High-accuracy optical clock based on the octupole transition in 171Yb+

Abstract: We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition 2S1/2(F=0) -> F7/2(F=3) in a single trapped 171Yb+ ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f136s2 configuration of the upper state. The electric quadrupole moment of the 2F7/2 state is measured as -0.041(5) e(a0)^2, where e is the elementary charge and a0 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 7.1x10^-17. The frequency is measured as 642 121 496 772 645.15(52) Hz.

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

This paper presents an intricate investigation into an optical frequency standard using the ${}^{171}\text{Yb}^+$ ion, capitalizing on the 467 nm electric-octupole transition ${}^2S_{1/2}(F=0)\rightarrow{}^2F_{7/2}(F=3)$. This research seeks to establish a high-precision optical clock with an impressively low sensitivity to frequency shifts induced by external fields, a critical advancement for timekeeping accuracy in metrology.

Key Findings and Methodology

The investigation rigorously measures various atomic parameters, including the electric-quadrupole moment and polarizability, to analyze the stability and accuracy of the optical clock. Critical achievements include:

• Electric-Quadrupole Moment: The state $^2F_{7/2}$ was measured to have a quadrupole moment of $-0.041(5)~ea^2_0$, underscoring its limited influence on transition frequency shifts from electric field gradients.
• Polarizability Measurements: A distinction was observed in both static and dynamic polarizability. The differential static scalar polarizability was calculated as $-1.3(6)\times10^{-40}$ J V$^{-2}$m$^2$, indicating minimal frequency variation due to static electric fields, which is a positive indicator for achieving high stability in the optical transition frequency.

Systematic Evaluations

The authors implemented a significant reduction in ac Stark shifts using a real-time extrapolation method, yielding an unperturbed transition frequency noted at $642,121,496,772,645.15(52)~\text{Hz}$. This frequency was achieved with a fractional uncertainty of $7.1\times10^{-17}$, a commendable enhancement over previous results. This minimization of perturbative effects showcases the potential of the octupole transition for precision timing applications where blackbody radiation and dc Stark shifts are typically pronounced.

Implications

The ${}^{171}\text{Yb}^+$ optical clock's heightened sensitivity to changes in the fine structure constant $\alpha$ underscores its relevance for fundamental physics tests, such as probing potential variations in $\alpha$. The confirmed reduced light shift and quadrupole moment further emancipate this frequency standard from influences that typically degrade precision, thus positioning it as a leading candidate for defining the SI second.

Future Directions

Prospectively, further refinement of this optical clock's accuracy is feasible through improved modeling of atomic interactions and enhancements in experimental techniques. Additionally, synergistic use of the quadrupole and octupole transitions may offset second-order frequency shifts due to environmental factors, leading toward a composite frequency standard with exceptional insensitivity to blackbody radiation.

In conclusion, this study illuminates a technically meticulous path towards realizing an optical clock rooted in the properties of the electric-octupole transition in ${}^{171}\text{Yb}^+$, contributing siginificantly to the domain of atomic clocks with unprecedented accuracy and potential applications in timekeeping technology and complementary tests of physical constants.