Mode coupling in a Penning trap:πpulses and a classical avoided crossing

An inhomogeneous radiofrequency electric field can couple the cyclotron and axial modes of a single ion in a Penning trap. The classical equations of motion are the same as those of a driven quantum-mechanical two-level system. We discuss an analog of the {π} pulse, which can exchange mode actions, and an analog of the avoided crossing. Experimental illustrations are presented.