Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0706.1705 · Physical Review A

Investigations of Ra+ properties to test possibilities for new optical-frequency standards

B. K. Sahoo, Bhanu Pratap Das, Rajat K. Chaudhuri, Debashis Mukherjee, Rob G. E. Timmermans, Klaus Peter Jungmann

Published Oct 31, 2007• 48 citations
arXivHTMLPDF

Abstract

The present work tests the suitability of the narrow transitions $7s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}6d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}$ and $7s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}6d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}$ in ${\mathrm{Ra}}^{+}$ for optical frequency standard studies. Our calculations of the lifetimes of the metastable $6d$ states using the relativistic coupled-cluster theory suggest that they are sufficiently long for ${\mathrm{Ra}}^{+}$ to be considered as a potential candidate for an atomic clock. This is further corroborated by our studies of the hyperfine interactions, dipole and quadrupole polarizabilities, and quadrupole moments of the appropriate states of this system.

DOI
10.1103/physreva.76.040504

Related papers

Radium single-ion optical clock

Oscar O. Versolato, L. W. Wansbeek, Klaus Peter Jungmann +3 more

We explore the potential of the electric quadrupole transitions $7s\,^2S_{1/2}$ - $6d\,^2D_{3/2}$, $6d\,^2D_{5/2}$ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive $^A$Ra$^+$ candidates with $A=$ 223 - 229 are identified. In particular, we show that the transition $7s\,^2S_{1/2}\,(F=2,m_F=0)$ - $6d\,^2D_{3/2}\,(F=0,m_F=0)$ at 828 nm in $^{223}$Ra$^+$, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of $10^{-17}$. With more experimental effort, the $^{223,225,226}$Ra$^+$ clocks could be pushed to a projected performance reaching the $10^{-18}$ level.

arXiv:1102.4988•Feb 24, 2011•0 citations

Potential of electric quadrupole transitions in radium isotopes for single-ion optical frequency standards

Oscar O. Versolato, L. W. Wansbeek, Klaus Peter Jungmann +3 more

We explore the potential of the electric quadrupole transitions $7s {}^{2}{S}_{1/2}$-$6d {}^{2}{D}_{3/2}$, $6d {}^{2}{D}_{5/2}$ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive ${}^{A}$Ra${}^{+}$ candidates, with $A=$ 223--229, are identified. In particular, we show that the transition $7s {}^{2}{S}_{1/2} (F=2,{m}_{F}=0)$-$6d {}^{2}{D}_{3/2} (F=0,{m}_{F}=0)$ at 828 nm in $^{223}\mathrm{Ra}$${}^{+}$, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of ${10}^{\ensuremath{-}17}$. With more experimental effort, the $^{223,225,226}\mathrm{Ra}$${}^{+}$ clocks could be pushed to a projected performance reaching the ${10}^{\ensuremath{-}18}$ level.

Physical Review A•Apr 22, 2011•21 citations

Spectroscopy of electric dipole and quadrupole transitions in Ra + 224

Spencer Kofford, Haoran Li, Robert Kwapisz +5 more

We report on spectroscopy of the low-lying electronic transitions in $^{224}\mathrm{Ra}^{+}$. We measured the frequencies of the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ cooling transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{5/2}$ clock transition, the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition, and the $^{2}D_{5/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ repump transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{3/2}$ electric quadrupole transition, and the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition. The ion's low charge-to-mass ratio and convenient wavelengths make ${}^{224}{\mathrm{Ra}}^{+}$ a promising optical clock candidate.

arXiv:2409.09873•Physical Review A•Mar 4, 2025•2 citations

Measurements of electric quadrupole transition frequencies in Ra+226

C. A. Holliman, Mingyu Fan, Andrew M. Jayich

We report the first driving of the $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}$ and $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ electric quadrupole (E2) transitions in ${\mathrm{Ra}}^{+}$. We measure the frequencies of both E2 transitions and two other low-lying transitions in $^{226}\mathrm{Ra}^{+}$ that are important for controlling the radium ion's motional and internal states: $6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}\ensuremath{\rightarrow}7p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$ and $6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}\ensuremath{\rightarrow}7p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$.

