Doppler and sympathetic cooling for the investigation of short-lived radioactive ions

At radioactive ion beam (RIB) facilities, ions of short-lived radionuclides are cooled and bunched in buffer-gas-filled Paul traps to improve the ion-beam quality for subsequent experiments. To deliver even colder ions, beneficial to RIB experiments' sensitivity or accuracy, we employ Doppler and sympathetic cooling in a Paul trap cooler-buncher. The improved emittance of ${\mathrm{Mg}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{O}}_2^{+}$ ion beams is demonstrated by a reduced time-of-flight spread of the extracted ion bunches with respect to room-temperature buffer-gas cooling. Cooling externally-produced hot ions with energies of at least 7 eV down to a few Kelvin is achieved in a timescale of $O$(100 ms) by combining a low-pressure helium background gas with laser cooling. This is sufficiently short to cool short-lived radioactive ions. As an example of this technique's use for RIB research, the mass-resolving power in a multireflection time-of-flight mass spectrometer is shown to increase by up to a factor of 4.6 with respect to buffer-gas cooling. Simulations show good agreement with the experimental results and guide further improvements and applications. These results open a path to a significant emittance improvement and, thus, unprecedented ion-beam qualities at RIB facilities, achievable with standard equipment readily available. The same method provides opportunities for future high-precision experiments with radioactive cold trapped ions.

Figure 1

(a) Layout of the experimental setup showing the main components with an enlarged, detailed view of the Paul trap cooler buncher. There, ${\mathrm{Mg}}^{+}$ ions are Doppler cooled by 280-nm laser light for direct or sympathetic laser cooling of other ions species. See text for details. (b) dc potential along the Paul-trap axis during trapping (solid blue) and extraction (dashed blue). The position of the individual dc trap electrodes is indicated in gray. The axial well depth $U_W$ and ions' excess energy $U_i$ are shown as vertical arrows.

Figure 2

(a) Time-of-flight spectrum of ${}^{24,25,26}\mathrm{Mg}^{+}$ ions from ion optical simulations including 300 K buffer-gas cooling (orange) and experimental data (blue). The simulation is normalized in intensity to the experimental data. (b) Simulated FWHM values of time-of-flight spectra as a function of buffer-gas temperature fitted to a square-root function (dashed orange line). (c) shows a zoom of (b) at lower temperatures. (d) shows a zoom of (a), with additional arrows indicating the FWHM and corresponding data point.

Figure 3

Time-of-flight spectrum of ${}^{24,25,26}\mathrm{Mg}^{+}$ ions after extraction from the Paul trap cooler-buncher as measured on the retractable ion detector in front of the MR-ToF device using Doppler cooling (blue), buffer-gas cooling (green), and residual gas cooling (orange).

Figure 4

(a) Photon-scattering rates calculated as a function of laser-frequency detuning from the D2 transition in ${}^{24}\mathrm{Mg}^{+}$ ions. ToF spectra for laser-cooling systematics at residual gas pressures as a function of (b) laser detuning at 3 mW and $500\mathrm{ms}$ cooling, (c) laser power at $200\mathrm{ms}$ cooling and $-200\mathrm{MHz}$ detuning, (d) cooling time at 3 mW and $-200\mathrm{MHz}$ detuning, as measured on the first, retractable ion detector.

Figure 5

FWHM of the time-of-flight spectra for ${}^{24,25,26}\mathrm{Mg}^{+}$ ions as a function of laser-frequency detuning with respect to the D2 transition in ${}^{24}\mathrm{Mg}^{+}$ ions. Resonance frequencies for ${}^{24,25,26}\mathrm{Mg}^{+}$ are represented as colored bands.

Figure 6

Sympathetic cooling of molecular oxygen, ${}^{16}\mathrm{O}_2^{+}$, and atomic potassium, ${}^{39}\mathrm{K}^{+}$ ions. Sympathetic cooling of oxygen at $800\mathrm{ms}$ loading time and $600\mathrm{ms}$ cooling time with 20 mW of laser power. Same settings for potassium. See text for details.

