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Bulletin of the American Physical Society

Strong Microwave Photon Coupling to the Electron Quadrupole Moment

Jonne Koski, Andreas Landig, Pasquale Scarlino, Maximilian Russ, David J. van Woerkom, Christian Reichl, W. Wegscheider, Guido Burkard, Andreas J. Wallraff, Thomas Ihn, K. Ensslin

Published Mar 5, 2019• 0 citations
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The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.
The moment coupling of an interacting ion and an atom with a 3 d -electron shell is analyzed for the ground state of identical atoms and ions where resonant charge exchange proceeds with transition of a 4 s -electron. The interaction of the ion charge with the atom quadrupole moment is important for this system along with the exchange interactions and spin-orbit interactions inside an isolated atom and an ion. The quadrupole moment for 3 d -atoms in the ground states is evaluated. The hierarchy of interactions in a molecular ion is analyzed depending on ion-atom distances and is compared with the standard Hund scheme. The resonant charge exchange proceeds effectively at separations corresponding to an intermediate case between cases “a” and “c” of the Hund coupling scheme.