Abstract
The electronic defect states resulting from doping $^{229}$Th in CaF$_2$ offer a unique opportunity to excite the nuclear isomeric state $^{229m}$Th at approximately 8 eV via electronic bridge mechanisms. We consider bridge schemes involving stimulated emission and absorption using an optical laser. The role of different multipole contributions, both for the emitted or absorbed photon and nuclear transition, to the total bridge rates are investigated theoretically. We show that the electric dipole component is dominant for the electronic bridge photon. In contradistinction, the electric quadrupole channel of the $^{229}$Th isomeric transition plays the dominant role for the bridge processes presented. The driven bridge rates are discussed in the context of background signals in the crystal environment and of implementation methods. We show that inverse electronic bridge processes quenching the isomeric state population can improve the performance of a solid-state nuclear clock based on $^{229m}$Th.
Highlights
The nuclear isomer 229mTh is our most compelling candidate for the development of the first nuclear clock
We show that inverse electronic bridge processes quenching the isomeric state population can improve the performance of a solid-state nuclear clock based on 229m Th
We have shown in Ref. [26] that using a vacuum ultraviolet (VUV) lamp [11] with N ≈ 3 photons/(s Hz), a focus of f = 0.5 mm2 which corresponds to I = N hωdo/(2π f ) ≈ 1.6 × 10−12 W/(m2 s−1), and a FWHM linewidth of ≈0.5 eV, the electronic bridge (EB) rate is more than 2 orders of magnitude faster than direct photoexcitation
Summary
The nuclear isomer 229mTh is our most compelling candidate for the development of the first nuclear clock. The 229mTh isomer could be accessible by narrow-band vacuum ultraviolet (VUV) lasers, which is the key to designing a frequency standard based on a nuclear transition [4,5]. A practical implementation will require development of such lasers and a more precise knowledge of the isomer energy. The isomer energy was reported as Em = 8.28(17) eV using a direct measurement of internal conversion electrons [1], Em = 8.30(92) eV [6] from determining the transition rates and energies from the above level at 29.2 keV in a calorimetric experiment, or Em = 8.10(17) eV from state-of-the-art gamma spectroscopy measurements using a dedicated cryogenic magnetic microcalorimeter [2]
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