Practical zero-shift tuning in geonium.

Compositeness of the electron may show up in a very small deviation of the measured electron g factor from one calculated for a point electron by quantum electrodynamics. The precision of our g measurements is currently limited by an interaction of the cyclotron motion with standing waves in the trap cavity containing the electron. The important element introduced here is the systematic exploration of the trap cavity modes and the electron's coupling to them by measuring the shifted electron g factor gc = gc(omega e) as a function of the cyclotron frequency omega e. By measuring gc values at five different omega e values and modeling the trap cavity by six lumped LC circuits, the L values for the four most important modes may be determined and finally the unshifted g value may be extracted. Auxiliary experiments are relied upon only for the L values of the two least critical cavity modes. By designing the trap as a high-Q microwave cavity, an electron cyclotron and anomaly resonance linewidth one or even two orders of magnitude narrower than in free space may be approached without introducing appreciable frequency shifts.