Measurement of the tune-out wavelength for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Cs</mml:mi><mml:mprescripts /><mml:none /><mml:mn>133</mml:mn></mml:mmultiscripts></mml:math> at 880 nm

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between ${D}_{1}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in ground hyperfine state $(F=3,{m}_{F}=+3)$. At frequency-dependent scalar polarizability is zero leading to ac Stark shift. measure as function wavelength using Kapitza-Dirac scattering Bose-Einstein condensate one-dimensional optical lattice, determine be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this we ratio reduced matrix elements ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement factor 10 over previous results derived from excited-state lifetime measurements. use present benchmark test high-precision theory.