Driven Quantum Cyclotron with One Electron or Positron

The first quantum calculation is presented for a harmonic detection oscillator coupled to a one-particle quantum cyclotron - one trapped electron or positron that occupies only its lowest cyclotron and spin states. The calculation is used to investigate new measurement methods that could circumvent and minimize the detector backaction that limited past measurements of these moments. New methods that allow new measurements are urgently needed because there is now an intriguing 2.4 standard deviation discrepancy between the most precise prediction of the standard model of particle physics, and the most accurate measurement of a property of an elementary particle.