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arXiv:physics/0309044 · Physical Review Letters

Spectroscopy of the S01−P03 Clock Transition of Sr87 in an Optical Lattice

Masao Takamoto, Hidetoshi Katori

Published Nov 25, 2003• 161 citations
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Abstract

We report on the spectroscopy of the $5{s}^{2}\text{ }^{1}S_{0}(F=9/2)\ensuremath{\rightarrow}5s5p\text{ }^{3}P_{0}(F=9/2)$ clock transition of $^{87}\mathrm{S}\mathrm{r}$ atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be $813.5\ifmmode\pm\else\textpm\fi{}0.9\text{ }\mathrm{n}\mathrm{m}$.

DOI
10.1103/physrevlett.91.223001

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We report on the spectroscopy of the 5s2 1S0(F=9/2)\ensuremath→5s5p 3P0(F=9/2)5{s}^{2}\text{ }^{1}S_{0}(F=9/2)\ensuremath{\rightarrow}5s5p\text{ }^{3}P_{0}(F=9/2)5s2 1S0​(F=9/2)\ensuremath→5s5p 3P0​(F=9/2) clock transition of 87Sr^{87}\mathrm{S}\mathrm{r}87Sr atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be 813.5\ifmmode±\else\textpm\fi0.9 nm813.5\ifmmode\pm\else\textpm\fi{}0.9\text{ }\mathrm{n}\mathrm{m}813.5\ifmmode±\else\textpm\fi0.9 nm.
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 report the experimental measurement of a magic wavelength at 476.823 62(8) nm for the ${}^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}5{s}^{2}{\phantom{\rule{0.1em}{0ex}}}^{1}{\mathrm{S}}_{0}\ensuremath{\rightarrow}5s5p{\phantom{\rule{0.1em}{0ex}}}^{3}{\mathrm{P}}_{0}$ clock transition. The magic wavelength is determined through an ac Stark shift spectroscopy of atoms in an optical dipole trap. The value is in reasonable agreement with the theoretical prediction, differing by 0.061(54) nm. This magic wavelength, being shorter than the commonly used one at 813 nm, will be important for applications such as Bragg-pulse matter-wave interferometry involving both clock states. This work also paves the way for quantum simulation with a shorter lattice constant.
With ultracold 87Srconfined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to date of the 1S0-3P0 optical clock transition with a detailed analysis of systematic shifts (19 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 869 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its hertz-level linewidth characterized by an octave-spanning femtosecond frequency comb.
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We optically excite the electronic state 3s3p ^{3}P_{0} in ^{24}Mg atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, -206.6(2.0) MHz/T^{2}, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.
With the aid of an optical frequency divider based on an optical frequency comb, the frequency of a laser at 431 nm is divided from a cavity-stabilized laser at 578 nm. Using the frequency-stabilized 431 nm laser, we observe a 2.5 kHz linewidth 4f146s2 1S0−4f135d6s2 (J = 2) transition of 171Yb atoms trapped in an optical lattice. By measuring the lattice-induced frequency shift, we determine the magic wavelength of the optical lattice for the 431 nm transition to be 797.97(20) nm. The frequency of the 431 nm transition is measured to be 695 171 054 856.9(1.1) kHz by referencing to the 1S0−3P0 transition at 578 nm of Yb atoms.