Figure 7

Simulated energy for a single ${}^{24}\mathrm{Mg}^{+}$ ion (orange) at each time when a photon-ion interaction takes place. The photon scattering rate per $50\mu \mathrm{s}$ (blue) is indicated on the right $y$ axis. The simulation is performed for an ion with 0.03 eV initial energy being cooled by a 200 MHz red-detuned cooling laser with 25 mW power and 2 mm diameter.

Figure 8

Calculated energy for a single ${}^{24}\mathrm{Mg}^{+}$ ion (orange) and instantaneous photon scattering rate (blue) as a function of time for an ion with 10 eV initial energy being cooled by a 300 K helium buffer gas at ${10}^{-5}\mathrm{mbar}$ and a 200 MHz red-detuned cooling laser with 25 mW power and 2 mm diameter.

Figure 9

Optimal laser-frequency detuning (blue) and corresponding ion energy (orange) as a function of time needed for cooling down a 10 eV ${}^{24}{\mathrm{Mg}}^{+}$ ion in absence of a buffer gas as obtained from the 1D numerical model.

Figure 10

(a)–(d) Kinetic energy and (e)–(h) scattered photon rate for the 1D numerical model (orange) and ion-optical simulations (blue) as a function of time for different laser detuning frequencies.

Figure 11

Time-of-flight spectrum of Doppler-cooled ${}^{24}\mathrm{Mg}^{+}$ ions. The experimental data are compared to ion-optical simulations. Both are obtained for a laser frequency detuning of $-600\mathrm{MHz}$ with respect to the D2 transition, a laser power of 25 mW, and a cooling time of $150\mathrm{ms}$. No residual gas is considered in the simulation. The only free simulation parameters are the ToF offset and the ion intensity, which were matched to experiment for better comparison.

Figure 12

Width of the experimental ToF signal of ${}^{24}\mathrm{Mg}^{+}$ ions as a function of the cooling-laser frequency at a residual buffer-gas pressure of $1\times {10}^{-8}\mathrm{mbar}$. Experimental data are shown as blue squares. Results from (a) the numerical model described in Sec. 4b and (b) ion-optical simulations described in Sec. 4a for different buffer-gas pressures. To obtain (a), the ion temperature obtained from the 1D Model is translated into a ToF width by employing the found relationship of Fig. 2. For reference, the experimental ToF width without injecting the laser beam into the Paul trap is shown as a grey band.

Figure 13

Mass resolving power for the ${}^{24}\mathrm{Mg}^{+}$ ion signal as a function of storage time in the MR-ToF device for three different cooling mechanisms. Solid lines are fits of Eq.(6) to the data. Dashed lines denote the saturation resolving power $R_{\infty }$.

Figure 14

Simulation (dashed) and experimental (full) ToF and energy-spread results for varying Paul-trap extraction field strengths of Doppler and buffer-gas cooled ions. Both observables are evaluated at the ion-detector position without trapping in the MR-ToF device.

Figure 15

(a) The spatial FWHM of the detected beam image after extraction from the Penning trap, as a function of beam temperature. In comparison to room temperature beam preparation, sub-Kelvin beam temperatures can yield an improvement in the precision of a PI-ICR measurement of well over an order of magnitude. (b)–(d) Example of simulated ion beamspots on the detector for three different ion cloud temperatures with their respective beam-spot sizes.

Figure 16

Width of the experimental ToF signal as a function of the cooling-laser frequency, spanning laser cooling and heating of ${}^{24}\mathrm{Mg}^{+}$ and ${}^{26}\mathrm{Mg}^{+}$ ions. The $x$-axis offset is taken as the literature value for the absolute frequency of the ${\text{D}}_2(3s{}^2\mathrm{S}_{1/2}\to 3p{}^2\mathrm{P}_{3/2})$ transition in ${}^{24}\mathrm{Mg}^{+}$ ions, ${\nu }_{24}=1072082934.33\left(16\right)$ MHz [96]. Two inserts on top show a zoom in near the regions of interest of the data shown in the bottom part.

Figure 17

Sketch of a future proposed cooler-buncher design for delivering low-emittance ion bunches and performing laser spectroscopy.