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Journal of Quantitative Spectroscopy and Radiative Transfer

Exploring the feasibility of laser cooling of atomic cobalt

Szymon Mieloch, Marcin Klempka, Jarosław Ruczkowski, Andrzej Krzykowski, Bogusław Furmann, Magdalena Elantkowska, Przemysław Głowacki, Jerzy Sobkowski, Gustaw Szawioła, Danuta Stefańska

Published Jul 30, 2026• 0 citations
Publisher

Abstract

Within this work a preliminary feasibility study of the laser cooling possibilities for atomic cobalt was performed, motivated by its potential as a platform for quantum-degenerate dipolar matter. Because of the relatively high electronic shells' magnetic moment of the cobalt atom, the approach of cooling and magneto-optical trapping, developed for highly magnetic lanthanide elements, was considered also for this element. Optical leaks from the proposed upper levels were identified and semi-empirical calculations of the transition probabilities for all the relevant transitions were carried out; in all the cases decays to a particular metastable state proved relatively strong - thus $\Lambda$-type cooling systems (with one repumper) were further discussed. In order to improve the precision of determination of the hyperfine structure for the proposed upper levels, selected spectral lines directly involving these levels were investigated with the method of laser induced fluorescence in a hollow cathode discharge lamp and evaluated. Additionally, also some spectral lines from Fourier transform spectra available online were analyzed. These experimental data enabled a more accurate determination of the hyperfine structure constants $A$ for 4 odd-parity levels with $J=11/2$; for 3 of those levels the accuracy for the constants $B$ was also improved, and for one level the constant $B$ was evaluated for the first time. The studies performed in this work allowed to indicate possible candidate cooling schemes, and discuss their basic merits and drawbacks.

