The Thorium-Isomer: Heartbeat for a Nuclear Clock

Abstract

More than 6,000 years ago, Sumerians used light to measure time. They built sundials. Nowadays, laser light forms the basis of the most precise timekeepers: the most accurate time and frequency measurements are performed with optical atomic clocks, presently reaching an accuracy for the deviation of a time measurement by 1 second in about 33 billion years. In general, a clock consists of an oscillator and a counting device for the frequency of the clock oscillation. Today’s definition of the SI unit “second” uses a microwave transition in the element cesium, which is particularly suited, as it has only one natural isotope, 133Cs, and an atom beam can easily be produced due to the low evaporation temperature. About 105 times higher frequencies are used in optical atomic clocks, still under development in the laboratory, while already reaching relative uncertainties of about 1 x 10−18. In 2003, in order to further reduce these uncertainties, Peik and Tammm [1] proposed using a nuclear transition instead of an atomic shell state for time measurements. Due to the small nuclear moments (corresponding to the different dimensions of atoms and nuclei) and thus due to the very small coupling to external perturbating electromagnetic fields, a so-called nuclear clock promises an accordingly reduced vulnerability to external perturbations affecting the presently best optical atomic clocks. This enables a potentially more accurate operation of a nuclear clock. In the concept of a nuclear clock [1, 2] (see Figure 1), a narrow-band laser will resonantly excite the nuclear clock transition, while the oscillations of the laser light will be counted using a frequency comb. After a certain number of oscillations, given by the frequency of the nuclear transition, one second has elapsed. This corresponds to the functional principle of optical atomic clocks, replacing their atomic shell transition by a nuclear transition. The necessity of a direct laser excitation results in strong constraints to applicable nuclear clock transitions. Their energy has to be low enough to be accessible with existing laser technology, while simultaneously exhibiting a linewidth as narrow as possible. As the linewidth is determined by the lifetime of the excited nuclear state, the latter has to be long enough (i.e., an isomeric state) to allow for highly stable clock operation. So far, only the first (isomeric) excited state of the actinide isotope 229Th qualifies as a promising candidate for a nuclear clock, due to its exceptionally low excitation energy allowing for direct laser excitation. The existence of this state was indirectly conjectured already in 1976 from γ spectroscopic measurements to determine the nuclear structure of 229Th [3]. Since then, nuclear physicists have searched for direct decay signatures of this exotic nuclear state. By the current state of knowledge, the excitation energy of this “thorium isomer” 229mTh amounts to only 8.28 ± 0.17 eV (corresponding to a wavelength of 149.7 ± 3.1 nm) [4] and as such is the lowest nuclear excitation among all of the about 3,300 known nuclides with about 184,000 presently known excited nuclear states. Moreover, 229mTh exhibits a lifetime of a few 103 seconds, according to τ = ћ/ΔE, resulting in an extremely narrow relative linewidth ΔE/E∼10−20 for its ground-state transition. Besides the high resilience against external perturbations, this represents another attractive property in favor of constructing a Thorium nuclear clock that could rival today’s most advanced optical atomic clocks. Figure 2 im-