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arXiv:1112.2766 · Physical Review Letters

High-Accuracy Measurement of Atomic Polarizability in an Optical Lattice Clock

Jeff A. Sherman, N. Lemke, N. Hinkley, Marco Pizzocaro, Richard W. Fox, Andrew D. Ludlow, Chris W. Oates

Published Apr 13, 2012• 131 citations
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Abstract

Presently, the Stark effect contributes the largest source of uncertainty in a ytterbium optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock levels ${\ensuremath{\alpha}}_{\mathrm{clock}}=36.2612(7)\text{ }\text{ }\mathrm{kHz}\text{ }(\mathrm{kV}/\mathrm{cm}{)}^{\ensuremath{-}2}$. The clock's uncertainty due to room temperature blackbody radiation is reduced by an order of magnitude to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$.

DOI
10.1103/physrevlett.108.153002

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Optical clocks have the potential to be 100 times more accurate than current best cesium atomic clocks within a fraction of the averaging time.This corresponds to a fractional uncertainty of the clock frequency on the level of 10 -18 and requires highaccuracy knowledge of systematic frequency shifts, such that they can be avoided or corrected for.In strontium optical lattice clocks an ensemble of ultracold strontium atoms is conned in an optical lattice, to allow for spectroscopy of the reference transition 5s 2 1 S 0 5s5p 3 P 0 in the Lamb-Dicke regime.The by far largest systematic frequency shift of the strontium clock transition is caused by its high sensitivity to blackbody radiation (BBR).The knowledge of the resulting frequency shift limited the achievable clock uncertainty to about 1 × 10 -16 .In this thesis for the rst time an experimental approach was followed, to determine the sensitivity of the strontium clock transition to blackbody radiation.At an environmental temperature of 300 K the resulting frequency shift corresponds to 2.277 8(23) Hz.The achieved uncertainty contributes with 5 × 10 -18 to the fractional systematic uncertainty of the clock frequency.The determination is based on a precision measurement of the dierence of static polarizabilities of the two clock states ∆α dc = α(5s5p 3 P 0 ) -α(5s 2 1 S 0 ) = 4.078 73(11) × 10 -39 Cm 2 /V.For this the dc Stark shift of the clock transition has been measured in the accurately known electric eld of a precision plate capacitor, which has been developed in this work.The attained static polarizability dierence ∆α dc corresponds to the rst term of a power series of the sensitivity to BBR.Higher orders are accumulated as dynamic part of the BBR shift.Which has been modelled using ∆α dc and experimental data for other atomic properties.To interrogate the ultracold atoms in the electric eld a novel transport technique has been developed, which uses the magic wavelength (813 nm) optical lattice to convey the atoms.For this, the interference pattern is translated together with the foci of the far-detuned lattice beams, by simultaneous translation of the lattice optics.In this way ultracold atoms have been transported within 250 ms over 5 cm, or several Rayleigh ranges respectively without signicant atom loss or heating.In the course of this work the rst frequency measurement with the strontium lattice clock of Physikalisch-Technischen Bundesanstalt (PTB) has been performed.The frequency of the 87 Sr clock transition was measured to be 429 228 004 229 872.9(5)Hz.The strontium lattice clock itself contributed with 1.5 × 10 -16 to the overall fractional uncertainty.Furthermore the thermal radiation eld in a cryogenic blackbody environment was modelled and a draft of a corresponding environment of the atoms was designed, which is suitable to be implemented in the strontium lattice clock of PTB.

