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Physical Review A

Spectroscopy of the electric-quadrupole transition 2S1/2(F=0)–2D3/2(F=2) in trapped 171Yb+

Chr. Tamm, D. Engelke, V. Bühner

Published Apr 10, 2000• 96 citations
Publisher

Abstract

We experimentally demonstrate laser spectroscopy of the electric-quadrupole transition $6s{}^{2}{S}_{1/2}--5d{}^{2}{D}_{3/2}$ of a single trapped ${}^{171}\mathrm{Yb}$ ion. The probed transition has a natural linewidth of 3.1 Hz, and is at a wavelength of 435.5 nm. A ${}^{171}\mathrm{Yb}$ ion is laser cooled to the range of the Doppler limit in a radio-frequency Paul trap. The $F=0--{F}^{\ensuremath{'}}=2,$ ${m}_{{F}^{\ensuremath{'}}}=0$ hyperfine component of the ${}^{2}{S}_{1/2}{--}^{2}{D}_{3/2}$ transition is excited by a laser source whose frequency is controlled by an optical reference cavity of high intrinsic stability. The recoilless carrier component of the vibrational sideband spectrum is resolved with a minimum linewidth of approximately 80 Hz, corresponding to a fractional frequency resolution of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}.$ This resolution limit is attributed to laser frequency instability. The effective decoherence rates of the residual ion motion are inferred from the observation that the axial and two radial low-frequency first-order secular-vibration sidebands show minimum linewidths in the range of 0.2--1 kHz. Prospects for an optical frequency standard based on the investigated atomic system are discussed.

DOI
10.1103/physreva.61.053405

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Optical frequency standard based on a trapped171Yb+ion

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We describe experimental investigations on an optical frequency standard based on a single laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The 435.5 nm electric-quadrupole transition from the 2S1/2(F=0) groudn state to the 2D3/2(F=2) state is probed using a diode laser system whose short-term frequency stability is derived from an environmentally isolated ULE cavity. The transition is resolved with a Foruier-limited full halfwidth of approximately 30 Hz. The absolute optical transition frequency is determined using a femtosecond frequency comb generator and a Cs fountain clock as the frequency reference. The measured frequency value is 688 358 979 321 Hz at an ambient blackbody radiation field of 300 K. The 1σ fractional uncertainty of this frequency measurement is 1×10-14.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 8, 2003•0 citations

COMPARISON OF TWO SINGLE-ION OPTICAL FREQUENCY STANDARDS AT THE SUB-HERTZ LEVEL

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We describe experimental investigations on an optical frequency standard based on a laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the 2S1/2(F=0) ground state to the 2D3/2(F=2) state at the wavelength of 436 nm is used as the reference transition. The reference transition is probed by a frequency-doubled, frequency-stabilized diode laser and is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. In order to compare two 171Yb+ standards, separate frequency shift and servo systems are employed to stabilise the probe frequency to the reference transition line centers of two independently stored 171Yb+ ions. The present experimental results indicate a relative instability (Allan standard deviation)of the optical frequency difference between the two systems of sigma_y(1000 s)=1.0E-15 and a mean frequency difference of 0.2 Hz. Shifts in the range of several Hertz are observed in the frequency difference if a stationary electric field gradient is superimposed on the radiofrequency trap field. This measurement permits a first experimental estimate of the electric quadrupole moment of the 2D3/2 state of Yb+.

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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 ${}^{171}{\mathrm{Yb}}^{+}$ 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 ${10}^{18}$ 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 ${10}^{18}$ level. The electric quadrupole shift may be the limiting systematic effect, but cannot yet be observed with the current resolution on the transition.

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Compared to other stable isotopes of $\rm{Yb}^+$, $^{173}\rm{Yb}^+$ 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 $^{173}\rm{Yb}^+$ ion. The previously unobserved $^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}$ electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between $^{171}\rm{Yb}^+$ and $^{173}\rm{Yb}^+$ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the ${}^2\!D_{3/2}$ state with a relative uncertainty below $10^{-8}$. From the HFS measurement data, we infer for ${}^{173}$Yb a nuclear magnetic octupole moment $Ω= -0.062(8)\,({\rm b} \times μ_N)$ 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 ${}^2\!S_{1/2}$ and ${}^2\!D_{3/2}$ states.

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Recoilless optical absorption and Doppler sidebands of a single trapped ion

Jonas Bergquist, Wayne M. Itano, David J. Wineland

Spectroscopic measurements of the electric-quadrupole-allowed 5${d}^{10}$6s ${\mathrm{}}^{2}$${S}_{1/2}$ to 5${d}^{9}$6${s}^{2}$ ${\mathrm{}}^{2}$${D}_{5/2}$ transition near 282 nm on a single, laser-cooled ${\mathrm{Hg}}^{+}$ ion give a recoil-free absorption line (carrier) and well-resolved motional sidebands. From the intensity ratio of the sidebands to the carrier, the effective temperature of the ${\mathrm{Hg}}^{+}$ ion was determined to be near the theoretical minimum of 1.7 mK. A fractional resolution of better than 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ for this ultraviolet transition is achieved.

