Sympathetic cooling of charged particles in Penning traps using electron cyclotron radiation

TL;DR

This work introduces a novel sympathetic cooling scheme for arbitrary charged particles in Penning traps by leveraging self-cooled electrons as a cooling medium. It develops a quantum-mechanical framework combining electron cyclotron radiation in a cylindrical waveguide, millimeter-wave sideband coupling, and image-charge coupling to transfer energy from a particle of interest to a cloud of cooled electrons, with simulations predicting temperatures in the 1.3–4.0 mK range and cooling times of 20–200 s. The experimental realization at ELCOTRAP is structured in three phases: commissioning, sideband coupling, and finally image-charge coupling between two traps, with a mm-wave delivery system achieving $\Omega_{\mathrm{sb}}$ in the 10–100 Hz range and a two-trap coupling pathway under development. If successful, this approach could outperform traditional resistive cooling and complement laser-cooling-based schemes, enabling ultra-low temperatures for high-precision Penning-trap experiments and fundamental physics tests.

Abstract

We present a new technique for cooling arbitrary charged particles in a Penning trap by utilizing self-cooled electrons stored in a separate, macroscopically distant Penning trap as the cooling medium. The electrons decay predominantly to their motional ground state by emission of cyclotron radiation, which results in extremely low temperatures in the realm of single-digit quantum numbers in the motional degrees of freedom of the sympathetically cooled particle species. This opens up an exciting new frontier of tests of fundamental physics in Penning traps. This article provides a conceptual overview as well as a quantum-mechanical description of the involved cooling dynamics. The first implementation of this technique is currently being realized at the dedicated ELCOTRAP experiment at the Max Planck Institute for Nuclear Physics, which introduces special features for a quick iterative technical development cycle. Its current status, first results from commissioning, and future prospects will be presented.

Figures (11)

• Figure 1: Inset a) depicts the full trajectory of a charged particle stored in a Penning trap in bright red, with its decomposed individual eigenmotions being drawn separately in different colors. Figure b) depicts the coupling of particles stored in separate Penning traps, in which a radially split electrode of the particle trap (PT) picks up the modified cyclotron motion of the particle-of-interest in the form of an image charge and couples it to the axial motion of the electron via electrical connection to an axially offset electrode of the electron trap (ET). Figure c) shows a block diagram of the full cooling chain between the three involved eigenmotions. For each motion, the eigenfrequencies are listed for a magnetic field of $7\,\text{T}$ and in case of the electron's axial motion for typical Penning-trap parameters and varying electrostatic potential depths. The red/blue arrows indicate the cooling/heating channels, while the direction of the arrows encode the primary energy flow during cooling.
• Figure 2: Rate of single-photon transitions between excitations of an electron's modified cyclotron motion and photons in a circular waveguide vs. free space. The rate is calculated by summing over the individual modes $\gamma = \sum_{s\sigma} \gamma_{s\sigma}$, while the distinct contributions from individual modes have been labeled using the convention $\text{TM}_{mn}$ for $\sigma = 1$ modes and $\text{TE}_{mn}$ for $\sigma = 2$ modes. The upper graph shows the frequency dependence for a fixed waveguide radius $\rho_0 = 1.5\,\text{mm}$, while the lower graph shows the rate for a constant frequency $\omega_+/2\pi = 197\,\text{GHz}$ and varying waveguide radius. In practice, the singularities occurring at the mode's cutoff frequencies $\omega_{0, s\sigma}$ would be "smeared out" by losses in the waveguide walls.
• Figure 3: Coupling rate between an electron's modified cyclotron motion at $\omega_+ / 2\pi \approx 197\,\text{GHz}$ and its axial motion at $\omega_z / 2\pi \approx 50\,\text{MHz}$. The transitions are induced by driving the motional sideband on resonance ($\delta = 0$) using individual modes of a circular waveguide with varying radius $\rho_0$ and different mode indices $n$ and $\sigma$.
• Figure 4: Schematic illustration of an electron and a particle-of-interest stored in two separate Penning traps being coupled by exchange of image charges between their pickup electrodes, shown in red. In the electron trap, an axially offset pickup electrode is employed to maximize sensitivity to the electron's axial motion, whereas in the particle trap, one half of a split electrode is used to enable coupling to the radial motion, as indicated by the motion-arrows. The capacitance $C$ is formed by the combined parasitic capacitance of the electrodes.
• Figure 5: Numerical simulation to evaluate the average quantum numbers of the electron's modified cyclotron and axial motion ($\bar{n}_{+, \text{e}}$ and $\bar{n}_{z, \text{e}}$) and the particle-of-interest's modified cyclotron motion ($\bar{n}_{+, \text{p}}$). The simulation uses a sideband coupling rate of $\Omega_\text{sb} = 2\pi \cdot 3\,\text{Hz}$ and detuning fluctuation with $\sigma = 1\,\text{Hz}$. Sideband coupling is initially disabled and switched on at $t=10\,\text{s}$. The dashed line represents an exponential fit to the modified cyclotron trajectory of the particle-of-interest, as used in the further analysis.