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arXiv:2409.18430 · Physical Review A

Energy levels and transition rates of the laser-cooling candidate T h −

Rui Zhang, Yuzhu Lu, Shuai-Ting Yan, Chuangang Ning

Published Feb 6, 2025• 5 citations
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Abstract

The energy levels and transition rates of promising laser-cooling candidate thorium anion ($\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$) are experimentally measured in the current work. Three excited states between the lower and upper states for the bound-bound electric dipole (E1) transition ${\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}^{o}\ensuremath{\leftrightarrow}{\phantom{\rule{4pt}{0ex}}}^{4}{F}_{3/2}^{e}$ of $\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$ are observed: ${\phantom{\rule{4pt}{0ex}}}^{4}{G}_{5/2}^{o}, {\phantom{\rule{4pt}{0ex}}}^{4}{F}_{9/2}^{e}$, and ${\phantom{\rule{4pt}{0ex}}}^{4}{F}_{7/2}^{o}$, and their energy levels are determined to be 1847(13), 3166.8(59), and 3666(12) $\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, respectively. Meanwhile, the lifetime of the upper state ${\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}^{o}$ of the E1 transition is experimentally determined to be 30(2) \textmu{}s, substantially shorter than the previously calculated result, which makes $\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$ the most promising candidate for laser cooling of negative ions. Furthermore, the lifetimes of two other short-lived odd-parity excited states of $\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$ are also measured to be 62(5) and 53(3) \textmu{}s, respectively.

