Transient dynamics of parametric driving for single-electron image current detection in a Paul trap

Abstract: Nondestructive detection of single-electron motion is crucial for quantum information processing with electrons trapped in Paul traps. The standard approach in Penning traps is to detect the image current induced on the trap electrodes by the electron's oscillatory motion. However, applying this approach in Paul traps for single electrons is currently hindered by motional frequency fluctuations arising from trap anharmonicities and instabilities in the rf trapping field. In this work, we propose a robust detection scheme exploiting the transient dynamics of parametric driving to overcome these limitations. Distinct from traditional steady-state approaches, our method focuses on the transient regime to break the temporal constraints imposed by steady-state assumptions, thereby enabling fast readout. We show that a controlled ramp of the parametric drive effectively locks the frequency of the electron motion in the transient regime, rendering the signal highly resilient to realistic experimental noise and inherent micromotion. This work paves the way for the experimental realization of nondestructive detection of single-electron motion in Paul traps.