Energy of the ^{229}Th Nuclear Clock Isomer Determined by Absolute γ-ray Energy Difference

Controlling 229Th isomeric state population in a VUV transparent crystal

The radioisotope thorium-229 (229Th) is renowned for its extraordinarily low-energy, long-lived nuclear first-excited state. This isomeric state can be excited by vacuum ultraviolet (VUV) lasers and 229Th has been proposed as a reference transition for ultra-precise nuclear clocks. To assess the feasibility and performance of the nuclear clock concept, time-controlled excitation and depopulation of the 229Th isomer are imperative. Here we report the population of the 229Th isomeric state through resonant X-ray pumping and detection of the radiative decay in a VUV transparent 229Th-doped CaF2 crystal. The decay half-life is measured to 447(25) s, with a transition wavelength of 148.18(42) nm and a radiative decay fraction consistent with unity. Furthermore, we report a new "X-ray quenching" effect which allows to de-populate the isomer on demand and effectively reduce the half-life. Such controlled quenching can be used to significantly speed up the interrogation cycle in future nuclear clock schemes.

Laser spectroscopy of triply charged 229Th isomer for a nuclear clock

Thorium-229 (229Th) possesses an optical nuclear transition between the ground state (229gTh) and low-lying isomer (229mTh). A nuclear clock based on this nuclear-transition frequency is expected to surpass existing atomic clocks owing to its insusceptibility to surrounding fields1-5. In contrast to other charge states, triply charged 229Th (229Th3+) is the most suitable for highly accurate nuclear clocks because it has closed electronic transitions that enable laser cooling, laser-induced fluorescence detection and state preparation of ions1,6-8. Although laser spectroscopic studies of 229Th3+ in the nuclear ground state have been performed8, properties of 229mTh3+, including its nuclear decay lifetime that is essential to specify the intrinsic linewidth of the nuclear-clock transition, remain unknown. Here we report the trapping of 229mTh3+ continuously supplied by a 233U source and the determination of nuclear decay half-life of the isolated 229mTh3+ to be1,400 - 300 + 600 s through nuclear-state-selective laser spectroscopy. Furthermore, by determining the hyperfine constants of 229mTh3+, we reduced the uncertainty of the sensitivity of the 229Th nuclear clock to variations in the fine-structure constant by a factor of four. These results offer key parameters for the 229Th3+ nuclear clock and its applications in the search for new physics.

Structures and Properties of High-Concentration Doped Th:CaF2 Single Crystals for Solid-State Nuclear Clock Materials

Thorium-doped vacuum ultraviolet (VUV) transparent crystals is a promising candidate for establishing a solid-state nuclear clock. Here, we report the research results on high-concentration doping of 232Th:CaF2 single crystals. The structures, defects, and VUV transmittance performances of highly doped Th:CaF2 crystals are investigated by theoretical and experimental methods. The defect configurations formed by Th and the charge compensation mechanism (Ca vacancy or interstitial F atoms) located at its first nearest neighbor position are mainly considered and studied. The preferred defect configuration is identified according to the doping concentration dependence of structural changes caused by the defects and the formation energies of the defects at different Ca or F chemical potentials. The cultivated Th:CaF2 crystals maintain considerable high VUV transmittance levels while accommodating high doping concentrations, showcasing an exceptional comprehensive performance. The transmittances of 1-mm-thick samples with doping concentrations of 1.91 × 1020 and 2.76 × 1020 cm-3 can reach ∼62% and 53% at 150 nm, respectively. The VUV transmittance exhibits a weak negative doping concentration dependence. The system factors that may cause distortion and additional deterioration of the VUV transmittance are discussed. Balancing and controlling the impacts of various factors will be of great significance for fully exploiting the advantages of Th:CaF2 and other Th-doped crystals for a solid-state nuclear optical clock.

Effects of Electrons on Nuclear Clock Transition Frequency in ^{229}Th Ions

We perform calculations of the energy shift of the nuclear clock transition frequency ^{229}Th as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant, for example, removing one electron from the atom leads to relative shift of the nuclear frequency ∼10^{-7}, which is 12 orders of magnitude larger than the expected relative uncertainty of the nuclear clock transition frequency (∼10^{-19}). This leads to the difference of the nuclear clock frequencies in Th IV, Th III, Th II, and Th I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.

Observation of the radiative decay of the 229Th nuclear clock isomer

The radionuclide thorium-229 features an isomer with an exceptionally low excitation energy that enables direct laser manipulation of nuclear states. It constitutes one of the leading candidates for use in next-generation optical clocks1-3. This nuclear clock will be a unique tool for precise tests of fundamental physics4-9. Whereas indirect experimental evidence for the existence of such an extraordinary nuclear state is substantially older10, the proof of existence has been delivered only recently by observing the isomer's electron conversion decay11. The isomer's excitation energy, nuclear spin and electromagnetic moments, the electron conversion lifetime and a refined energy of the isomer have been measured12-16. In spite of recent progress, the isomer's radiative decay, a key ingredient for the development of a nuclear clock, remained unobserved. Here, we report the detection of the radiative decay of this low-energy isomer in thorium-229 (229mTh). By performing vacuum-ultraviolet spectroscopy of 229mTh incorporated into large-bandgap CaF2 and MgF2 crystals at the ISOLDE facility at CERN, photons of 8.338(24) eV are measured, in agreement with recent measurements14-16 and the uncertainty is decreased by a factor of seven. The half-life of 229mTh embedded in MgF2 is determined to be 670(102) s. The observation of the radiative decay in a large-bandgap crystal has important consequences for the design of a future nuclear clock and the improved uncertainty of the energy eases the search for direct laser excitation of the atomic nucleus.

