Measurement of the tune-out wavelength for Cs133 at 880 nm

Abstract

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