Physical Review Letters

Sub-Hertz Optical Frequency Comparisons between Two Trapped Yb+171 Ions

T. Schneider, E. Peik, Chr. Tamm

Published Jun 16, 2005• 205 citations

Abstract

We compare the frequencies of the $6s\text{ }^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}5d\text{ }^{2}D_{3/2}(F=2)$ reference transition in $^{171}\mathrm{Yb}^{+}$ for two single ions stored in independent traps. The quadrupole moment of the $5d\text{ }^{2}D_{3/2}$ state is measured to be $9.32(48)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{C}\text{ }\mathrm{m}}^{2}$ and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be ${\ensuremath{\alpha}}_{S}({S}_{1/2})\ensuremath{-}{\ensuremath{\alpha}}_{S}({D}_{3/2})=\ensuremath{-}6.9(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}$ and ${\ensuremath{\alpha}}_{T}({D}_{3/2})=\ensuremath{-}13.6(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}$, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of $3.8(6.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.

DOI: 10.1103/physrevlett.94.230801

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

T. Schneider, Chr. Tamm, E. Peik

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)Jul 8, 20046 citations

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

Chr. Tamm, T. Schneider, E. Peik

arXiv:physics/0402120Laser SpectroscopyFeb 1, 20043 citations

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

Chr. Tamm, D. Engelke, V. Bühner

Physical Review AApr 10, 200096 citations

High-Resolution Spectroscopy of $^{173}$Yb$^{+}$ Ions

J. Jiang, A. V. Viatkina, Saaswath JK +7 more

physics.atom-phCross-listedarXiv:2601.09585Physical Review LettersJan 15, 20261 citation

High-Accuracy Optical Clock Based on the Octupole Transition in Yb+171

Nils Huntemann, Maksim V. Okhapkin, B. Lipphardt +3 more

arXiv:1111.2446Physical Review LettersFeb 29, 2012241 citations

Stray-field-induced quadrupole shift and absolute frequency of the 688-THz Y171b+ single-ion optical frequency standard

Chr. Tamm, S. Weyers, B. Lipphardt +1 more

Physical Review AOct 6, 2009103 citations

Physical Review Letters

Sub-Hertz Optical Frequency Comparisons between Two Trapped Yb+171 Ions

T. Schneider, E. Peik, Chr. Tamm

Published Jun 16, 2005• 205 citations

Publisher

Abstract

We compare the frequencies of the

6s\text{ }^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}5d\text{ }^{2}D_{3/2}(F=2)

reference transition in

^{171}\mathrm{Yb}^{+}

for two single ions stored in independent traps. The quadrupole moment of the

5d\text{ }^{2}D_{3/2}

state is measured to be

9.32(48)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{C}\text{ }\mathrm{m}}^{2}

and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be

{\ensuremath{\alpha}}_{S}({S}_{1/2})\ensuremath{-}{\ensuremath{\alpha}}_{S}({D}_{3/2})=\ensuremath{-}6.9(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}

and

{\ensuremath{\alpha}}_{T}({D}_{3/2})=\ensuremath{-}13.6(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}

, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of

3.8(6.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}

. This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.

DOI: 10.1103/physrevlett.94.230801

Related papers

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.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, 20046 citations

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

Chr. Tamm, T. Schneider, E. Peik

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+.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+.

arXiv:physics/0402120Laser SpectroscopyFeb 1, 20043 citations

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

Chr. Tamm, D. Engelke, V. Bühner

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.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.

Physical Review AApr 10, 200096 citations

High-Resolution Spectroscopy of $^{173}$ Yb $^{+}$ IonsHigh-Resolution Spectroscopy of $^{173}$Yb$^{+}$ Ions

J. Jiang, A. V. Viatkina, Saaswath JK +7 more

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.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.

physics.atom-phCross-listedarXiv:2601.09585Physical Review LettersJan 15, 20261 citation

High-Accuracy Optical Clock Based on the Octupole Transition in Yb+171

Nils Huntemann, Maksim V. Okhapkin, B. Lipphardt +3 more

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.

arXiv:1111.2446Physical Review LettersFeb 29, 2012241 citations

Stray-field-induced quadrupole shift and absolute frequency of the 688-THz Y171b+ single-ion optical frequency standard

