A cryogenic Paul trap for probing the nuclear isomeric excited state $^{229\text{m}}$Th$^{3+}$

While laser excitation of the nuclear isomeric transition in $^{229}$Th has been recently achieved for thorium atoms embedded in large-bandgap crystals, laser excitation and characterization of the nuclear transition in trapped $^{229}$Th$^{3+}$ ions has not yet been accomplished. To address these experiments, a cryogenic Paul trap setup has been designed, built, and commissioned at LMU Munich. Here, we present the specifications of the new experimental platform and demonstrate its successful operation, showing the extraction, subsequent ion-guiding, mass-purification, and trapping of $^{229}$Th$^{3+}$ and $^{229\text{m}}$Th$^{3+}$ ions from a newly designed buffer-gas stopping cell as well as of $^{88}$Sr$^{+}$ ions from laser ablation of a solid target. Further, we show sympathetic laser cooling of $^{229\text{(m)}}$Th$^{3+}$ by Doppler-cooled $^{88}$Sr$^{+}$ ions and the formation of mixed-species Coulomb crystals.