We sympathetically cool highly charged ions (HCI) in Coulomb crystals of Doppler-cooled Be+ ions confined in a cryogenic linear Paul trap that is integrated into a fully enclosing radio-frequency resonator manufactured from superconducting niobium. By preparing a single Be+ cooling ion and a single HCI, quantum logic spectroscopy toward frequency metrology and qubit operations with a great variety of species are enabled. While cooling down the assembly through its transition temperature into the superconducting state, an applied quantization magnetic field becomes persistent, and the trap becomes shielded from subsequent external electromagnetic fluctuations.
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