theory and experiment. The presence of two valence electrons allows the production of singlet and triplet Rydberg states that can exhibit a variety of attractive or repulsive interactions. The availability of weak intercombination lines is advantageous for laser cooling and for applications such as Rydberg dressing. Excitation of one electron to a Rydberg state leaves behind an optically active core ion allowing, for high- L states, the optical imaging of Rydberg atoms and their (spatial) manipulation using light scattering. The second valence electron offers the possibility of engineering long-lived doubly excited states such as planetary atoms. Recent advances in both theory and experiment are highlighted together with a number of possible directions for the future.
We have calculated quadrupole moments, Qzz{\mathit{Q}}_{\mathit{z}\mathit{z}}Qzz​, of helium in several of its doubly excited states and in two of its singly excited Rydberg states, and of the alkaline-earth atoms Be, Mg, Ca, Sr, and Ba in their ground and low-lying excited states. The calculations use well-converged, frozen-core configuration-interaction (CI) wave functions and, for interpretive purposes, Hartree-Fock (HF) atomic wave functions and single-term, optimized, molecular rotor-vibrator (RV) wave functions. The quadrupole moments calculated using RV wave functions serve as a test of the validity of the correlated, moleculelike model, which has been used to describe the effects of electron correlation in these two-electron and pseudo-two-electron atoms. Likewise, the quadrupole moments calculated with HF wave functions test the validity of the independent-particle model. In addition to their predictive use and their application to testing simple models, the quadrupole moments calculated with CI wave functions reveal previously unavailable information about the electronic structure of these atoms. Experimental methods by which these quadrupole moments might be measured are also discussed. The quadrupole moments computed from CI wave functions are presented as predictions; measurements of Qzz{\mathit{Q}}_{\mathit{z}\mathit{z}}Qzz​ have been made for only two singly excited Rydberg states of He, and a value of Qzz{\mathit{Q}}_{\mathit{z}\mathit{z}}Qzz​ has been computed previously for only one of the states reported here. We present these results in the hope of stimulating others to measure some of these quadrupole moments.
Highly excited Rydberg states and their interactions play an important role in quantum computing and simulation. These properties can be predicted accurately for alkali atoms with simple Rydberg level structures. However, an extension of these methods to more complex atoms such as alkaline-earth atoms has not been demonstrated or experimentally validated. Here, we present multichannel quantum defect models for highly excited Yb 174 and Yb 171 Rydberg states with L ≤ 2 . The models are developed using a combination of existing literature data and new, high-precision laser and microwave spectroscopy in an atomic beam, and validated by detailed comparison with experimentally measured Stark shifts and magnetic moments. We then use these models to compute interaction potentials between two Yb atoms, and find excellent agreement with direct measurements in an optical tweezer array. From the computed interaction potential, we identify an anomalous Förster resonance that likely degraded the fidelity of previous entangling gates in Yb 171 using F = 3 / 2 Rydberg states. We then identify a more suitable F = 1 / 2 state, and achieve a state-of-the-art controlled- gate fidelity of F = 0.994 ( 1 ) , with the remaining error fully explained by known sources. This work establishes a solid foundation for the continued development of quantum computing, simulation, and entanglement-enhanced metrology with Yb neutral atom arrays.
Orbital dynamics in two-electron alkaline earth atoms in a static electric field are studied using scaled-energy recurrence spectroscopy. Photoabsorption spectra for Ba and Ca Rydberg atoms are measured as continuous functions of static electric field and energy. In both Ba and Ca the laser excitation proceeds through the singly excited ndndnd series which is strongly perturbed by doubly excited valence configurations. Clear signatures of the two-electron dynamics associated with these perturbing configurations are identified.
Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states ∣0〉 and ∣1〉 are excited to Rydberg states ∣ r 〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state ∣1〉 can be fully excited to the Rydberg state while ∣0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.
Conditional probability distributions for the valence electrons of alkaline-earth atoms in their ground and valence excited states are constructed using large-basis Sturmlan configuration-interaction wave functions for two electrons in frozen, effective-core potentials. The distributions indicate that the ground states of Be, Mg, Ca, Sr, and Ba, and the valence excited states of Be, are much more like linear triatomic molecules, akin to doubly excited He, than like independent-particle systems such as the ground states of He and He-like ions.