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Physical Review A

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

Oscar O. Versolato, L. W. Wansbeek, Klaus Peter Jungmann, Rob G. E. Timmermans, Lorenz Willmann, H. W. Wilschut

Published Apr 22, 2011• 21 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.043829

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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 ^{223}\mathrm{Ra}$${}^{+}, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of 10\ensuremath−17{10}^{\ensuremath{-}17}10\ensuremath−17. With more experimental effort, the ^{223,225,226}\mathrm{Ra}$${}^{+} clocks could be pushed to a projected performance reaching the 10\ensuremath−18{10}^{\ensuremath{-}18}10\ensuremath−18 level.
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 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 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.
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 $6d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}\ensuremath{\rightarrow}7p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$.
The electric quadrupole shift is presently the most significant source of uncertainty on the systematic shifts for several single-ion optical frequency standards. We present a simple method for cancelling this shift based on measurements of the Zeeman spectrum of the clock transition. This method is easy to implement and yields very high cancellation levels. A fractional uncertainty of 5 x 10(-18) for the canceled quadrupole shift is estimated for a measurement of the absolute frequency of the 5s (2)S(1/2)-4d (2)D(5/2) clock transition of 88Sr+.
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 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.