  A cryogenic radio-frequency ion trap system designed for quantum logic
spectroscopy of highly charged ions is presented. It includes a segmented
linear Paul trap, an in-vacuum imaging lens and a helical resonator. We
demonstrate ground state cooling of all three modes of motion of a single
$^9$Be$^+$ ion and determine their heating rates as well as excess axial
micromotion. The trap shows one of the lowest levels of electric field noise
published to date. We investigate the magnetic-field noise suppression in
cryogenic shields made from segmented copper, the resulting magnetic field
stability at the ion position and the resulting coherence time. Using this trap
in conjunction with an electron beam ion trap and a deceleration beamline, we
have been able to trap single highly charged Ar$^{13+}$ (Ar XIV) ions
concurrently with single Be$^+$ ions, a key prerequisite for the first quantum
logic spectroscopy of a highly charged ion.
