Current precision experiments with single (anti)protons to test CPT symmetry progress at a rapid pace, but are complicated by the need to cool particles to sub-thermal energies. We describe a cryogenic Penning-trap setup for
9Be
+ ions designed to allow coupling of single (anti)protons to laser-cooled atomic ions for sympathetic cooling and quantum logic spectroscopy. We report on trapping and laser cooling of clouds and single
9Be
+ ions. We discuss prospects for a microfabricated trap to allow coupling of single (anti)protons to laser-cooled
9Be
+ ions for sympathetic laser cooling to sub-mK temperatures on ms time scales.
The comparison of the g-factors of the proton and the antiproton is a stringent test of CPT invariance. The state-of-the-art method for the determination of the (anti-)proton's g-factor is the application of the continuous Stern-Gerlach effect. With this method, precisions in the low parts per billion regime could be achieved. However, preparation times for cold enough particles are on the order of minutes to hours. The implementation of sympathetic cooling using a co-trapped atomic ion could lead to preparation times in the milliseconds regime. Furthermore, the applicability of sympathetic cooling would enable an alternative readout scheme using quantum logic methods. This thesis presents a Penning trap system that is designed for ground state cooling, adiabatic transport, and motional coupling of single 9Be+ ions. It has been built in a modular manner, giving the option of adapting it for motional coupling and sympathetic cooling of single (anti-)protons. In the course of this work, the prerequisites for motional coupling of 9Be+ ions have been fulfilled: A cloud of 9Be+ ions was cooled to a temperature of 1.7~mK applying Doppler cooling. The achieved temperature is about three times the Doppler limit which is 0.5~mK for beryllium ions. Furthermore, a scheme for reproducible loading of the trap and reducing the particle number was developed. Finally, first transport in our apparatus was demonstrated with clouds of beryllium ions. The method used for that is directly applicable to single ions. The results of this work pave the way towards adiabatic transport of single 9Be+ ions, which is crucial for sympathetic cooling of (anti-)protons in a double-well potential as well as for implementing quantum logic spectroscopy with single (anti-)protons.