Elementary Laser‐Less Quantum Logic Operations with (Anti‐)Protons in Penning Traps

Static magnetic field gradients superimposed on the electromagnetic trapping potential of a Penning trap can be used to implement laser-less spin–motion couplings that allow the realization of elementary quantum logic operations in the radio-frequency regime. An important scenario of practical interest is the application to g-factor measurements with single (anti-)protons to test the fundamental charge, parity, time reversal (CPT) invariance as pursued in the Baryon Antibaryon Symmetry Experiment (BASE) collaboration. The classical and quantum behavior of a charged particle in a Penning trap with a superimposed magnetic field gradient is discussed. Using analytic and numerical calculations, it is found that it is possible to carry out a SWAP gate between the spin and the motional qubit of a single (anti-)proton with high fidelity, provided the particle has been initialized in the motional ground state. The implications of the findings for the realization of quantum logic spectroscopy in this system are discussed.