Quadrupole coupling of circular Rydberg qubits to inner shell excitations

Abstract: Divalent atoms provide excellent means for advancing control in Rydberg atom-based quantum simulation and computing, due to the second optically active valence electron available. Particularly promising in this context are circular Rydberg atoms, for which long-lived ionic core excitations can be exploited without suffering from detrimental autoionization. Here, we report the implementation of electric quadrupole coupling between the metastable 4D$_{3/2}$ level and a very high-$n$ ($n=79$) circular Rydberg qubit, realized in doubly excited $^{88}$Sr atoms prepared from an optical tweezer array. We measure the kHz-scale differential level shift on the circular Rydberg qubit via beat-node Ramsey interferometry comprising spin echo. Observing this coupling requires coherent interrogation of the Rydberg states for more than one hundred microseconds, which is assisted by tweezer trapping and circular state lifetime enhancement in a black-body radiation suppressing capacitor. Further, we find no noticeable loss of qubit coherence under continuous photon scattering on the ion core, paving the way for laser cooling and imaging of Rydberg atoms. Our results demonstrate access to weak electron-electron interactions in Rydberg atoms and expand the quantum simulation toolbox for optical control of highly excited circular state qubits via ionic core manipulation.