arXiv:1910.06351•Physical Review A•Dec 19, 2019•9 citations

Radium Ion Optical Clock

C. A. Holliman, Mingyu Fan, A. Contractor +2 more

We report the first operation of a ${\mathrm{Ra}}^{+}$ optical clock, a promising high-performance clock candidate. The clock uses a single trapped $^{226}{\mathrm{Ra}}^{+}$ ion and operates on the $7s\text{ }^{2}{S}_{1/2}\ensuremath{\rightarrow}6d\text{ }^{2}{D}_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$, where $\ensuremath{\tau}$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}/\ensuremath{\nu}=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. Using the clock, we realize the first measurement of the ratio of the ${D}_{5/2}$ state to the ${S}_{1/2}$ state Land\'e $g$-factors: ${g}_{D}/{g}_{S}=0.598\text{ }805\text{ }3(11)$. A ${\mathrm{Ra}}^{+}$ optical clock could improve limits on the time variation of the fine structure constant, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

arXiv:2201.07330•Physical Review Letters•Jan 20, 2022•29 citations

Relativistic coupled-cluster calculations of the polarizabilities of atomic thallium

Yong-Bo Tang, Ningning Gao, Bing-Qiong Lou +1 more

Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$, $7s$, $7p$, $8s$, $8p$, and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7{s}_{1/2}$, $7{p}_{1/2}$, $8{p}_{1/2}$, and $8{p}_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6{p}_{1/2}$--$7s$ and $6{p}_{3/2}$--$7s$ transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7{s}_{1/2}$--$7{p}_{1/2}$ and $7{s}_{1/2}$--$7{p}_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6{p}_{1/2}$--$7{p}_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.

