Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation.

R Lange,A Surzhykov,E Peik,A A Peshkov,Chr Tamm,N Huntemann

doi:10.1103/physrevlett.127.213001

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.

Highlights

Coherent interrogation of trapped particles facilitates the determination of atomic transition frequencies with high accuracy, recently demonstrated below the 10−18 fractional uncertainty level [1]
We report a measurement of the radiative lifetime of the 2F7=2 level of 171Ybþ that is coupled to the 2S1=2 ground state via an electric octupole transition
The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift

Summary

Published by the American Physical Society

Independence from the electric field amplitude E0 of the laser at the ion position can be achieved by simultaneously measuring the differential quadratic Stark shift ΔνQS 1⁄4 E20Δαegðν0Þ=ð2hÞ and defining the relative excitation strength ξ 1⁄4 Ω2=ΔνQS This quantity together with the differential polarizability Δαeg at the transition frequency ν0, obtained independently from experiments or theory, permitspthffiffieffiffiffiffidffiffieffiffiffitffieffiffirffimffiffiffiffiiffinffiffiffiaffiffitffiiffion of the matrix element: jVegj 1⁄4 1=ð2πÞ hξΔαegðν0Þ=2. The matrix element of the E3 transition of 171Ybþ is determined from the relative excitation strength and the differential polarizability to be jVegðE3Þj 1⁄4 2.62ð7Þ × 10−37 Jm=V: In order to use this value for a determination of the natural lifetime τ, we recall general expressions from atomic structure theory. The matrix element for the coupling of a photon to a many-electron atom can be expressed as

Xεαq eikrq γgFgMg

Findings

Fg Je