Hyperfine spectroscopy of optical-cycling transitions in singly ionized thulium

TL;DR

This work provides a comprehensive spectroscopic foundation for using 169Tm+ as a quantum platform by mapping hyperfine-structure constants for key excited levels and establishing viable optical-cycling transitions at 313 nm and 448/453 nm, complemented by repumping pathways in the near-IR. It also characterizes a long-lived metastable state (the Gollum state at 12,457.29 cm^-1) as a potential qubit carrier, including its Zeeman-resolved microwave spectrum, enabling microwave-based gates. The authors propose multiple cooling schemes and discuss sympathetic cooling with Ba+, outlining practical routes to implement laser cooling and SPAM for future metrology and quantum information tasks. Overall, the results enable a closed, MHz-precision HFS map and provide a roadmap toward direct Doppler cooling and robust qubit operations in a non-alkali-like rare-earth ion system. The work paves the way for compact, diode-based laser-cooling implementations and advanced quantum architectures leveraging high-J manifolds and I=1/2 nuclear spin.

Abstract

We present a spectroscopic investigation of $^{169}\mathrm{Tm}^+$ that provides two key foundations for its use as a platform for advanced quantum applications. First, we establish the complete spectroscopic road map for optical cycling (including laser cooling) by performing high-resolution spectroscopy on $^{169}\mathrm{Tm}^+$ ions in an ion trap. We characterize the primary $313\,\mathrm{nm}$ and complementary $448/453\,\mathrm{nm}$ cycling transitions, identify the essential near-infrared repumping frequencies, and determine the magnetic-dipole hyperfine $A$ constants for all relevant levels. Second, we report detailed characterization of a metastable state as a candidate for hosting a robust qubit, performing lifetime measurements and Zeeman-resolved microwave hyperfine spectroscopy with $\mathrm{kHz}$ precision.

Figures (5)

• Figure 1: Image of an illuminated cloud of $^{}\text{Tm}^+$ ions, taken with an EMCCD camera. Both the $448$- and $453$-nm lasers cross the trap center twice, forming an X shape. The image was post-processed with a median and a Gaussian filter to reduce image noise and improve contrast.
• Figure 2: Measured $E$1 transitions and hyperfine splittings in $^{169}\text{Tm}^+$. Levels with the same $J$ value are aligned vertically, with $F$ values labeling the hyperfine sublevels. Level energies are indicated in $\text{cm}^{-1}$ and the measured hyperfine splittings are given in GHz. The level spacings are not to scale, and levels irrelevant to this work are omitted. The vacuum wavelength and corresponding frequency are shown next to one of the two strongest hyperfine components ($\Delta F = \Delta J$) of each transition. Gray levels and gray dash-dotted lines indicate levels and expected transitions, respectively, that were searched for but not observed in this work.
• Figure 3: Hyperfine-structure (HFS) spectra of $^{169}\text{Tm}^+$: (a,b) recorded using absorption spectroscopy with a hollow-cathode lamp, and (c--i) using fluorescence spectroscopy with an ionic cloud in a linear quadrupole trap. (c--f) A fresh ion cloud was produced for each data point; the laser light was generated using external-cavity diode lasers (ECDLs) and the laser frequencies were set to fixed values for each point. (g--i) Each spectrum was recorded with a single cloud of ions using the continuous-scan function of the optical parametric oscillator (OPO) laser.
• Figure 4: (a) Solution of the rate equations for the 450-nm cycle. State labels are given in cm$^{-1}$. Dashed lines are without repumping lasers, solid lines include $749$, $846$ and $855$-nm repumping lasers. Unknown Einstein $A_{21}$-coefficients were taken from the DREAM database Quinet.1999Quinet.DREAMPalmeri.2025. (b) Experimental scattering rate without the infrared repumping lasers at a He pressure of $4.7\cdot 10^{-6}$ Torr. Blocking the $450$-nm lasers for $2$ minutes pauses the optical population transfer. (c) Increase of the steady-state scattering rate with He-buffer-gas pressure.
• Figure 5: The decay curve, pump-and-probe experiment, microwave spectrum and magnetic substructure of the $12457.29$-cm$^{-1}$ [$^3\mathrm{H}_6$] state. (a) Population in this state as a function of time. An exponential function was fitted to the data, yielding a decay constant of $5.2(3)$ min into the $^3\mathrm{F}_4$ ground state through $M2$ or $E3$ decay. (b) Example of a pump-and-probe measurement used to determine the lifetime of the $12457.29$-cm$^{-1}$ state. (c) Zeeman-resolved microwave spectrum of the transitions between the two hyperfine states of the $12457.29$-cm$^{-1}$ level, measured at a magnetic field of $1.34$ G. A sum-of-Gaussians model was fitted to the data, with peak widths proportional to the peak's Zeeman shifts, to account for the variation of the magnetic field across the ion cloud. (d) Pairwise degenerate transitions, which contribute to the twelve inner peaks in the spectrum, are shown as solid lines, with the degenerate pair having the same color. Non-degenerate transitions, which contribute to the twelve outer peaks, are shown as dashed gray lines.