Lifetime of the ${}^2{F}_{7/2}$ Level in ${\mathrm{Yb}}^{+}$ for Spontaneous Emission of Electric Octupole Radiation

We report a measurement of the radiative lifetime of the ${}^2{F}_{7/2}$ level of ${}^{171}{\mathrm{Yb}}^{+}$ that is coupled to the ${}^2{S}_{1/2}$ ground state via an electric octupole transition. The radiative lifetime is determined to be $4.98(25)\times {10}^7\mathrm{s}$, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.

Figure 1

Comparison of experimental (blue) and theoretical (red) values of the ${\mathrm{Yb}}^{+}$ excited ${}^2{F}_{7/2}$ state lifetime $\tau$. Previous experimental estimates [15, 16] were based on observed laser excitation events and a rate equation analysis. Theoretical values are given in Refs. [17, 18, 19, 20].

Figure 2

Investigation of the relative excitation strength of the ${}^{171}{\mathrm{Yb}}^{+}$ E3 transition. At different intensity settings of the probe laser, the quadratic Stark shift $\mathrm{\Delta }{\nu }_{\mathrm{QS}}$ and the resonant Rabi frequency $\mathrm{\Omega }$ are measured. Each Rabi frequency is obtained from a Rabi oscillation as shown in the inset for $\mathrm{\Omega }=2\pi \times 19.2(3)\mathrm{Hz}$ at $\mathrm{\Delta }{\nu }_{\mathrm{QS}}=477(1)\mathrm{Hz}$, where $p$ is the ${}^2{F}_{7/2}$ state excitation probability and $t$ the Rabi pulse duration. The observed damping of the Rabi oscillation is attributed to the ion temperature. Assuming a linear dependence between quadratic Stark shift and squared Rabi frequency yields the relative excitation strength $\xi ={\mathrm{\Omega }}^2/\mathrm{\Delta }{\nu }_{\mathrm{QS}}=30.3(9)\mathrm{Hz}$.