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arXiv:2012.14187 · Physical Review A

Precision characterization of the D 5 / 2 2 state and the quadratic Zeeman coefficient in Yb + 171

Ting Rei Tan, Claire Edmunds, Alistair R. Milne, Michael J. Biercuk, Cornelius Hempel

Published Jul 30, 2021• 18 citations
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Abstract

We report measurements of the branching fraction, hyperfine constant, and second-order Zeeman coefficient of the ${D}_{5/2}$ level in $^{171}\mathrm{Yb}^{+}$ with up to a two-orders-of-magnitude reduction in uncertainty compared to previously reported values. We estimate the electric quadrupole reduced matrix element of the ${S}_{1/2}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}{D}_{5/2}$ transition to be 12.5(4) $e{a}_{0}^{2}$. Furthermore, we determine the transition frequency of the ${F}_{7/2}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}{\phantom{\rule{4pt}{0ex}}}^{1}D{[3/2]}_{3/2}$ at 760 nm with a $\ensuremath{\sim}$25-fold improvement in uncertainty. These measurements provide benchmarks for quantum-many-body atomic-physics calculations and provide valuable data for efforts to improve quantum information processors based on ${}^{171}{\text{Yb}}^{+}$.

DOI
10.1103/physreva.104.l010802

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The hyperfine structure of the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{D}_{5/2}$ quadrupole transition at 674 nm in 87Sr+{}^{87}{\mathrm{Sr}}^{+}87Sr+ has been observed. The ion was confined in a Paul trap and cooled using laser radiation at 422 and 1092 nm. The quadrupole transition was observed by monitoring quantum jumps in the 422-nm fluorescence. The odd isotope of strontium has ``clock'' transitions independent of the first-order Zeeman shift and the 2D5/2{}^{2}{D}_{5/2}2D5/2​ state hyperfine structure constants have been determined as AD5/2=2.1743(14)MHz{A}_{{D}_{5/2}}=2.1743(14)\mathrm{MHz}AD5/2​​=2.1743(14)MHz and BD5/2=49.11(6)MHz.{B}_{{D}_{5/2}}=49.11(6)\mathrm{MHz}.BD5/2​​=49.11(6)MHz. Standard uncertainties have been added in parentheses. These values allow the second-order Zeeman shifts to be calculated. The ${}^{88}{\mathrm{Sr}}^{+}{\ensuremath{-}}^{87}{\mathrm{Sr}}^{+}$ isotope shift for the 674-nm quadrupole transition has been measured to be 247.99(4) MHz.
High-Resolution Spectroscopy of 173^{173}173Yb+^{+}+ Ions
Compared to other stable isotopes of Yb+\rm{Yb}^+Yb+, 173Yb+^{173}\rm{Yb}^+173Yb+ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped 173Yb+^{173}\rm{Yb}^+173Yb+ ion. The previously unobserved 2 ⁣S1/2→2 ⁣D3/2^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}2S1/2​→2D3/2​ electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between 171Yb+^{171}\rm{Yb}^+171Yb+ and 173Yb+^{173}\rm{Yb}^+173Yb+ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the 2 ⁣D3/2{}^2\!D_{3/2}2D3/2​ state with a relative uncertainty below 10−810^{-8}10−8. From the HFS measurement data, we infer for 173{}^{173}173Yb a nuclear magnetic octupole moment Ω=−0.062(8) (b×μN)Ω= -0.062(8)\,({\rm b} \times μ_N)Ω=−0.062(8)(b×μN​) with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the 2 ⁣S1/2{}^2\!S_{1/2}2S1/2​ and 2 ⁣D3/2{}^2\!D_{3/2}2D3/2​ states.
Spectroscopy of the 411-nm transition in 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The 2S1/2(F=0,mF=0)−−2D5/2(F=2,mF=0){}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)2S1/2​(F=0,mF​=0)−−2D5/2​(F=2,mF​=0) frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu}T)2{\mathrm{T})}^{2}T)2. In addition, the hyperfine structure of the 2D5/2{}^{2}{D}_{5/2}2D5/2​ level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The 2D5/2{}^{2}{D}_{5/2}2D5/2​ hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.
