Decay-Resolved Charge Changes from Radioactive Decays in Levitated Microparticles

Abstract

We measure event-by-event discrete changes in the net electric charge of an optically levitated silica microsphere arising from individual radioactive decays within the sphere, in coincidence with energy depositions in a nearby scintillation detector. The net charge of the levitated sphere is continuously monitored by measuring its driven response to an oscillating electric field, allowing individual charge-change events to be resolved on millisecond timescales with precision below an elementary charge. Simultaneously, $α$ and $β$ particles emitted during decays of implanted $^{212}$Pb and its daughters are detected using a scintillator read out with an array of silicon photomultipliers. By correlating reconstructed charge-change times with the scintillator response, we can directly attribute abrupt changes in the sphere's net charge to individual nuclear decays, and identify differences in the distribution of charges ejected for $α$ and $β$ decays. These results establish a new approach for studying low energy charged particles emitted by radioactive decays at the single-decay level, and identify showers of radiogenically produced low-energy electrons emitted by $α$-decaying radon daughters implanted near solid surfaces.

Figures (7)

• Figure 1: Overview of the experimental setup and radioactive decay chain. (a) Schematic view of the apparatus, showing the focused laser beam (red, not to scale), surrounding electrode structure, and the scintillator detector. A $2\,\mathrm{cm}\times2\,\mathrm{cm}$ scintillator, shielded with aluminized Mylar to suppress scattered light from the levitated particle, is positioned $\approx1\,\mathrm{cm}$ from the trapping region. The slide carrying radioactive spheres (whose location is denoted by the trefoil symbol) can be positioned above the beam to load spheres into the trap. (b) Schematic of a silica sphere carrying radioactive isotopes trapped by a focused laser beam with an electric field applied to monitor the net electric charge. (c) Exploded view of the particle detector showing the entrance window, scintillator, and SiPM array. (d) $^{220}$Rn decay chain relevant to this work. Half-lives are indicated within each isotope box. Blue arrows denote $\alpha$ decays, with the dominant $\alpha$ energies and branching ratios indicated, while red arrows indicate relevant $\beta$ decays and their branching ratios.
• Figure 2: Charge detection for a radioactive sphere. Upper left: Measured net charge of a silica sphere implanted with $^{212}$Pb as a function of time. Net charge in units of $-e$ indicates the excess of electrons over protons in the sphere. The black curve shows the measured charge averaged in $\sim$3 s intervals, while the orange curve shows the best-fit charge trajectory obtained after reconstructing the times of individual charge-change events. Light red vertical lines indicate periods during which electrons were added to the sphere using the filament, while gray shaded bands indicate ultraviolet illumination used to remove excess charge. Lower left: Residuals of the fit to the measured charge, demonstrating precise determination of the discrete charge state. Top right: A zoomed in view of the net charge of the silica sphere from 6.3 h to 8 h demonstrating the fit to several charge-change events. Bottom right: Histogram of residual with a Gaussian fit (pink).
• Figure 3: Distribution of reconstructed charge changes for all spheres (open markers). A fit (red line) to the sum of a Gaussian component (purple shaded) and a log-normal component (orange shaded) is also shown. The inset shows the same distribution on a log-scale. The bottom pane shows the residual between the data and fit, normalized by the Poisson counting error, $\sigma$.
• Figure 4: Calibration spectra measured with the scintillator detector. The top panel shows the spectrum acquired while a $^{212}$Pb source was positioned within $100\,\mu\mathrm{m}$ of the sphere trapping location in vacuum. The measured spectrum is shown by the open black markers, with the overall fit to the spectrum shown in blue. The fit model includes $\alpha$ peaks from $^{212}$Bi (pink) and $^{212}$Po (orange), as well as a slowly falling continuum above 500 keV from multiple $\beta$ decays, which is approximately modeled by an exponential dependence (red, dotted). The bottom panel shows the spectrum acquired in a $\sim$1 h exposure with a sphere trapped in high vacuum, dominated by background events from the loading slide, which had an initial measured activity of $\sim4\times10^{3}\,\mathrm{Bq}$ for this dataset. The red line shows the interpolation of this spectrum used for modeling this background in the coincidence analysis.
• Figure 5: Comparison of charge–change event reconstruction and scintillator detector events. Two representative events with a non-coincidence (a) and a reconstructed coincidence between the charge-change and scintillator (b) are shown. The upper panels show the scintillator reconstructed energy (pink) on the right axis, and the normalized optimal-filter response to the sphere charge change (blue) on the left axis, indicated by a Gaussian at the reconstructed charge change time with the temporal resolution of the filter. The bottom panels show the net sphere charge versus time extracted at the drive frequency averaged over 25.6 ms (red). Insets show a magnified $\pm0.12~\mathrm{s}$ view around the reconstructed charge-change time.