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arXiv:1710.00339 · Journal of Physics B Atomic Molecular and Optical Physics

Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the 6S 1/2 5D 3/2 clock transition in Yb +

A Roy, S De, Bindiya Arora, B K Sahoo

Published Sep 29, 2017• 23 citations
arXivHTMLPDF

Abstract

Abstract We present precise values of the dipole polarizabilities ( α ) of the ground [ 4 f 14 6 s ] 2 S 1 / 2 and metastable [ 4 f 14 5 d ] 2 D 3 / 2 states of Yb + , that are important in reducing systematics in the clock frequency of the [ 4 f 14 6 s ] 2 S 1 / 2 → [ 4 f 14 5 d ] 2 D 3 / 2 transition. The static values of α for the ground and [ 4 f 14 5 d ] 2 D 3 / 2 states are estimated to be 9.8 ( 1 ) × 10

DOI
10.1088/1361-6455/aa8bae

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arXiv:1208.0552•Physical Review A•Nov 29, 2012•68 citations
Abstract We present precise values of the dipole polarizabilities ( α ) of the ground [ 4 f 14 6 s ] 2 S 1 / 2 and metastable [ 4 f 14 5 d ] 2 D 3 / 2 states of Yb + , that are important in reducing systematics in the clock frequency of the [ 4 f 14 6 s ] 2 S 1 / 2 → [ 4 f 14 5 d ] 2 D 3 / 2 transition. The static values of α for the ground and [ 4 f 14 5 d ] 2 D 3 / 2 states are estimated to be 9.8 ( 1 ) × 10
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.
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.
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.
The zero crossing of the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ clock transition in 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ has been determined to be 459.1614(28)THz459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}459.1614(28)THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.
The polarizabilities of the three lowest states of the beryllium atom are determined from a large basis configuration interaction calculation. The polarizabilities of the 2s22{s}^{2}2s2 1Se{}^{1}{S}^{e}1Se ground state (37.7337.7337.73a03{a}_{0}^{3}a03​) and the 2s2p2s2p2s2p 3P0o{}^{3}{P}_{0}^{o}3P0o​ metastable state (39.0439.0439.04a03{a}_{0}^{3}a03​) are found to be very similar in size and magnitude. This leads to an anomalously small blackbody radiation shift at 300300300 K of $\ensuremath{-}$0.018(4)0.018(4)0.018(4) Hz for the 2s22{s}^{2}2s2 1Se{}^{1}{S}^{e}1Se--2s2p2s2p2s2p 3P0o{}^{3}{P}_{0}^{o}3P0o​ clock transition. Magic wavelengths for simultaneous trapping of the ground and metastable states are also computed.
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.