In high- $L$ Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high- $L$ term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a ${}^{2}{S}_{1/2}$ state. However, observations in barium Rydberg states and recent observations in Rydberg states of ${\mathrm{Si}}^{2+}$ reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, ${\mathrm{Si}}^{2+},$ and barium.In high-$L$ Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-$L$ term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a ${}^{2}{S}_{1/2}$ state. However, observations in barium Rydberg states and recent observations in Rydberg states of ${\mathrm{Si}}^{2+}$ reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, ${\mathrm{Si}}^{2+},$ and barium.

Physical Review AAug 29, 200316 citations

Theory of long-range interactions for Rydberg states attached to hyperfine-split cores

F. Robicheaux, Donald W. Booth, Mark E. Saffman

The theory is developed for one- and two-atom interactions when the atom has a Rydberg electron attached to a hyperfine-split core state. This situation is relevant for some of the rare-earth and alkaline-earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare-earth atoms, the core electrons can have a very substantial total angular momentum $J$ and a nonzero nuclear spin $I$ . In the alkaline-earth atoms there is a single ( $s$ ) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions ( ${C}_{5}$ and ${C}_{6}$ matrices).The theory is developed for one- and two-atom interactions when the atom has a Rydberg electron attached to a hyperfine-split core state. This situation is relevant for some of the rare-earth and alkaline-earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare-earth atoms, the core electrons can have a very substantial total angular momentum $J$ and a nonzero nuclear spin $I$. In the alkaline-earth atoms there is a single ($s$) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions (${C}_{5}$ and ${C}_{6}$ matrices).

arXiv:1711.10518Physical Review AFeb 15, 201825 citations

Spin-Spin Interaction for Very Large Atomic Separations

Edwin Albert Power, William J. Meath, Joseph O. Hirschfelder

Physical Review LettersOct 10, 196612 citations

Atom–light superposition oscillation and Ramsey-like atom–light interferometer

Cheng Qiu, Shuying Chen, L. Q. Chen +4 more

Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interaction between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between atom and light and a coherent mixing of light wave with excited atomic spin wave in a Raman process. We construct a new kind of hybrid interferometer based on the atom-light coherent superposition state. Interference fringes are observed in both optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interaction between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between atom and light and a coherent mixing of light wave with excited atomic spin wave in a Raman process. We construct a new kind of hybrid interferometer based on the atom-light coherent superposition state. Interference fringes are observed in both optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.

arXiv:1602.05685OpticaJul 12, 201623 citations

Exchange interaction between an atom and a multiply charged ion

E. Duman, L. I. Men’shikov

Zhurnal Eksperimentalnoi i Teoreticheskoi FizikiSep 1, 19790 citations

In high-

L

Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-

L

term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a

{}^{2}{S}_{1/2}

state. However, observations in barium Rydberg states and recent observations in Rydberg states of

{\mathrm{Si}}^{2+}

reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium,

{\mathrm{Si}}^{2+},

and barium.

J

and a nonzero nuclear spin

I

. In the alkaline-earth atoms there is a single (

s

) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions (

{C}_{5}

and

{C}_{6}

matrices).