•Jan 1, 2013•0 citations
Presently, the Stark effect contributes the largest source of uncertainty in a ytterbium optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock levels \ensuremathαclock=36.2612(7)  kHz (kV/cm)\ensuremath−2{\ensuremath{\alpha}}_{\mathrm{clock}}=36.2612(7)\text{ }\text{ }\mathrm{kHz}\text{ }(\mathrm{kV}/\mathrm{cm}{)}^{\ensuremath{-}2}\ensuremathαclock​=36.2612(7)  kHz (kV/cm)\ensuremath−2. The clock's uncertainty due to room temperature blackbody radiation is reduced by an order of magnitude to 3\ifmmode×\else\texttimes\fi10\ensuremath−173\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}3\ifmmode×\else\texttimes\fi10\ensuremath−17.
Optical lattice clocks, which are based on highly-forbidden1S0↔3P0transitions of ultracold alkaline-earth atoms confined in standing-wave optical potentials [1], offer exquisite frequency stability and uncertainty. We leverage these advantages to determine the sensitivity of a ytterbium optical lattice clock to external electric fields at 20 part-per-million (ppm) accuracy [2]. We describe an electrode design compatible with various neutral optical atomic clocks and capable of absolute electric field generation at the ppm level. Importantly, the result bounds the uncertainty of the ytterbium clock frequency due to room-temperature blackbody radiation at the level of 3×10-17.
The Stark shift due to blackbody radiation (BBR) is the key factor limiting the performance of many atomic frequency standards, with the BBR environment inside the clock apparatus being difficult to characterize at a high level of precision. Here we demonstrate an in-vacuum radiation shield that furnishes a uniform, well-characterized BBR environment for the atoms in an ytterbium optical lattice clock. Operated at room temperature, this shield enables specification of the BBR environment to a corresponding fractional clock uncertainty contribution of 5.5×10(-19). Combined with uncertainty in the atomic response, the total uncertainty of the BBR Stark shift is now 1×10(-18). Further operation of the shield at elevated temperatures enables a direct measure of the BBR shift temperature dependence and demonstrates consistency between our evaluated BBR environment and the expected atomic response.
The Stark shift of the ytterbium (Yb) optical clock transition due to room-temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room-temperature realization of the clock at ${10}^{\ensuremath{-}18}$ uncertainty requires a dynamic contribution to this static approximation. This dynamic term largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of 6s6p3P16s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}6s6p3P1​ and 5d6s3D15d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}5d6s3D1​, we report the clock shift due to an ideal 300 K blackbody environment to 0.05% precision.
A modification to a successfull technique to measure static differential polarizabilities of ultracold atoms and molecules is presented. Ultracold atoms are trapped in a magic wavelength optical lattice and transported into the field of a precision capacitor. The change of the transition frequency induced by the applied field, which is controlled to better than 10-4, is measured. For atomic clocks, the difference of the static polarizabilies of ground and excited state is closely related to their response to a blackbody radiation field, which is a significant contribution to the uncertainty budget of many atomic clocks.
Ytterbium lattice frequency standard is an outstanding optical clock with a demonstrated relative frequency accuracy of 3.4·10-16, presently limited by the uncertainty on the blackbody radiation (BBR), lattice polarizabilities and cold collisions shifts. In particular the BBR shift is looming as a major component in the uncertainty budget of many optical frequency standards. In fact the uncertainty on BBR systematic shift in Ytterbium atoms is due both to experimental and theoretical limits in the knowledge of the atomic system: presently Ytterbium has the largest theoretical uncertainty on the BBR shift. Then, both for atomic physics and metrology, new measurements of the Ytterbium atomic properties are strongly demanded, such as the determination of transition matrix elements, lifetimes, branching ratios, polarizabilities and hyperfine constants. In this work we present a set of new measurements for the radiative decay and for the cold collisions trap losses in laser-cooled Ytterbium atoms. These data are relevant to the blackbody radiation shift evaluation and to the cold collisions shift theory.
Optical clocks have the potential to be 100 times more accurate than current best cesium atomic clocks within a fraction of the averaging time.This corresponds to a fractional uncertainty of the clock frequency on the level of 10 -18 and requires highaccuracy knowledge of systematic frequency shifts, such that they can be avoided or corrected for.In strontium optical lattice clocks an ensemble of ultracold strontium atoms is conned in an optical lattice, to allow for spectroscopy of the reference transition 5s 2 1 S 0 5s5p 3 P 0 in the Lamb-Dicke regime.The by far largest systematic frequency shift of the strontium clock transition is caused by its high sensitivity to blackbody radiation (BBR).The knowledge of the resulting frequency shift limited the achievable clock uncertainty to about 1 × 10 -16 .In this thesis for the rst time an experimental approach was followed, to determine the sensitivity of the strontium clock transition to blackbody radiation.At an environmental temperature of 300 K the resulting frequency shift corresponds to 2.277 8(23) Hz.The achieved uncertainty contributes with 5 × 10 -18 to the fractional systematic uncertainty of the clock frequency.The determination is based on a precision measurement of the dierence of static polarizabilities of the two clock states ∆α dc = α(5s5p 3 P 0 ) -α(5s 2 1 S 0 ) = 4.078 73(11) × 10 -39 Cm 2 /V.For this the dc Stark shift of the clock transition has been measured in the accurately known electric eld of a precision plate capacitor, which has been developed in this work.The attained static polarizability dierence ∆α dc corresponds to the rst term of a power series of the sensitivity to BBR.Higher orders are accumulated as dynamic part of the BBR shift.Which has been modelled using ∆α dc and experimental data for other atomic properties.To interrogate the ultracold atoms in the electric eld a novel transport technique has been developed, which uses the magic wavelength (813 nm) optical lattice to convey the atoms.For this, the interference pattern is translated together with the foci of the far-detuned lattice beams, by simultaneous translation of the lattice optics.In this way ultracold atoms have been transported within 250 ms over 5 cm, or several Rayleigh ranges respectively without signicant atom loss or heating.In the course of this work the rst frequency measurement with the strontium lattice clock of Physikalisch-Technischen Bundesanstalt (PTB) has been performed.The frequency of the 87 Sr clock transition was measured to be 429 228 004 229 872.9(5)Hz.The strontium lattice clock itself contributed with 1.5 × 10 -16 to the overall fractional uncertainty.Furthermore the thermal radiation eld in a cryogenic blackbody environment was modelled and a draft of a corresponding environment of the atoms was designed, which is suitable to be implemented in the strontium lattice clock of PTB.