CYCLOTRON-RESONANCE WITH 10(-11) RESOLUTION - ANHARMONIC DETECTION AND BEATING A COHERENT DRIVE WITH THE NOISE

We describe the detection of the radial motions of a trapped charge in a Penning trap via a fourth-order electrostatic coupling to the axial degree of freedom. Two basic approaches are demonstrated. The first uses a standard resonant drive to determine the cyclotron frequency and has a resolution of 0.1 ppb. The second approach beats the motion due to an off-resonant drive against the motion due to thermal drives to give a continuous phase-coherent monitor of the cyclotron motion with a resolution of 0.01 ppb. The inherent systematic shift of these "anharmonic-detection" schemes is discussed, and approaches are given to reduce or eliminate it.