Physical Review A•Jul 1, 1987•185 citations

Comparison of two single-ion optical frequency standards at the hertz level

T. Schneider, Chr. Tamm, E. Peik

We describe experimental investigations of an optical frequency standard based on a single laser-cooled /sup 171/Yb/sup +/ ion confined in a radiofrequency Paul trap. The electric quadrupole transition from the /sup 2/S/sub 1/2 /(F=0) ground state to the /sup 2/D/sub 3/2/(F=2) state at 435.5 nm is used as the reference transition. The transition was resolved with a Fourier-limited width of approximately 30 Hz. In order to investigate the instability and accuracy of a future frequency standard based on the reference transition, a first experiment was done comparing two laser frequencies stabilized individually to two separate ions in different traps. As a result we found a relative frequency instability /spl sigma//sub y/(640 s)=1.5/spl middot/10/sup -15/ for the difference of the two laser frequencies. We also derived a first estimate /spl Theta/(/sup 2/D/sub 3/2/)=(3.9/spl plusmn/1.9)ea/sub 0//sup 2/ for the electric quadrupole moment of the /sup 2/D/sub 3/2/ state.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jul 8, 2004•6 citations
We experimentally demonstrate laser spectroscopy of the electric-quadrupole transition 6s2S1/2−−5d2D3/26s{}^{2}{S}_{1/2}--5d{}^{2}{D}_{3/2}6s2S1/2​−−5d2D3/2​ of a single trapped 171Yb{}^{171}\mathrm{Yb}171Yb ion. The probed transition has a natural linewidth of 3.1 Hz, and is at a wavelength of 435.5 nm. A 171Yb{}^{171}\mathrm{Yb}171Yb ion is laser cooled to the range of the Doppler limit in a radio-frequency Paul trap. The F=0−−F\ensuremath′=2,F=0--{F}^{\ensuremath{'}}=2,F=0−−F\ensuremath′=2, mF\ensuremath′=0{m}_{{F}^{\ensuremath{'}}}=0mF\ensuremath′​=0 hyperfine component of the 2S1/2−−2D3/2{}^{2}{S}_{1/2}{--}^{2}{D}_{3/2}2S1/2​−−2D3/2​ transition is excited by a laser source whose frequency is controlled by an optical reference cavity of high intrinsic stability. The recoilless carrier component of the vibrational sideband spectrum is resolved with a minimum linewidth of approximately 80 Hz, corresponding to a fractional frequency resolution of 1.2\ifmmode×\else\texttimes\fi10\ensuremath−13.1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}.1.2\ifmmode×\else\texttimes\fi10\ensuremath−13. This resolution limit is attributed to laser frequency instability. The effective decoherence rates of the residual ion motion are inferred from the observation that the axial and two radial low-frequency first-order secular-vibration sidebands show minimum linewidths in the range of 0.2--1 kHz. Prospects for an optical frequency standard based on the investigated atomic system are discussed.
We describe experimental investigations on an optical frequency standard based on a single laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The 435.5 nm electric-quadrupole transition from the 2S1/2(F=0) groudn state to the 2D3/2(F=2) state is probed using a diode laser system whose short-term frequency stability is derived from an environmentally isolated ULE cavity. The transition is resolved with a Foruier-limited full halfwidth of approximately 30 Hz. The absolute optical transition frequency is determined using a femtosecond frequency comb generator and a Cs fountain clock as the frequency reference. The measured frequency value is 688 358 979 321 Hz at an ambient blackbody radiation field of 300 K. The 1σ fractional uncertainty of this frequency measurement is 1×10-14.
We describe experimental investigations on an optical frequency standard based on a laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the 2S1/2(F=0) ground state to the 2D3/2(F=2) state at the wavelength of 436 nm is used as the reference transition. The reference transition is probed by a frequency-doubled, frequency-stabilized diode laser and is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. In order to compare two 171Yb+ standards, separate frequency shift and servo systems are employed to stabilise the probe frequency to the reference transition line centers of two independently stored 171Yb+ ions. The present experimental results indicate a relative instability (Allan standard deviation)of the optical frequency difference between the two systems of sigma_y(1000 s)=1.0E-15 and a mean frequency difference of 0.2 Hz. Shifts in the range of several Hertz are observed in the frequency difference if a stationary electric field gradient is superimposed on the radiofrequency trap field. This measurement permits a first experimental estimate of the electric quadrupole moment of the 2D3/2 state of 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.
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.
Spectroscopic measurements of the electric-quadrupole-allowed 5${d}^{10}$6s 2{\mathrm{}}^{2}2S1/2{S}_{1/2}S1/2​ to 5${d}^{9}666{s}^{2}$ 2{\mathrm{}}^{2}2D5/2{D}_{5/2}D5/2​ transition near 282 nm on a single, laser-cooled Hg+{\mathrm{Hg}}^{+}Hg+ ion give a recoil-free absorption line (carrier) and well-resolved motional sidebands. From the intensity ratio of the sidebands to the carrier, the effective temperature of the Hg+{\mathrm{Hg}}^{+}Hg+ ion was determined to be near the theoretical minimum of 1.7 mK. A fractional resolution of better than 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ for this ultraviolet transition is achieved.
We describe experimental investigations of an optical frequency standard based on a single laser-cooled /sup 171/Yb/sup +/ ion confined in a radiofrequency Paul trap. The electric quadrupole transition from the /sup 2/S/sub 1/2 /(F=0) ground state to the /sup 2/D/sub 3/2/(F=2) state at 435.5 nm is used as the reference transition. The transition was resolved with a Fourier-limited width of approximately 30 Hz. In order to investigate the instability and accuracy of a future frequency standard based on the reference transition, a first experiment was done comparing two laser frequencies stabilized individually to two separate ions in different traps. As a result we found a relative frequency instability /spl sigma//sub y/(640 s)=1.5/spl middot/10/sup -15/ for the difference of the two laser frequencies. We also derived a first estimate /spl Theta/(/sup 2/D/sub 3/2/)=(3.9/spl plusmn/1.9)ea/sub 0//sup 2/ for the electric quadrupole moment of the /sup 2/D/sub 3/2/ state.