Rydberg spectrum of a single trapped Ca${}^{+}$ ion: A Floquet analysis

Abstract

We compute the Rydberg spectrum of a single Ca${}^{+}$ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in Ca${}^{+}$, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for e${}^{-}$+Ca${}^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of Ca${}^{+}(23P)$ and Ca${}^{+}(52F)$ Rydberg lines.

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• Impact of micromotion and field-axis misalignment on the excitation of Rydberg states of ions in a Paul trap
• Microwave transitions in atomic sodium: Radiometry and polarimetry using the sodium layer
• Spin Phonon Relaxation Dynamics from a Conical Intersection of Trapped Rydberg Ions