We report on spectroscopic results on the $^{2}S_{1/2}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}$ transition in single trapped Yb+{\mathrm{Yb}}^{+}Yb+ ions. We measure the isotope shifts for all stable Yb+{\mathrm{Yb}}^{+}Yb+ isotopes except 173Yb+^{173}\mathrm{Yb}^{+}173Yb+, as well as the hyperfine splitting of the 2P3/2^{2}P_{3/2}2P3/2​ state in 171Yb+^{171}\mathrm{Yb}^{+}171Yb+. Our results are in agreement with previous measurements but are a factor of 5--9 more precise. For the hyperfine constant A(2P3/2)=875.4(10)MHzA(^{2}P_{3/2})=875.4(10)\phantom{\rule{4pt}{0ex}}\mathrm{MHz}A(2P3/2​)=875.4(10)MHz our results also agree with previous measurements but deviate significantly from theoretical predictions. We present experimental results on the branching ratios for the decay of the 2P3/2^{2}P_{3/2}2P3/2​ state. We find branching fractions for the decay to the 2D3/2^{2}D_{3/2}2D3/2​ state and 2D5/2^{2}D_{5/2}2D5/2​ state of 0.17(1)% and 1.08(5)%, respectively, in rough agreement with theoretical predictions. Furthermore, we measured the isotope shifts of the $^{2}F_{7/2}\ensuremath{\rightarrow}^{1}D{[5/2]}_{5/2}$ transition and determine the hyperfine structure constant for the 1D[5/2]5/2^{1}D{[5/2]}_{5/2}1D[5/2]5/2​ state in 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ to be $A(^{1}D{[5/2]}_{5/2})=\ensuremath{-}107(6)\phantom{\rule{4pt}{0ex}}\mathrm{MHz}$.
We report on the first coherent excitation of the highly forbidden ${^{2}S}_{1/2}\ensuremath{\rightarrow}{^{2}F}_{7/2}$ electric octupole (E3) transition in a single trapped 172Yb+^{172}{\mathrm{Yb}}^{+}172Yb+ ion, an isotope without nuclear spin. Using the transition in 171Yb+^{171}{\mathrm{Yb}}^{+}171Yb+ as a reference, we determine the transition frequency to be 642 116 784 950 887.6(2.4) Hz. We map out the magnetic field environment using the forbidden ${^{2}S}_{1/2}\ensuremath{\rightarrow}{^{2}D}_{5/2}$ electric quadrupole (E2) transition and determine its frequency to be 729 476 867 027 206.8(4.4) Hz. Our results are a factor of $1\ifmmode\times\else\texttimes\fi{}{10}^{5}$ ($3\ifmmode\times\else\texttimes\fi{}{10}^{5}$) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable 2F7/2{^{2}F}_{7/2}2F7/2​ state of Yb+{\mathrm{Yb}}^{+}Yb+.
Spectroscopy has been performed on $\mathrm{the}{}^{2}{S}_{1/2}(F=0,{m}_{F}{=0)\ensuremath{-}}^{2}{F}_{7/2}{(F=3,m}_{F}=0)$ electric octupole transition in 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ with kilohertz resolution. A quantum jump rate of more than one per second has been achieved, a factor of 100 improvement on previous work. Spectra including the sidebands at the trap secular frequency show the ion to be in the Lambe-Dicke regime and hence the Doppler effect has been eliminated to first order. The dynamic Stark shift is a significant perturbation to the frequency because of the high intensity required to drive the octupole transition. It has been measured as ${42}_{\ensuremath{-}10}^{+12} \ensuremath{\mu}\mathrm{Hz}{\mathrm{W}}^{\ensuremath{-}1}{\mathrm{m}}^{2}$ and with further reduction in the probe laser linewidth, it should be possible to reduce the relative uncertainty in this shift to the parts in 1018{10}^{18}1018 level. The transition is free from the Zeeman effect to first order and has a measured second-order shift of $1.9(3) \mathrm{mHz}(\ensuremath{\mu}\mathrm{T}{)}^{\ensuremath{-}2}.$ It should be possible to reduce the relative uncertainty in this shift to below the part in 1018{10}^{18}1018 level. The electric quadrupole shift may be the limiting systematic effect, but cannot yet be observed with the current resolution on the transition.