DOI
10.1103/physreva.111.023102

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The energy levels and transition rates of promising laser-cooling candidate thorium anion (Th\ensuremath−\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}Th\ensuremath−) are experimentally measured in the current work. Three excited states between the lower and upper states for the bound-bound electric dipole (E1) transition 2S1/2o\ensuremath↔4F3/2e{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}^{o}\ensuremath{\leftrightarrow}{\phantom{\rule{4pt}{0ex}}}^{4}{F}_{3/2}^{e}2S1/2o​\ensuremath↔4F3/2e​ of Th\ensuremath−\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}Th\ensuremath− are observed: 4G5/2o,4F9/2e{\phantom{\rule{4pt}{0ex}}}^{4}{G}_{5/2}^{o}, {\phantom{\rule{4pt}{0ex}}}^{4}{F}_{9/2}^{e}4G5/2o​,4F9/2e​, and 4F7/2o{\phantom{\rule{4pt}{0ex}}}^{4}{F}_{7/2}^{o}4F7/2o​, and their energy levels are determined to be 1847(13), 3166.8(59), and 3666(12) cm\ensuremath−1\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}cm\ensuremath−1, respectively. Meanwhile, the lifetime of the upper state 2S1/2o{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}^{o}2S1/2o​ of the E1 transition is experimentally determined to be 30(2) \textmu{}s, substantially shorter than the previously calculated result, which makes Th\ensuremath−\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}Th\ensuremath− the most promising candidate for laser cooling of negative ions. Furthermore, the lifetimes of two other short-lived odd-parity excited states of Th\ensuremath−\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}Th\ensuremath− are also measured to be 62(5) and 53(3) \textmu{}s, respectively.
High-resolution photoelectron energy spectra of osmium anions are obtained using the slow-electron velocity-map imaging method. The energy levels of excited states 4 F 7/2, 4 F 5/2 and 4 F 3/2 of Os− are determined to be 148.730(13), 155.69(15), and 176.76(13) THz [or 4961.09(41), 5193.4(49), and 5896.1(42) cm−1], respectively. The lifetime of the opposite-parity excited state 6 D 9 / 2 o is determined to be 201(10) μs using a cold ion trap, about 15 times shorter than the previous result 3(1) ms. Our high-level multi-configuration Dirac–Hartree–Fock calculations yield a theoretical lifetime 527 μs. Our work shows that the laser cooling rate of Os− is as fast as that of Th−. The advantages of Os− are its near-IR range cooling transition and simple electronic structure, which make Os− a promising candidate for laser cooling of negative ions. We propose a general approach to produce cold atoms and molecules based on the sympathetic cooling of negative ions in combination with a threshold photodetachment.
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Despite the fact that the laser-cooling method is a well-established technique to obtain ultracold neutral atoms and atomic cations, it has rarely if ever been applied to atomic anions due to the lack of suitable electric-dipole transitions. Efforts of more than a decade have until recently only resulted in ${\mathrm{La}}^{\ensuremath{-}}$ as a promising anion candidate for laser cooling, but our previous work [Tang et al., Phys. Rev. Lett. 123, 203002 (2019)] showed that ${\mathrm{Th}}^{\ensuremath{-}}$ is also a potential candidate. Here we report on a combination of experimental and theoretical studies to determine the frequencies and rates, as well as branching ratios, for the relevant transitions in ${\mathrm{Th}}^{\ensuremath{-}}$. The resonant frequency of the laser-cooling transition is determined to be $\ensuremath{\nu}=123.455(30)$ THz $[\ensuremath{\lambda}=2428.4(6)\phantom{\rule{0.16em}{0ex}}\mathrm{nm}]$. The transition rate is calculated as $A=1.17\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Since the branching fraction to dark states is negligible, $1.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, this represents an ideal closed cycle in ${\mathrm{Th}}^{\ensuremath{-}}$ for laser cooling. Furthermore, the zero nuclear spin of 232Th^{232}\mathrm{Th}232Th makes the cooling process possible in a Penning trap, which can be used to confine both antiprotons and ${\mathrm{Th}}^{\ensuremath{-}}$ ions. The presented ion dynamics simulations show that the laser-cooled ${\mathrm{Th}}^{\ensuremath{-}}$ anions can effectively cool antiprotons to a temperature around 10 mK.
Laser cooling is a well-established technique for the creation of ensembles of ultracold neutral atoms or positive ions. This ability has opened many exciting new research fields over the past 40 years. However, no negatively charged ions have been directly laser cooled because a cycling transition is very rare in atomic anions. Efforts of more than a decade currently have La^{-} as the most promising candidate. We report on experimental and theoretical studies supporting Th^{-} as a new promising candidate for laser cooling. The measured and calculated electron affinities of Th are, respectively, 4901.35(48) cm^{-1} and 4832 cm^{-1}, or 0.607 690(60) and 0.599 eV, almost a factor of 2 larger than the previous theoretical value of 0.368 eV. The ground state of Th^{-} is determined to be 6d^{3}7s^{2} ^{4}F_{3/2}^{e} rather than 6d^{2}7s^{2}7p ^{4}G_{5/2}^{o}. The consequence of this is that there are several strong electric dipole transitions between the bound levels arising from configurations 6d^{3}7s^{2} and 6d^{2}7s^{2}7p in Th^{-}. The potential laser-cooling transition is ^{2}S_{1/2}^{o}↔^{4}F_{3/2}^{e} with a wavelength of 2.6 μm. The zero nuclear spin and hence lack of hyperfine structure in Th^{-} reduces the potential complications in laser cooling as encountered in La^{-}, making Th^{-} a new and exciting candidate for laser cooling.
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Despite the tremendous advances in laser cooling of neutral atoms and positive ions, no negatively charged ion has been directly laser cooled. The negative ion of lanthanum, La(-), has been proposed as the best candidate for laser cooling of any atomic anion [ and , Phys. Rev. A 81, 032503 (2010)]. Tunable infrared laser photodetachment spectroscopy is used to measure the bound-state structure of La(-), revealing a spectrum of unprecedented richness with multiple bound-bound electric dipole transitions. The potential laser-cooling transition ((3)F(2)(e)→(3)D(1)(o)) is identified and its excitation energy is measured. The results confirm that La^{-} is a very promising negative ion for laser-cooling applications.