QUANTUM-NONDEMOLITION MEASUREMENT OF CYCLOTRON EXCITATIONS AND WAVE-FUNCTION COLLAPSE

The quantum non-demolition measurement of the cyclotron excitations of an electron trapped in a Penning trap is shown to be accessible, with the modern technology, by only considering the coupling between the axial and the cyclotron motions induced by the relativistic correction to the electron's mass. It is shown that such a measurement is possible only when the spin state of the electron is preassigned and the wave function will then collapse into a Fock state. When this is not the case the wave function of the electron will collapse into an entangled state.