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arXiv:physics/0402120 · Laser Spectroscopy

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

Chr. Tamm, T. Schneider, E. Peik

Published Feb 1, 2004• 3 citations
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Abstract

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+.

DOI
10.1142/9789812703002_0007

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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.

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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.

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

T. Schneider, E. Peik, Chr. Tamm

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.

Physical Review Letters•Jun 16, 2005•205 citations
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 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 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 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 $F=0--{F}^{\ensuremath{'}}=2,$ ${m}_{{F}^{\ensuremath{'}}}=0$ 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 $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}.$ 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 report experimental investigations of a single-ion optical frequency standard based on 171Yb+{^{171}\text{Y}\text{b}}^{+}171Yb+. 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 2D3/2{^{2}D}_{3/2}2D3/2​ 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 $688\text{ }358\text{ }979\text{ }309\text{ }306.62\ifmmode\pm\else\textpm\fi{}0.73\text{ }\text{Hz}$.
The171Yb+ion possesses two transitions that are applicable as references for optical frequency standards and several general features make this ion attractive: All relevant radiations for cooling and excitation can be generated from diode lasers. A nuclear spin of 1/2 ensures a simple sublevel structure. Long storage times of Yb+in ion traps are easily obtained. The2S1/2(F = 0) →2D3/2(F = 2, mF= 0) electric quadrupole transition at 436 nm with a natural linewidth of 3.1 Hz provides a quantum noise limited instability of a single-ion frequency standard of about 2 × 10-15in 1 s. The electric octupole transition2S1/2(F = 0)→2F7/2(F = 3, mF= 0) at 467 nm with a natural linewidth in the nHz range will allow to surpass that instability level. It also possesses a lower sensitivity to field-induced frequency shifts. In this system the Fourier-limited interrogation linewidth can be adapted to that of the best available laser sources, which are presently at the level below 1 Hz. Both transitions have been recommended as secondary representations of the SI second.
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 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ for two single ions stored in independent traps. The quadrupole moment of the 5d 2D3/25d\text{ }^{2}D_{3/2}5d 2D3/2​ 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.