High-Accuracy Optical Clock Based on the Octupole Transition in ${}^{171}\mathrm{Yb}^{+}$

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition ${}^{2}S_{1/2}(F=0)\to {}^{2}F_{7/2}(F=3)$ in a single trapped ${}^{171}\mathrm{Yb}^{+}$ ion. The extraordinary features of this transition result from the long natural lifetime and from the $4f^{13}6s^2$ configuration of the upper state. The electric-quadrupole moment of the ${}^{2}F_{7/2}$ state is measured as $-0.041(5)e{a}_0^2$, where $e$ is the elementary charge and $a_0$ the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of $7.1\times {10}^{-17}$. The frequency is measured as 642 121 496 772 645.15(52) Hz.

Figure 1

Partial level scheme of ${}^{171}\mathrm{Yb}^{+}$. The solid black arrow indicates the octupole transition under investigation. The cooling transition is shown by the dashed arrow, and solid gray arrows represent repumping transitions. Relevant spontaneous decay paths are indicated by dotted arrows.

Figure 2

Excitation spectrum of the ${}^{2}S_{1/2}(F=0)\to {}^{2}F_{7/2}(F=3,m_F=0)$ transition obtained with a probe pulse duration of 120 ms. For each laser detuning step, 20 measurement cycles were performed. The solid line shows the theoretical line shape for $\pi$-pulse excitation.

Figure 3

Quadrupole shift of the octupole transition frequency resulting from an applied electric field gradient, measured using an interleaved servo technique (see text). The solid line is a linear least-square fit through the origin. The error bars denote statistical uncertainty.

Figure 4

Fractional Allan deviation ${\sigma }_y(\tau )$ of (a) the absolute frequency measurement versus the fountain clock CSF1 and (b) the light-shift-induced offset frequency ${\nu }_{\mathrm{offset}}$ (see text) in measurement 5 in Table .