In a Penning trap with an extremely large magnetic gradient, the axial frequency of a one-proton self-excited oscillator is resolved at the level of the shift from a proton spin flip. This sensitivity opens a possible path towards detection of single-proton spin flips, novel measurements of the proton and antiproton g-factors, and a stringent test of CPT invariance by comparing proton and antiproton magnetic moments at precision likely to be a million times higher than achieved to date.

The central challenge of extending similar electron magnetic moment measurements to one proton is overcoming the substantially larger mass and weaker magnetic moment, which conspire to greatly reduce the frequency shift that signals a spin flip. Within a magnetic bottle gradient 50 times larger than used in the recent electron g-factor measurements, the proton spin-flip shift is still only 60 mHz out of a 553 kHz axial frequency. In such a large gradient, standard application of sideband cooling to reduce the magnetron radius changes the axial frequency by an amount greater than this spin-flip shift on average.

Proton axial frequency resolution at the 60 mHz level is enabled by feedback techniques realized previously only with one electron. Self-excitation produces a narrow feature with large signal-to-noise, ideal for rapid frequency measurements at high precision. Unwanted effects of the strong magnetic gradient are minimized by axial and radial cooling. Feedback cooling is used to reduce the proton axial motion below the temperature of a damping resistor. Axial-magnetron sideband cooling of the undamped radial motion is then demonstrated to reach a 14 mK theoretical limit.