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Wuhan University Journal of Natural Sciences

Suppress Blackbody Radiation Shift with Two Clock Ytterbium Clock Transition

Jingjing Cheng, Kunliang Jiang, Lingxiang He

Published Sep 12, 2019• 1 citation
Publisher

Abstract

In order to suppress the blackbody radiation shift of ytterbium (Yb) lattice clock, we adopt the idea of the synthetic frequency by means of the two clock transitions which correspond to the static values of the scalar and tensor dipole polarizabilities with the AMBiT software package. We have obtained the synthetic wavelength around 647.7 nm and expected when the clock laser is working at the synthetic wavelength, the systematic uncertainty due to the BBR shift can be suppressed at the level of 10 −18 or even lower.

DOI
10.1007/s11859-019-1417-3

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In order to suppress the blackbody radiation shift of ytterbium (Yb) lattice clock, we adopt the idea of the synthetic frequency by means of the two clock transitions which correspond to the static values of the scalar and tensor dipole polarizabilities with the AMBiT software package. We have obtained the synthetic wavelength around 647.7 nm and expected when the clock laser is working at the synthetic wavelength, the systematic uncertainty due to the BBR shift can be suppressed at the level of 10 −18 or even lower.
Differential static polarizability and black body radiation (BBR) shift for Ytterbium ion (171Yb+) clock transition from ground state2S1/2to metastable state2D3/2corresponding to the wavelength 435.5 nm are calculated accurately for frequency standard applications. The values are found to be −7.5(5) × 10−40Jm2/V and −0.4(1) Hz, respectively, which are well in agreement with pre-available data and more accurate than the previous theoretical results. We further determine the values of dynamic polarizability of these states to find out the magic and tune-out wavelengths for the above mentioned clock transition.
Abstract We develop a method of synthetic frequency generation to construct an atomic clock with blackbody radiation (BBR) shift uncertainties below 10−19 at environmental conditions with a very low level of temperature control. The proposed method can be implemented for atoms and ions, which have two different clock transitions with frequencies ν 1 and ν 2 allowing to form a synthetic reference frequency ν syn = (ν 1 − ɛν 2)/(1 − ɛ), which is absent in the spectrum of the involved atoms or ions. Calibration coefficient ɛ can be chosen such that the temperature dependence of the BBR shift for the synthetic frequency ν syn has a local extremum at an arbitrary operating temperature T 0. This leads to a weak sensitivity of BBR shift with respect to the temperature variations near operating temperature T 0. As a specific example, the Yb+ ion is studied in detail, where the utilized optical clock transitions are of electric quadrupole (S → D) and octupole (S → F) type. In this case, temperature variations of ±7 K lead to BBR shift uncertainties of less than 10−19, showing the possibility to construct ultra-precise combined atomic clocks (including portable ones) without the use of cryogenic techniques.
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.
We develop a concept of atomic clocks where the blackbody radiation shift and its fluctuations can be suppressed by 1--3 orders of magnitude independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$) which are exposed to the same thermal environment, there exists a ``synthetic'' frequency ${\ensuremath{\nu}}_{\mathrm{syn}}$ $\ensuremath{\propto}$ (${\ensuremath{\nu}}_{1}\ensuremath{-}{\ensuremath{\epsilon}}_{12}{\ensuremath{\nu}}_{2}$) largely immune to the blackbody radiation shift. For example, in the case of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ it is possible to create a synthetic-frequency-based clock in which the fractional blackbody radiation shift can be suppressed to the level of ${10}^{\ensuremath{-}18}$ in a broad interval near room temperature ($300\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{K}$). We also propose a realization of our method with the use of an optical frequency comb generator stabilized to both frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$, where the frequency ${\ensuremath{\nu}}_{\mathrm{syn}}$ is generated as one of the components of the comb spectrum.
We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground 6s 2 1 S 0 and the first excited 6s6p 3 P o 0 states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the 6s 2 1 S 0 –6s6p 3 P o 0 transition. We determine (i) the first four magic wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the fourth magic wavelengths to be 551 nm, 465 nm and 413 nm. (ii) We re-evaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at T = 300 K being −1.41(17) Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) C 6 (6s 2 1 S 0 + 6s 2 1 S 0 ) = 1909(160), C 6 (6s 2 1 S 0 + 6s6p 3 P 0 ) = 2709(338) and C 6 (6s6p 3 P 0 + 6s6p 3 P 0 ) = 3886(360). Finally, we determine the atom-wall interaction coefficients (in a.u.), C 3 (6s 2 1 S 0 ) = 3.34 and C 3 (6s6p 3 P 0 ) = 3.68. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.
An optical lattice clock probes a spectrally narrow electronic transition in an ensemble of optically trapped, laser-cooled atoms, for use as a time and frequency standard. To date, several lattice clocks have been demonstrated with superior stability and accuracy compared to primary frequency standards based on microwave transitions. Yet, the question of which atomic system (including the element and isotope) performs best as a lattice clock remains unsettled. This thesis describes the first detailed investigation of an optical lattice clock using a spin-1/2 isotope of the ytterbium atom. A spin-1/2 system possesses several advantages over higher-spin systems, including a simplified level structure (allowing for straightforward manipulation of the nuclear spin state) and the absence of any tensor light shift from the confining optical lattice. Moreover, the ytterbium atom (Yb) stands among the leading lattice clock candidates, offering a high-performance optical clock with some degree of experimental simplicity. The frequency stability of the Yb clock is highlighted by resolving an ultra-narrow clock spectrum with a full-width at half-maximum of 1 Hz, corresponding to a record quality factor Q = ν0/Δν = 5 × 1014. Moreover, this system can be highly accurate, which is demonstrated by characterizing the Yb clock frequency at the 3 × 10-16 level of fractional uncertainty, with further progress toward a ten-fold improvement also presented. To reach this low level of uncertainty required careful consideration of important systematic errors, including the identification of the Stark-canceling wavelength, where the clock’s sensitivity to the lattice intensity is minimized, a precise determination of the static polarizability of the clock transition, and the measurement and control of atom-atom collisions.