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arXiv:0802.0222 · Physical Review Letters

Optical Lattice Induced Light Shifts in an Yb Atomic Clock

Zeb W. Barber, J. E. Stalnaker, N. Lemke, N. Poli, Chris W. Oates, Tara M. Fortier, Scott A. Diddams, Leo W. Hollberg, Chad Hoyt, А. В. Тайченачев, Valeriy I. Yudin

Published Mar 11, 2008• 160 citations
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Abstract

We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).

DOI
10.1103/physrevlett.100.103002

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We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).
We report calculations assessing the ultimate precision of an atomic clock based on the 578 nm $6{}^{1}{S}_{0}\ensuremath{\rightarrow}6{}^{3}{P}_{0}$ transition in Yb atoms confined in an optical lattice trap. We find that this transition has a natural linewidth less than 10 mHz in the odd Yb isotopes, caused by hyperfine coupling. The shift in this transition due to the trapping light acting through the lowest order ac polarizability is found to become zero at the magic trap wavelength of about 752 nm. The effects of Rayleigh scattering, multipole polarizabilities, vector polarizability, and hyperfine induced electronic magnetic moments can all be held below 1 mHz (about one part in 1018).{10}^{18}).1018). In the case of the hyperpolarizability, however, larger shifts due to nearly resonant terms cannot be ruled out without an accurate measurement of the magic wavelength.
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.
We present measurements of three distinctive state-dependent wavelengths for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition in 174Yb{}^{\text{174}}\text{Yb}174Yb atoms. Specifically, we determine two magic wavelengths at 652.281(21) and 542.50205(19)THz542.502\phantom{\rule{0.16em}{0ex}}05(19)\phantom{\rule{0.16em}{0ex}}\text{THz}542.50205(19)THz, where the differential light shift on the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition vanishes, and one tune-out wavelength at 541.8325(5)THz541.8325(5)\phantom{\rule{0.16em}{0ex}}\text{THz}541.8325(5)THz, where the polarizability of the 1S0^{1}S_{0}1S0​ ground state exhibits a zero crossing. The two magic wavelengths are identified by spectroscopically interrogating cold 174Yb{}^{\text{174}}\text{Yb}174Yb atoms on the clock transition in a one-dimensional optical lattice. The ground-state tune-out wavelength is determined via a parametric heating scheme. With a simple empirical model, we then extrapolate the ground- and excited-state polarizability over a broad range of wavelengths in the visible spectrum.
We report an uncertainty evaluation of an171Yb optical lattice clock with a total fractional uncertainty of 3.6 × 10-16, which is mainly limited by the lattice-induced light shift and the blackbody radiation shift. Our evaluation of the lattice-induced light shift, the density shift, and the second-order Zeeman shift is based on an interleaved measurement where we measure the frequency shift using the alternating stabilization of a clock laser to the 6s21S0-6s6p3P0clock transition with two different experimental parameters. In the present evaluation, the uncertainties of two sensitivity coefficients for the lattice-induced hyperpolarizability shift d incorporated in a widely used light shift model by RIKEN and the second-order Zeeman shift aZare improved compared with the uncertainties of previous coefficients. The hyperpolarizability coefficient d is determined by investigating the trap potential depth and the light shifts at the lattice frequencies near the two-photon transitions 6s6p3P0-6s8p3P0, 6s8p3P2, and 6s5f3F2. The obtained values are d=-1.1(4) μHz and aZ=-6.6(3) Hz/mT2. These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.
The light-induced frequency shift due to hyperpolarizability (i.e., terms of second-order in intensity) is studied for a forbidden optical transition, J = 0 --> J = 0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular, or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.
We report direct single-laser excitation of the strictly forbidden (6s2)1S0 <--> (6s6p)3P0 clock transition in 174Yb atoms confined to a 1D optical lattice. A small (approximately 1.2 mT) static magnetic field was used to induce a nonzero electric dipole transition probability between the clock states at 578.42 nm. Narrow resonance linewidths of 20 Hz (FWHM) with high contrast were observed, demonstrating a resonance quality factor of 2.6 x 10(13). The previously unknown ac Stark shift-canceling (magic) wavelength was determined to be 759.35 +/- 0.02 nm. This method for using the metrologically superior even isotope can be easily implemented in current Yb and Sr lattice clocks and can create new clock possibilities in other alkaline-earth-like atoms such as Mg and Ca.