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Physical Review A

Candidates for laser cooling of atomic anions: La − versus Os −

Lin Pan, Donald R. Beck

Published Jul 6, 2010• 32 citations
Publisher

Abstract

This brief report is a follow-up to the recent proposal to use La${}^{\ensuremath{-}}$ as another candidate, in addition to Os${}^{\ensuremath{-}}$, in laser cooling of anions, which can then be used to cool antiprotons sympathetically. Using the relativistic configuration interaction formalism, we calculate the photodetachment cross sections of the upper laser cooling state La${}^{\ensuremath{-}}$ $5d$$6{s}^{2}$$6p {}^{3}{D}_{1}$ and Os${}^{\ensuremath{-}}$ $5{d}^{6}$$6{s}^{2}$$6p {}^{6}{D}_{9/2}$. Our results show that La${}^{\ensuremath{-}}$ has a very similar two-photon detachment loss as Os${}^{\ensuremath{-}}$, retaining it as another promising candidate for cooling antiprotons sympathetically.

DOI
10.1103/physreva.82.014501

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Physical Review A•Jun 1, 2016•10 citations
This brief report is a follow-up to the recent proposal to use La\ensuremath−{}^{\ensuremath{-}}\ensuremath− as another candidate, in addition to Os\ensuremath−{}^{\ensuremath{-}}\ensuremath−, in laser cooling of anions, which can then be used to cool antiprotons sympathetically. Using the relativistic configuration interaction formalism, we calculate the photodetachment cross sections of the upper laser cooling state La\ensuremath−{}^{\ensuremath{-}}\ensuremath− 5d$$6{s}^{2}$$6p {}^{3}{D}_{1} and Os\ensuremath−{}^{\ensuremath{-}}\ensuremath− 5{d}^{6}$$6{s}^{2}$$6p {}^{6}{D}_{9/2}. Our results show that La\ensuremath−{}^{\ensuremath{-}}\ensuremath− has a very similar two-photon detachment loss as Os\ensuremath−{}^{\ensuremath{-}}\ensuremath−, retaining it as another promising candidate for cooling antiprotons sympathetically.
Relativistic configuration-interaction calculations have been performed for all possible E1E1E1, M1M1M1, and E2E2E2 transitions between bound anion states of ${\mathrm{La}}^{\ensuremath{-}}$ and ${\mathrm{Os}}^{\ensuremath{-}}$. We pay particular attention to E1E1E1 transitions in each case that may be of use in laser cooling of these anions. Although the ${\mathrm{La}}^{\ensuremath{-}}$ transition energy is approximately one-third of the ${\mathrm{Os}}^{\ensuremath{-}}$ transition, our results indicate that the Einstein AAA coefficient is nearly two orders of magnitude larger, which would lead to more efficient laser cooling. We have also explored long-lived opposite-parity excited states in ${\mathrm{Lu}}^{\ensuremath{-}}$ and ${\mathrm{Lr}}^{\ensuremath{-}}$ which are restricted to M2M2M2 decay by selection rules. Finally, in ${\mathrm{Pr}}^{\ensuremath{-}}$, we find sufficient mixing between a weakly bound excited 4f25d26s24{f}^{2}5{d}^{2}6{s}^{2}4f25d26s2 state with a nearby 4f36s26p4{f}^{3}6{s}^{2}6p4f36s26p resonance to result in a lifetime similar to that of the other excited anion states, despite the fact that the dominant configurations of these M1M1M1 and E2E2E2 transitions differ by two electrons.
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.
We propose to extend laser-cooling techniques, so far only achieved for neutral molecules, to molecular anions. A detailed computational study is performed for molecules stored in Penning traps using GPU based Monte Carlo simulations. Two cooling schemes—Doppler laser cooling and photodetachment cooling—are investigated. The sympathetic cooling of antiprotons is studied for the Doppler cooling scheme, where it is shown that cooling of antiprotons to subKelvin temperatures could becomes feasible, with impacts on the field of antimatter physics. The presented cooling schemes also have applications for the generation of cold, negatively charged particle sources and for the sympathetic cooling of other molecular anions.
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.
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.
This study reinterprets an earlier experimental photoelectron kinetic energy spectrum of the negative ion of lanthanum [A. M. Covington, D. Calabrese, J. S. Thompson, and T. J. Kvale, J. Phys. B 31, L855 (1998)] by carrying out relativistic configuration interaction (RCI) photodetachment calculations. The results confirm the earlier RCI calculation for the electron affinity of lanthanum (0.545 eV) [S. M. O'Malley and D. R. Beck, Phys. Rev. A 79, 012511 (2009)] and revise it to a slightly larger value of 0.550 eV, thus modifying the experimental interpretation of $0.47\ifmmode\pm\else\textpm\fi{}0.02$ eV. The calculation also yields the binding energies of the other thirteen bound states of ${\mathrm{La}}^{\ensuremath{-}}$. Good agreement has been found when these energies are compared to the results of a recent experimental study on ${\mathrm{La}}^{\ensuremath{-}}$ [C. W. Walter, N. D. Gibson, D. J. Matyas, C. T. Crocker, K. A. Dungan, B. R. Matola, and J. Rohl\'en, Phys. Rev. Lett. 113, 063001 (2014)]. Finally, our analysis confirms the transition energy for the potential laser cooling transition of ${}^{3}{F}_{2}^{e}\ensuremath{\rightarrow}{}^{3}{D}_{1}^{o}$ in ${\mathrm{La}}^{\ensuremath{-}}$.