Nuclear spin quenching of the $^2S_{1/2}\rightarrow {^2}F_{7/2} $ electric octupole transition in $^{173}$Yb$^+$

Abstract

We report the coherent excitation of the highly forbidden $^2S_{1/2} \rightarrow {^2}F_{7/2}$ clock transition in the odd isotope $^{173}\mathrm{Yb}^+$ with nuclear spin $I = 5/2$, and reveal the hyperfine-state-dependent, nuclear spin induced quenching of this transition. The inferred lifetime of the $F_e = 4$ hyperfine state is one order of magnitude shorter than the unperturbed ${^2}F_{7/2}$ clock state of $^{171}\mathrm{Yb}^+$. This reduced lifetime lowers the required optical power for coherent excitation of the clock transition, thereby reducing the AC Stark shift caused by the clock laser. Using a 3-ion Coulomb crystal, we experimentally demonstrate an approximately 20-fold suppression of the AC Stark shift, a critical improvement for the scalability of future multi-ion $\mathrm{Yb}^+$ clocks. Furthermore, we report the $|^2S_{1/2},F_g=3\rangle~\rightarrow~|^2F_{7/2},F_e=6\rangle$ unquenched reference transition frequency as $642.11917656354(43)$ THz, along with the measured hyperfine splitting and calculated quadratic Zeeman sensitivities of the ${^2}F_{7/2}$ clock state. Our results pave the way toward multi-ion optical clocks and quantum computers based on $^{173}\mathrm{Yb}^+$.

Figures (16)

• Figure 1: Level scheme of the $^{173}\mathrm{Yb}^{+}$ ion. The 370 nm dipole transition is used for Doppler cooling and state detection. The 935 nm laser prevents population trapping in the $^2$D$_{3/2}$ state. A 467 nm laser excites the highly forbidden electric octupole transition. Laser light at 760 nm repumps the electron from the $^2$F$_{7/2}$ state. For spectroscopic measurements, the electron population can be prepared in the $|F_g=3, m_g=0,\pm3\rangle$ or $|F_g=2, m_g=0\rangle$ (red) of the $^2S_{1/2}$ state. The interrogated $^2$F$_{7/2}$ HF states are marked in green (coherent excitation) or blue (rapid adiabatic passage).
• Figure 2: Experimentally measured Rabi oscillations for clock transitions from $|^2S_{1/2}, F_g=3, m_g=0 \rangle$ ground state to $^2F_{7/2}$$F_e=2$ (blue), $F_e=4$ (orange) and $F_e=6$ (green) HF states. The experimental data (circle) is fitted with the Jaynes-Cumming model (solid line) with $\bar{n} = 17.6(1.4)$, leading to $\Omega^{(3\rightarrow2)}~=~2\pi~\times~6.74(5)$ Hz, $\Omega^{(3\rightarrow4)}= 2\pi~\times~30.12(36)$ Hz, and $\Omega^{(3\rightarrow6)}= 2\pi\times~6.78(5)$ Hz. The error bar shows the QPN. The quenched transition ($F_e=4$) can be driven at a much higher $\Omega$ with the same optical intensity.
• Figure 3: Experimentally measured clock resonances of a 3-ion Coulomb crystal with $10~\mathrm{\mu m}$ inter-ion spacing. The inset illustrates the laser intensity and ion positions (not to scale). The laser beam radius is $w = 30~\mathrm{\mu m}$, pulse time $\tau=55$ ms and $\Omega^{(3\rightarrow6)}\approx\Omega^{(3\rightarrow4)}= 2\pi \times 9.1(1.2)$ Hz. The relative intensity between the two measurements is $I^{(3\rightarrow6)}_\mathrm{Laser}/I^{(3\rightarrow4)}_\mathrm{Laser}=20.6(1.5)$. Referencing to the transition frequency of ion 2, $\nu_\mathrm{ion2}^{(F_g\rightarrow F_e)}$, we observe a differential AC Stark shift of $\nu_\mathrm{ion1}^{(3\rightarrow4)}=-0.9(4)$ Hz, $\nu_\mathrm{ion3}^{(3\rightarrow4)}=-4.2(4)$ Hz, $\nu_\mathrm{ion1}^{(3\rightarrow6)}=-25.8(4)$ Hz and $\nu_\mathrm{ion3}^{(3\rightarrow6)}=-93.3(4)$ Hz. Hence for a similarly Fourier-limited linewidth $\Delta\nu\approx16$ Hz, the transition from $F_g=3$ to $F_e=4$ state (Fig. 3a) requires less laser intensity than to the $F_e=6$ state (Fig. 3b), which results in a smaller AC Stark shift.
• Figure 4: Experimental setup. A $^{173}\mathrm{Yb}^{+}$ ion (blue sphere) is trapped in a linear Paul trap. The red arrow indicates the axial direction of the RF trap, which coincides with the $z$-axis. The blue arrow shows the propagation direction of the vertical 370 nm beam (370V) and the 467 nm beam. The polarization of both the 370V and 467 nm beams is aligned with the magnetic field (pink arrow). The angle between the spectroscopy beam and the trap axis, $\varphi$, is 90$^{\circ}$, and the angle between the magnetic field and the trap axis, $\alpha$, is approximately 26$^{\circ}$.
• Figure 5: Illustration of the Rabi frequency and transition rate for the $F_e=4, m_e=0 \rightarrow F_g=3$ case, with an E1 decay channel. Each Zeeman sublevel $m_e$ of the excited state has the same transition rate $\mathcal{R}^{(F_e \rightarrow F_g)}$, obtained by summing over the rates of all allowed decay channels to the ground state (here $r_0 + r_{1} + r_{-1}$).