[Paper Review] Lifetime of the $^2F_{7/2}$ level in Yb$^+$ for spontaneous emission of electric octupole radiation

R. Lange, A. A. Peshkov+4 more|PubMed|Jul 23, 2021

Atomic and Molecular Physics1 references4 citations

TL;DR

This paper presents a precise measurement of the radiative lifetime of the $^2F_{7/2}$ metastable state in $^{171}$Yb$^+$, which decays via electric octupole (E3) transition. By coherently driving the transition and simultaneously measuring the Rabi frequency and quadratic Stark shift, the authors extract the transition matrix element and determine the lifetime as $4.98(25)\times10^7$ s (1.58(8) years), reducing uncertainty by an order of magnitude compared to prior estimates.

ABSTRACT

We report a measurement of the radiative lifetime of the ^{2}F_{7/2} level of ^{171}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)×10^{7} 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.

Motivation & Objective

• To determine the radiative lifetime of the $^2F_{7/2}$ state in $^{171}$Yb$^+$ with high precision, as this state decays via an electric octupole (E3) transition with an exceptionally long natural lifetime.
• To overcome the challenges of direct decay measurement in long-lived states, which are dominated by competing processes like collisions and off-resonant light, especially when lifetimes exceed seconds.
• To develop and apply a method that eliminates dependence on laser intensity by simultaneously measuring the resonant Rabi frequency and the quadratic Stark shift, enabling accurate extraction of the transition matrix element.
• To provide a benchmark for atomic structure calculations and to support high-precision tests of fundamental symmetries and optical clock development.
• To enable future studies of hyperfine quenching effects in other Yb isotopes, particularly $^{173}$Yb$^+$, by establishing a reference for the unperturbed E3 decay lifetime.

Proposed method

• The experiment uses a single trapped $^{171}$Yb$^+$ ion coherently driven by a resonant laser to induce Rabi oscillations between the $^2S_{1/2}$ ground state and the $^2F_{7/2}$ excited state.
• The Rabi frequency $\Omega$ is measured from the oscillation of the population between the two levels, providing a direct measure of the transition matrix element.
• Simultaneously, the quadratic Stark shift $\Delta\nu_{\text{QS}}$ is measured as a function of laser intensity to eliminate systematic dependence on $E_0$.
• The relative excitation strength $\xi = \Omega^2 / \Delta\nu_{\text{QS}}$ is used to extract the matrix element $|V_{eg}|$ via the relation $|V_{eg}| = \frac{1}{2\pi} \sqrt{h \xi \Delta\alpha_{eg}(\nu_0)/2}$, where $\Delta\alpha_{eg}$ is the differential polarizability at the transition frequency.
• The natural lifetime $\tau$ is then calculated from Fermi’s golden rule using the derived matrix element and known atomic parameters, including the fine structure constant and angular momentum coupling.
• The method avoids theoretical modeling of the matrix element and is robust against intensity fluctuations, making it suitable for highly forbidden transitions.

Experimental results

Research questions

• RQ1 What is the precise radiative lifetime of the $^2F_{7/2}$ state in $^{171}$Yb$^+$, which decays via an electric octupole (E3) transition?
• RQ2 Can the transition matrix element for a highly forbidden E3 transition be extracted with high precision without relying on theoretical models?
• RQ3 How can competing decay processes and laser intensity fluctuations be mitigated in lifetime measurements of long-lived metastable states?
• RQ4 What is the impact of hyperfine interactions on the E3 decay lifetime in $^{173}$Yb$^+$, and how does the measured lifetime in $^{171}$Yb$^+$ serve as a reference?
• RQ5 To what extent can this method be generalized to other systems with long-lived states, such as highly charged ions or alkaline-earth ions?

Key findings

• The radiative lifetime of the $^2F_{7/2}$ state in $^{171}$Yb$^+$ is measured to be $4.98(25)\times10^7$ s, corresponding to 1.58(8) years, with a relative uncertainty of 5%.
• This result reduces the relative uncertainty in the lifetime by one order of magnitude compared to previous experimental estimates, which were based on rate equation analysis of laser excitation events.
• The measurement is the first precise determination of an electric octupole (E3) radiative lifetime and represents the longest experimentally determined natural lifetime of an electronic state to date.
• The method's immunity to laser intensity fluctuations and its reliance on simultaneous Rabi and Stark shift measurements enable high-precision extraction of the transition matrix element without theoretical input.
• The measured lifetime serves as a benchmark for atomic structure calculations and provides a reference for studying hyperfine quenching effects in $^{173}$Yb$^+$, where the lifetime is expected to be significantly shortened due to nuclear electric quadrupole coupling.
• The approach is generalizable to other systems with long-lived metastable states, such as $^{175}$Lu$^+$, Pb$^{2+}$, alkaline-earth ions, and highly charged ions, supporting future optical clock development and tests of fundamental symmetries.