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

Abstract

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 non-zero nuclear spin, I. In the alkaline earth atoms there is a single, s, core electron whose spin can couple to a non-zero 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 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 (C5 and C6 matrices).

Spectroscopy of Rydberg States in Erbium using Electromagnetically Induced Transparency

“…1(b) a zoom-in onto the most relevant Rydberg series attached to the lowest two ionization thresholds. The electronic ground-state configuration of erbium reads as (4f 12 ( 3 H 6 )6s 2 ( 1 S 0 )) 6 . This type of configuration is often called sub-merged because the partially-filled inner f-shell is surrounded by the outer sshell.…”

“…For our two-photon Rydberg spectroscopy, we couple the ground-state to the intermediate state (4f 12 ( 3 H 6 )6s6p( 1 P°1)) 7 . Here, the angular momentum coupling results from the small size of the 4f -orbital compared to that of the sp electrons.…”

“…Here, the angular momentum coupling results from the small size of the 4f -orbital compared to that of the sp electrons. This leads to the 4f 12 electrons coupling together to give a particular angular momentum term, ( 3 H 6 ), and the sp electrons coupling to give ( 1 P°1). These two partial-J's are then coupled to give the total J = 7 for the intermediate state.…”

“…Recently, there has been a growing interest in extending the Rydberg toolbox to more complex multi-valenceelectron atomic species, opening new possibilities for e.g. laser cooling and trapping, high-fidelity optical readout, and quantum-information storage [9][10][11][12]. In multivalence-electron atoms, the key paradigm shift is that, after Ry excitation of one of the available valence electrons, the core remains optically active, effectively resembling a single-charged positive ion.…”

“…Pushing the boundaries even further, the next step is to consider atomic species with more than two valence electrons, like open-shell lanthanides for which laser cooling and quantum degeneracy have been demonstrated [23][24][25][26][27]. Compared to alkaline-earth, these species might exhibit an ionic-core polarizability resembling even more the ground-state polarizability, and might allow access to a large hyperfine manifold [9,28]. They also could allow to directly excite high orbital-momentum Ry states, and provide an even larger plethora of laser cooling transitions.…”