DOI
10.1016/j.jqsrt.2026.110078

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Within this work a preliminary feasibility study of the laser cooling possibilities for atomic cobalt was performed, motivated by its potential as a platform for quantum-degenerate dipolar matter. Because of the relatively high electronic shells' magnetic moment of the cobalt atom, the approach of cooling and magneto-optical trapping, developed for highly magnetic lanthanide elements, was considered also for this element. Optical leaks from the proposed upper levels were identified and semi-empirical calculations of the transition probabilities for all the relevant transitions were carried out; in all the cases decays to a particular metastable state proved relatively strong - thus Λ\LambdaΛ-type cooling systems (with one repumper) were further discussed. In order to improve the precision of determination of the hyperfine structure for the proposed upper levels, selected spectral lines directly involving these levels were investigated with the method of laser induced fluorescence in a hollow cathode discharge lamp and evaluated. Additionally, also some spectral lines from Fourier transform spectra available online were analyzed. These experimental data enabled a more accurate determination of the hyperfine structure constants AAA for 4 odd-parity levels with J=11/2J=11/2J=11/2; for 3 of those levels the accuracy for the constants BBB was also improved, and for one level the constant BBB was evaluated for the first time. The studies performed in this work allowed to indicate possible candidate cooling schemes, and discuss their basic merits and drawbacks.
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We have studied possible candidates for laser cooling transitions in 169 Tm in the spectral region 410 –420 nm. By means of saturation absorption spectroscopy we have measured the hyperfine structure and rates of two nearly closed cycling transitions from the ground state 4f 13 6s 2 ( 2 F0)(Jg = 7/2) to upper states 4f 12 ( 3 H5)5d3/26s 2 (Je = 9/2) at 410.6 nm and 4f 12 ( 3 F4)5d5/26s 2 (Je = 9/2) at 420.4 nm and evaluated the life times of the excited levels as 16.1(8) ns and 40(4) ns respectively. Decay rates from these levels to neighboring opposite-parity levels are evaluated by means of Hartree-Fock calculations. We conclude, that the strong transition at 410.6 nm has an optical leak rate of less then 2·10 −5 and can be used for efficient laser cooling of 169 Tm from a thermal atomic beam. In addition we give a calculated value of 7(2) s −1 for the rate of magnetic-dipole transition at 1.14 µm between the fine structure levels (Jg = 7/2) ↔ (J ′ g = 5/2) of the ground state. Due to efficient shielding by the closed 6s 2 shell, this transition is insensitive to collisions which makes it a promising candidate for applications in atomic clocks. PACS numbers: I.
We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare earth element Holmium. Atoms are loaded from an atomic beam source and captured in six-beam σ+−σ−σ_+ - σ_-σ+​−σ−​ molasses using a strong J=15/2↔J=17/2J=15/2 \leftrightarrow J=17/2J=15/2↔J=17/2 cycling transition at λ=410.5nmλ=410.5 \rm nmλ=410.5nm. Due to the small difference in hyperfine splittings and Landé ggg-factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio ∼10−5\sim 10^{-5}∼10−5 which is adequate for state resolved measurements on hyperfine encoded qubits.
The efficiency of laser cooling relies on the existence of an almost closed optical-transition cycle in the energy spectrum of the considered species. In this respect, rare-earth elements exhibit many transitions which are likely to induce noticeable leaks from the cooling cycle. In this work, to determine whether laser cooling of singly ionized erbium Er+{\mathrm{Er}}^{+}Er+ is feasible, we have performed accurate electronic-structure calculations of energies and spontaneous-emission Einstein coefficients of Er+{\mathrm{Er}}^{+}Er+, using a combination of ab initio and least-squares-fitting techniques. We identify five weak closed transitions suitable for laser cooling, the broadest of which is in the kilohertz range. For the strongest transitions, by simulating the cascade dynamics of spontaneous emission, we show that repumping is necessary, and we discuss possible repumping schemes. We expect our detailed study on Er+{\mathrm{Er}}^{+}Er+ to give good insight into the laser cooling of neighboring ions such as Dy+{\mathrm{Dy}}^{+}Dy+.
We have studied possible candidates for laser cool- ing transitions in 169 Tm in the spectral region of 410-420 nm. By means of saturation absorption spectroscopy, we have meas- ured the hyperfine structure and rates of two nearly closed cy- cling transitions from the ground state 4 f 13 6s 2 ( 2 F0)(Jg = 7/2) to upper states 4 f 12 ( 3 H5)5d3/26s 2 (Je = 9/2) at 410. 6n m and 4 f 12 ( 3 F4)5d5/26s 2 (Je = 9/2) at 420.4 nm and evaluated the life times of the excited levels as 15.9(8) ns and 48 (6) ns, respectively. Decay rates from these levels to neighboring opposite-parity levels are evaluated by means of Hartree-Fock calculations. We conclude that the strong transition at 410. 6n m has an optical leak rate of less then 2 × 10 −5 and can be used for efficient laser cooling of 169 Tm from a thermal atomic beam. The hyperfine structure of two other even-parity levels, which can be excited from the ground state at 409. 5n m and 418.9 nm, is also measured by the same technique. In addition, we give a calculated value of 7(2) s −1 for the rate of magnetic- dipole transition at 1.14 µm between the fine structure levels (Jg = 7/2) ↔ (J � = 5/2) of the ground state which can be con- sidered as a candidate for applications in atomic clocks.
Laser cooling and trapping of heavy alkaline-earth element barium have been demonstrated for the first time ever. For any possible cycling transition in barium that could provide strong cooling forces, the excited state has a very large branching probability to metastable states. Additional lasers are thus needed to bring the atoms back in to the cooling cycle. In this work barium atoms were efficiently collected in a magneto-optical trap (MOT) by large optical forces from the strong 6s2 1S0 – 6s6p 1P1 transition. Trapping of barium has been achieved using up to seven lasers simultaneously. The properties of the barium MOT were characterized. The efficiency of capturing an atom from a thermal atomic beam into the MOT is 0.4(1) %. The developed scheme is very efficient for collecting atoms. Loss rate mechanisms from the trap were studied by observing the decay of the trap population. Typical lifetimes of the MOT cloud are on the order of one second and are limited mainly due to insufficient repumping of metastable states. The range of velocities from which barium atoms can be captured into the MOT is about 30 m/s. Different laser transitions were employed for repumping barium atoms from the 6s5d 3D1 and the 6s5d 3D2 states. They lead to similar trap populations and lifetimes. The temperature of the cold atomic barium cloud was determined to about 5 mK. Atomic properties of the 5d2 3F2 state were studied with trapped atoms, in particular it's lifetime was determined as 160(10) s. This work has shown a possible scheme to trap atoms with a leaky cooling cycle. Since atoms with such properties are the majority of the elements in the periodic table, the number of optically trapable elements can be significantly enlarged. Of particular high interest is radium, which is chemical homologue to barium. The interest in radium stems from it's high sensitivity to possible nuclear and electron permanent electric dipole moments (EDM's). An EDM violates parity as well as time reversal and is therefore of fundamental importance. Searches for such EDM's are among the main research goals of the recently commissioned TRImP facility at KVI.