Physical Review A•Dec 14, 2018•10 citations
The present work tests the suitability of the narrow transitions 7s2S1∕2\ensuremath→6d2D3∕27s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}6d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}7s2S1∕2​\ensuremath→6d2D3∕2​ and 7s2S1∕2\ensuremath→6d2D5∕27s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}6d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}7s2S1∕2​\ensuremath→6d2D5∕2​ in Ra+{\mathrm{Ra}}^{+}Ra+ for optical frequency standard studies. Our calculations of the lifetimes of the metastable 6d6d6d states using the relativistic coupled-cluster theory suggest that they are sufficiently long for Ra+{\mathrm{Ra}}^{+}Ra+ to be considered as a potential candidate for an atomic clock. This is further corroborated by our studies of the hyperfine interactions, dipole and quadrupole polarizabilities, and quadrupole moments of the appropriate states of this system.
We explore the potential of the electric quadrupole transitions 7s 2S1/27s\,^2S_{1/2}7s2S1/2​ - 6d 2D3/26d\,^2D_{3/2}6d2D3/2​, 6d 2D5/26d\,^2D_{5/2}6d2D5/2​ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive A^AARa+^++ candidates with A=A=A= 223 - 229 are identified. In particular, we show that the transition 7s 2S1/2 (F=2,mF=0)7s\,^2S_{1/2}\,(F=2,m_F=0)7s2S1/2​(F=2,mF​=0) - 6d 2D3/2 (F=0,mF=0)6d\,^2D_{3/2}\,(F=0,m_F=0)6d2D3/2​(F=0,mF​=0) at 828 nm in 223^{223}223Ra+^++, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of 10−1710^{-17}10−17. With more experimental effort, the 223,225,226^{223,225,226}223,225,226Ra+^++ clocks could be pushed to a projected performance reaching the 10−1810^{-18}10−18 level.
We explore the potential of the electric quadrupole transitions 7s2S1/27s {}^{2}{S}_{1/2}7s2S1/2​-6d2D3/26d {}^{2}{D}_{3/2}6d2D3/2​, 6d2D5/26d {}^{2}{D}_{5/2}6d2D5/2​ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive A{}^{A}ARa+{}^{+}+ candidates, with A=A=A= 223--229, are identified. In particular, we show that the transition 7s2S1/2(F=2,mF=0)7s {}^{2}{S}_{1/2} (F=2,{m}_{F}=0)7s2S1/2​(F=2,mF​=0)-6d2D3/2(F=0,mF=0)6d {}^{2}{D}_{3/2} (F=0,{m}_{F}=0)6d2D3/2​(F=0,mF​=0) at 828 nm in 223Ra^{223}\mathrm{Ra}223Ra+{}^{+}+, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of ${10}^{\ensuremath{-}17}$. With more experimental effort, the 223,225,226Ra^{223,225,226}\mathrm{Ra}223,225,226Ra+{}^{+}+ clocks could be pushed to a projected performance reaching the ${10}^{\ensuremath{-}18}$ level.
We report on spectroscopy of the low-lying electronic transitions in 224Ra+^{224}\mathrm{Ra}^{+}224Ra+. We measured the frequencies of the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ cooling transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{5/2}$ clock transition, the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition, and the $^{2}D_{5/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ repump transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{3/2}$ electric quadrupole transition, and the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition. The ion's low charge-to-mass ratio and convenient wavelengths make 224Ra+{}^{224}{\mathrm{Ra}}^{+}224Ra+ a promising optical clock candidate.
We report the first driving of the $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}$ and $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ electric quadrupole (E2) transitions in Ra+{\mathrm{Ra}}^{+}Ra+. We measure the frequencies of both E2 transitions and two other low-lying transitions in 226Ra+^{226}\mathrm{Ra}^{+}226Ra+ that are important for controlling the radium ion's motional and internal states: $6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}\ensuremath{\rightarrow}7p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$ and $6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}\ensuremath{\rightarrow}7p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$.
We report the first operation of a Ra+{\mathrm{Ra}}^{+}Ra+ optical clock, a promising high-performance clock candidate. The clock uses a single trapped 226Ra+^{226}{\mathrm{Ra}}^{+}226Ra+ ion and operates on the $7s\text{ }^{2}{S}_{1/2}\ensuremath{\rightarrow}6d\text{ }^{2}{D}_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$, where $\ensuremath{\tau}$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}/\ensuremath{\nu}=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. Using the clock, we realize the first measurement of the ratio of the D5/2{D}_{5/2}D5/2​ state to the S1/2{S}_{1/2}S1/2​ state Land\'e ggg-factors: gD/gS=0.598 805 3(11){g}_{D}/{g}_{S}=0.598\text{ }805\text{ }3(11)gD​/gS​=0.598 805 3(11). A Ra+{\mathrm{Ra}}^{+}Ra+ optical clock could improve limits on the time variation of the fine structure constant, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.
Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the 6p6p6p, 7s7s7s, 7p7p7p, 8s8s8s, 8p8p8p, and 6d6d6d states and the dynamic dipole polarizabilities of the 6p6p6p and 7s7s7s states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the 7s1/27{s}_{1/2}7s1/2​, 7p1/27{p}_{1/2}7p1/2​, 8p1/28{p}_{1/2}8p1/2​, and 8p3/28{p}_{3/2}8p3/2​ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the 6p1/26{p}_{1/2}6p1/2​--7s7s7s and 6p3/26{p}_{3/2}6p3/2​--7s7s7s transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the 7s1/27{s}_{1/2}7s1/2​--7p1/27{p}_{1/2}7p1/2​ and 7s1/27{s}_{1/2}7s1/2​--7p3/27{p}_{3/2}7p3/2​ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the 6p1/26{p}_{1/2}6p1/2​--7p1/27{p}_{1/2}7p1/2​ transition, are also evaluated and compared with available theoretical and experimental values.