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State-dependent potentials for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>S</mml:mi><mml:mn>0</mml:mn><mml:none /><mml:mprescripts /><mml:none /><mml:mn>1</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mn>0</mml:mn><mml:none /><mml:mprescripts /><mml:none /><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math> clock states of neutral ytterbium atoms
We present measurements of three distinctive state-dependent wavelengths for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition in ${}^{\text{174}}\text{Yb}$ atoms. Specifically, we determine two magic wavelengths at 652.281(21) and $542.502\phantom{\rule{0.16em}{0ex}}05(19)\phantom{\rule{0.16em}{0ex}}\text{THz}$, where the differential light shift on the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition vanishes, and one tune-out wavelength at $541.8325(5)\phantom{\rule{0.16em}{0ex}}\text{THz}$, where the polarizability of the $^{1}S_{0}$ ground …