Chr. Tamm, S. Weyers, B. Lipphardt +1 more

We report experimental investigations of a single-ion optical frequency standard based on ${^{171}\text{Y}\text{b}}^{+}$ . The ion is confined in a cylindrically symmetric radiofrequency Paul trap. The reference transition is the ${^{2}S}_{1/2}(F=0)--{^{2}D}_{3/2}({F}^{\ensuremath{'}}=2)$ electric quadrupole transition at 688 THz. Using a differential measurement scheme, we determine the shift of the reference transition frequency that occurs due to the interaction of the electric quadrupole moment of the ${^{2}D}_{3/2}$ state with the gradient of the electrostatic stray field in the trap. We determine an upper limit for the instability of the quadrupole shift over times between 100 s to 20 h. We also observe the variations in the shift and in the applied stray-field compensation voltages that result from loading a new ion into the trap and during a subsequent storage period of 74 days. This information is utilized to measure the absolute frequency of the reference transition with an uncertainty that is a factor of 3 smaller than that of the previous measurement. Using a fiber laser based optical frequency comb generator and the cesium fountain clock CSF1 of PTB (Physikalisch-Technische Bundesanstalt), the frequency at 300 K temperature is determined as $688\text{ }358\text{ }979\text{ }309\text{ }306.62\ifmmode\pm\else\textpm\fi{}0.73\text{ }\text{Hz}$.We report experimental investigations of a single-ion optical frequency standard based on ${^{171}\text{Y}\text{b}}^{+}$. The ion is confined in a cylindrically symmetric radiofrequency Paul trap. The reference transition is the ${^{2}S}_{1/2}(F=0)--{^{2}D}_{3/2}({F}^{\ensuremath{'}}=2)$ electric quadrupole transition at 688 THz. Using a differential measurement scheme, we determine the shift of the reference transition frequency that occurs due to the interaction of the electric quadrupole moment of the ${^{2}D}_{3/2}$ state with the gradient of the electrostatic stray field in the trap. We determine an upper limit for the instability of the quadrupole shift over times between 100 s to 20 h. We also observe the variations in the shift and in the applied stray-field compensation voltages that result from loading a new ion into the trap and during a subsequent storage period of 74 days. This information is utilized to measure the absolute frequency of the reference transition with an uncertainty that is a factor of 3 smaller than that of the previous measurement. Using a fiber laser based optical frequency comb generator and the cesium fountain clock CSF1 of PTB (Physikalisch-Technische Bundesanstalt), the frequency at 300 K temperature is determined as $688\text{ }358\text{ }979\text{ }309\text{ }306.62\ifmmode\pm\else\textpm\fi{}0.73\text{ }\text{Hz}$.

Physical Review AOct 6, 2009103 citations

We compare the frequencies of the

6s\text{ }^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}5d\text{ }^{2}D_{3/2}(F=2)

reference transition in

^{171}\mathrm{Yb}^{+}

for two single ions stored in independent traps. The quadrupole moment of the

5d\text{ }^{2}D_{3/2}

state is measured to be

9.32(48)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{C}\text{ }\mathrm{m}}^{2}

and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be

{\ensuremath{\alpha}}_{S}({S}_{1/2})\ensuremath{-}{\ensuremath{\alpha}}_{S}({D}_{3/2})=\ensuremath{-}6.9(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}

and

{\ensuremath{\alpha}}_{T}({D}_{3/2})=\ensuremath{-}13.6(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}

, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of

3.8(6.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}

. This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.

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.

High-Resolution Spectroscopy of

^{173}

^{+}

Ions

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.

We report experimental investigations of a single-ion optical frequency standard based on

{^{171}\text{Y}\text{b}}^{+}

. The ion is confined in a cylindrically symmetric radiofrequency Paul trap. The reference transition is the ${^{2}S}_{1/2}(F=0)--{^{2}D}_{3/2}({F}^{\ensuremath{'}}=2)$ electric quadrupole transition at 688 THz. Using a differential measurement scheme, we determine the shift of the reference transition frequency that occurs due to the interaction of the electric quadrupole moment of the

{^{2}D}_{3/2}

state with the gradient of the electrostatic stray field in the trap. We determine an upper limit for the instability of the quadrupole shift over times between 100 s to 20 h. We also observe the variations in the shift and in the applied stray-field compensation voltages that result from loading a new ion into the trap and during a subsequent storage period of 74 days. This information is utilized to measure the absolute frequency of the reference transition with an uncertainty that is a factor of 3 smaller than that of the previous measurement. Using a fiber laser based optical frequency comb generator and the cesium fountain clock CSF1 of PTB (Physikalisch-Technische Bundesanstalt), the frequency at 300 K temperature is determined as $688\text{ }358\text{ }979\text{ }309\text{ }306.62\ifmmode\pm\else\textpm\fi{}0.73\text{ }\text{Hz}$.