Measurement of the ${}^{87}\mathrm{Rb} D$-line vector tune-out wavelength

We report a precision measurement of a tune-out wavelength for ${}^{87}\mathrm{Rb}$ using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using ${\sigma }_{-}$ polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.

Figure 1

Electric polarizability of ${}^{87}\mathrm{Rb}$ in the $F=2, m=2$ ground state, as a function of optical wavelength. The red curve shows the case of linearly polarized light, and exhibits a tune-out wavelength near 790 nm. The blue curve shows the case of ${\sigma }_{-}$ polarized light, with a tune-out wavelength near 785 nm.

Figure 2

Tune-out measurement data. For each of the points in the main graph, an interferometric measurement is performed to determine $\kappa =\varphi /P$, where $\varphi$ is the interferometer phase and $P$ is the peak power of the Stark beam pulses. The inset graphs show example plots of the interferometer signal vs power, from which $\kappa$ is determined via a fit to the form of Eq. (10). The scatter of the points illustrates our typical measurement noise, and the error bars for $\kappa$ are estimated as the offset needed to double the goodness of fit parameter ${\chi }^2$. The $\kappa$ data in the main graph are fit to a line, and the $x$ intercept of 785.1525 nm is taken as the tune-out wavelength value.