Circumventing Detector Backaction on a Quantum Cyclotron

Detector backaction can be completely evaded when the state of a one-electron quantum cyclotron is detected, but it nonetheless significantly broadens the quantum-jump resonance line shapes from which the cyclotron frequency can be deduced. This limits the accuracy with which the electron magnetic moment can be determined to test the standard model’s most precise prediction. A steady-state solution to a master equation, the first quantum calculation for the open quantum cyclotron system, illustrates a method to circumvent the detection backaction upon the measured frequency.

Figure 1

Lowest energy levels for the combined quantum cyclotron and axial detection oscillator (not to scale).

Figure 2

(a) Quantum cyclotron line shape for ${\overline{n}}_z=10$ and a weak drive (${\mathrm{\Omega }}_c=0.1{\gamma }_c$) resolves the axial states as ${\gamma }_z$ is reduced. (b) The $n_z=0$ peak for ${\gamma }_z/(2\pi )=0.003\mathrm{Hz}$ and ${\gamma }_c/(2\pi )=0.03\mathrm{Hz}$ for a weak (solid curve) and strong drive (dashed) and a $T=0\mathrm{K}$ Lorentzian line shape (dotted).