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arXiv:2605.15087 · Physical Review Applied

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

Baiyi Yu, Andris Huang, Isabel Sacksteder, Hartmut Haeffner

quant-phnlin.CDphysics.atom-phphysics.ins-detSubmitted May 14, 2026• Announced May 15, 2026• 0 citations

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.

DOI: 10.1103/krxg-clfg
Comments: 7 pages, 5 figures

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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.

We report the image current detection of electrons in a room-temperature Paul trap at microwave frequencies. By selectively leveraging distinct cavity modes for trapping and detection, our approach effectively extracts electron signals otherwise buried in the microwave drive used for pseudo-potential formation. When the trapped electrons resonate with the cavity mode, we observe a mode excitation and its exponential decay attributed to resistive cooling. Detuning electrons from the cavity resonance halts this decay, and sweeping electrons' secular frequency reveals their oscillatory spectrum. Implementing this experiment at cryogenic temperatures could enable the image current detection and ground-state cooling of a single electron in Paul traps.

We propose a scheme to read out the spin of a single electron quantum bit in a surface Paul trap using oscillating magnetic-field gradients. The readout sequence is composed of cooling, driving, amplification, and detection of the electron's motion. We study the scheme in the presence of noise and trap anharmonicities at liquid-helium temperatures. An analysis of the four procedures shows short measurement times ($25\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$) and high fidelities (

99.7%

) are achievable with realistic experimental parameters. Our scheme performs the function of fluorescence detection in ion trapping schemes, highlighting the potential to build all-electric quantum computers based on trapped electron-spin qubits.

Precise control of charged particles in radio-frequency (Paul) traps requires minimising excess micromotion induced by stray electric fields. We present a method to detect and compensate such fields through amplitude modulation of the radio-frequency trapping field. Modulation at frequencies close to the motional modes of the trapped particle excites coherent motion whose amplitude linearly depends on the stray field. In trapped-ion experiments, this motion can be detected by recording the arrival times of photons scattered during laser cooling. Only a single laser beam is required to resolve fields in multiple directions. In a demonstration using a

^{88}\mathrm{Sr}^{+}

ion in a surface electrode trap, we achieve a sensitivity of

0.1\, \mathrm{V}\, \mathrm{m}^{-1}\, /\, \sqrt{\mathrm{Hz}}

and a minimal uncertainty of

0.015\, \mathrm{V}\, \mathrm{m}^{-1}

.

We present a theoretical study of trapping an electron in a two-frequency Paul trap, motivated by future hybrid architecture consisting of a doubly charged calcium ion (Ca

^{2+}

) and an electron. By isolating the electron from ionic-electron interactions, we formulate the equations of motion for the electron in the time-dependent trap potentials and cast them in the Hill form. Stability and dynamics are then analysed in terms of the dimensionless q-parameters, which encode the applied voltages, drive frequencies, trap geometry, and the particle's charge-to-mass ratio. Under the combined action of the two radio-frequency fields, the trapped electron's classical motion is shown to be approximated well by a slow secular oscillation modulated by two distinct motion sidebands originating from the low- and high-frequency RF drives. The approximation method presented here enables a quick evaluation of the relation between the device-design q-parameters and the electron motion. It offers a crucial foundation for developing physical models of electron-ion interactions in electron-ion traps.

We demonstrate a simple electronic detection method for trapped ions in a linear Paul trap. Singly charged calcium ions are confined in a linear Paul trap and are driven by an ac electric field at their secular frequency. The collective motion of the ions causes induced current on the trap electrodes, and the current signal is detected by a tuned circuit. This paper describes the design of the tuned circuit and the performance of this detection method. This method can be applied to various species of ions in different trap geometries. It serves as a simple tool to probe the existing ions in the trap, while in some cases, optical detection is not feasible. This method is particularly suitable for demonstration in teaching laboratories where the ion trap systems and detection circuits can be constructed by undergraduate students.

We present a thorough analysis of the electronic detection of charged particles, confined in a Penning trap, via image charges induced in the trap electrodes. Trapping of charged particles in an electrode structure leads to frequency shifts, which are due to image charge and space charge effects. These effects are of importance for Penning trap experiments which involve high charge densities or require high precision in the motional frequencies. Our analysis of image charges shows that only (higher order) odd powers of the particle displacement lead to induced charge differences, giving rise to a signal. This implies that, besides the centre-of-mass frequency of a trapped particle cloud, also higher order individual particle frequencies induce a signal, which can be picked up by an electronic detection circuit attached to the trap electrodes. We also derive analytic expressions for the image charge and space charge induced frequency shifts and perform simulations of space charge effects. In relation to this, we discuss the consequences of the shifted particle frequencies for resistive cooling of the particle motion.