Measurement of the tune-out wavelength for $^{133}$Cs at $880$ nm

TL;DR

This paper precisely measures the tune-out wavelength for cesium-133 at 880 nm, providing a benchmark for high-precision atomic theory and improving previous measurements by a factor of ten.

Contribution

The authors accurately determine the tune-out wavelength for $^{133}$Cs and extract matrix element ratios, serving as a benchmark test for atomic theory.

Findings

Tune-out wavelength measured as 880.21790(40) nm.

Ratio of reduced matrix elements determined as 1.9808(2).

Improved measurement precision by a factor of 10.

Abstract

We perform a measurement of the tune-out wavelength, $\lambda_{0}$, between the $D_{1}$, $6^2S_{1/2}\rightarrow6^2P_{1/2}$, and $D_{2}$, $6^2S_{1/2}\rightarrow6^2P_{3/2}$, transitions for $^{133}$Cs in the ground hyperfine state $(F=3, m_{F}=+3)$. At $\lambda_{0}$, 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 $^{133}$Cs Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be $\lambda_{0}=880.21790(40)_{\textrm{stat}}(8)_{\textrm{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be $\left|\left<{6P_{3/2}\| d\|6S_{1/2}}\right>\right|^{2}\left|\left<{6P_{1/2}\| d\|6S_{1/2}}\right>\right|^{2}=1.9808(2)$. 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.