Below-threshold harmonic generation in gas-jets for Th-229 nuclear spectroscopy

The generation of below-threshold harmonics in gas-jets constitutes a promising path towards optical frequency combs in the vacuum ultra-violet (VUV) spectral range. Of particular interest is the 150 nm range, which can be exploited to probe the nuclear isomeric transition of the Thorium-229 isotope. Using widely available high-power, high-repetition-rate Ytterbium-based laser sources, VUV frequency combs can be generated through the process of below-threshold harmonic generation, in particular 7^th harmonic generation of 1030 nm. Knowledge about the achievable efficiencies of the harmonic generation process is crucial for the development of suitable VUV sources. In this work, we measure the total output pulse energies and conversion efficiencies of below-threshold harmonics in gas-jets in a phase-mismatched generation scheme using Argon and Krypton as nonlinear media. Using a 220 fs, 1030 nm source, we reach a maximum conversion efficiency of 1.1 × 10^-5 for the 7^th harmonic (147 nm) and 0.78 × 10^-4 for the 5^th harmonic (206 nm). In addition, we characterize the 3^rd harmonic of a 178 fs, 515 nm source with a maximum efficiency of 0.3%.

Trap-Induced ac Zeeman Shift of the Thorium-229 Nuclear Clock Frequency

We examine the effect of a parasitic rf magnetic field, attributed to ion trapping, on the highly anticipated nuclear clock based on ^{229}Th^{3+} [C. J. Campbell et al., Phys. Rev. Lett. 108, 120802 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.120802]. The rf magnetic field induces an ac Zeeman shift to the clock frequency. As we demonstrate, this shift threatens to be the dominant systematic frequency shift for the clock, exceeding other systematic frequency shifts and the projected systematic uncertainty of the clock by orders of magnitude. We propose practical means to suppress or eliminate this shift.

Ground-State g Factor of Highly Charged ^{229}Th Ions: An Access to the M1 Transition Probability between the Isomeric and Ground Nuclear States

A method is proposed to determine the M1 nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying (∼8  eV) first isomeric state and the ground state of ^{229}Th from a measurement of the ground-state g factor of few-electron ^{229}Th ions. As a tool, the effect of nuclear hyperfine mixing in highly charged ^{229}Th ions such as ^{229}Th^{89+} or ^{229}Th^{87+} is used. The ground-state-only g-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like ^{229}Th ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.

Exciting the Isomeric ^{229}Th Nuclear State via Laser-Driven Electron Recollision

We propose a new approach to excite the isomeric ^{229}Th nuclear state, which has attracted much attention recently as a potential "nuclear clock." Our approach is based on a laser-driven electron recollision process, the core process of strong-field atomic physics. Bringing together knowledge of recollision physics and of the related nuclear physics, we calculate the isomeric excitation probability. This new approach does not require precise knowledge of the energy of the isomeric state. The excitation is well timed which may be exploited to control the coherence of the isomeric state. Experimental realization is within reach using tabletop laser systems.

Shape and electromagnetic properties of the 229mTh isomer

We examine the physical conditions, and specifically the role of the quadrupole-octupole deformation, for the emergence of the 8 eV “clock” isomer 229mTh. Our nuclear structure model suggests that such an extremely low-energy state can be the result of a very fine interplay between the shape and single-particle (s.p.) dynamics in the nucleus. We find that the isomer can only appear in a rather limited region of quadrupoleoctupole deformation space close to a line along which the ground-state and isomer s.p. orbitals 5/2[633] and 3/2[631], respectively, cross each other providing the isomer-formation quasi-degeneracy condition. The crucial role of the octupole deformation in the formation mechanism is pointed out. Our calculations within the outlined deformation region show a smooth behaviour of the 229Th electromagnetic properties, including the isomer decay rate, allowing for their more precise theoretical determination

Absolute X-ray energy measurement using a high-accuracy angle encoder

This paper presents an absolute X-ray photon energy measurement method that uses a Bond diffractometer. The proposed system enables the prompt and rapid in situ measurement of photon energies over a wide energy range. The diffractometer uses a reference silicon single-crystal plate and a highly accurate angle encoder called SelfA. The performance of the system is evaluated by repeatedly measuring the energy of the first excited state of the potassium-40 nuclide. The excitation energy is determined as 29829.39 (6) eV, and this is one order of magnitude more accurate than the previous measurement. The estimated uncertainty of the photon energy measurement was 0.7 p.p.m. as a standard deviation and the maximum observed deviation was 2 p.p.m.

Measurement of the ^{229}Th Isomer Energy with a Magnetic Microcalorimeter

We present a measurement of the low-energy (0-60 keV) γ-ray spectrum produced in the α decay of ^{233}U using a dedicated cryogenic magnetic microcalorimeter. The energy resolution of ∼10  eV, together with exceptional gain linearity, allows us to determine the energy of the low-lying isomeric state in ^{229}Th using four complementary evaluation schemes. The most precise scheme determines the ^{229}Th isomer energy to be 8.10(17) eV, corresponding to 153.1(32) nm, superseding in precision previous values based on γ spectroscopy, and agreeing with a recent measurement based on internal conversion electrons. We also measure branching ratios of the relevant excited states to be b_{29}=9.3(6)% and b_{42}<0.7%.