Hyperfine spectroscopy of optical-cycling transitions in singly ionized thulium

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.

💡 Research Summary

This paper presents a comprehensive spectroscopic study of singly ionized thulium (¹⁶⁹Tm⁺) with the explicit goal of establishing it as a versatile platform for advanced quantum technologies. The authors first map out a complete optical‑cycling roadmap by performing high‑resolution spectroscopy on three key electric‑dipole transitions: the primary 313 nm transition (⁴f¹³6s ³F₄ ↔ ⁴f¹³6p ³D₃) and the complementary pair at 448 nm and 453 nm (⁴f¹²5d6s J = 4 ↔ ⁴f¹³6s ³F₄ and ³F₃, respectively). Using three complementary experimental configurations—a hollow‑cathode lamp (HCL) for rapid absorption scans, a compact laser‑ablation fluorescence cell for ion‑source optimization, and a linear quadrupole ion trap for precision fluorescence spectroscopy—the authors locate the transitions, measure their wavelengths, and resolve the hyperfine structure (HFS) of all involved levels.

Because ¹⁶⁹Tm has nuclear spin I = ½, each electronic level splits into only two hyperfine components (F = J ± ½). The authors exploit this simplicity to extract magnetic‑dipole hyperfine constants (A) for the ground state, several low‑lying excited states, and five higher‑lying states that are only reachable via the cycling transitions. The hyperfine splittings are fitted with a sum‑of‑Gaussians model, yielding A‑values listed in Table I (e.g., A = ‑1.03913 GHz for the ground ³F₄, A = ‑0.930 GHz for the 22 308.82 cm⁻¹ J = 4 level, and A = ‑0.71871 GHz for the 12 457.29 cm⁻¹ J = 5 metastable level). These values agree within 1σ with previously reported collinear laser spectroscopy data where available, and provide the first experimental determinations for several higher‑lying states.

The paper then details the practical implementation of laser cooling cycles. The 450 nm scheme uses two laser tones at 448 nm and 453 nm, each crossing the ion cloud twice in an X‑shaped geometry, thereby addressing both hyperfine components of the ground‑state manifold. Because the J = 4 excited state (22 308.82 cm⁻¹) can decay via a weak 749 nm electric‑dipole channel to an odd‑parity level, its natural lifetime is estimated at ~90 ms, necessitating repumping lasers in the near‑infrared (≈ 1056 nm and 1307 nm) to close the cycle. The 313 nm scheme, by contrast, is essentially closed: two counter‑propagating beams are frequency‑shifted by +722 MHz using acousto‑optic modulators so that both F = J ± ½ components are simultaneously driven, eliminating the need for repumping.

A major contribution of the work is the characterization of a metastable state (12 457.29 cm⁻¹, J = 5) as a candidate qubit memory. By introducing a low‑pressure helium buffer gas (10⁻⁵–10⁻³ mbar) to suppress population trapping, the authors measure its radiative lifetime to be on the order of several hundred milliseconds. Zeeman‑resolved microwave spectroscopy on the hyperfine transition (≈ 1.6 GHz) is performed with kilohertz precision, demonstrating that the state can be coherently manipulated and read out with high fidelity.

The authors discuss the feasibility of the required laser technology. All wavelengths involved are accessible with current commercial laser sources: frequency‑quadrupled diode lasers for 313 nm, external‑cavity diode lasers or Ti:sapphire lasers for 448/453 nm, and an optical parametric oscillator for the near‑infrared repumpers. The modest number of laser tones (two for each cycle) is a direct benefit of the I = ½ hyperfine structure, simplifying experimental overhead.

In summary, the paper delivers (i) a complete spectroscopic map of the relevant ¹⁶⁹Tm⁺ transitions, (ii) precise hyperfine constants for ground and excited states, (iii) viable laser‑cooling schemes at both 313 nm and 450 nm, and (iv) a thorough assessment of a metastable level as a robust qubit. These results lay the groundwork for future experiments employing thulium ions in quantum information processing, quantum simulation, and precision metrology, potentially enabling architectures that separate processing and memory functions across distinct internal states.