The electronic bridge (EB) excitation of nuclei has been found as a versatile approach to efficiently excite the ^{229}Th isomers. Previous studies on EB excitation have typically disregarded the hyperfine structure as well as the decay of the excited atoms and ions by just treating the nucleus-electron coupling perturbatively. In the present work, we apply a quantum-optical approach to nonperturbatively investigate EB excitation of ^{229}Th^{3+} ions. This approach considers both the hyperfine structure and atomic decay through dressed hyperfine state and quantum master equation techniques. Numerical results show that the isomeric steady-state population of the time-independent scheme is constrained by atomic decay to a maximum of only 27.9%. By leveraging the dark state, however, the (time-dependent) stimulated Raman adiabatic passage method theoretically reaches a remarkable 99.7% isomeric population transfer and demonstrates a potential nuclear-laser scheme via the EB mechanism. Our quantum-optical approach exhibits a large flexibility and paves a promising avenue for utilizing advanced quantum-control technologies to design and optimize experimental schemes of EB excitation.
The electronic bridge (EB) excitation of nuclei has been found as a versatile approach to efficiently excite the ^{229}Th isomers. Previous studies on EB excitation have typically disregarded the hyperfine structure as well as the decay of the excited atoms and ions by just treating the nucleus-electron coupling perturbatively. In the present work, we apply a quantum-optical approach to nonperturbatively investigate EB excitation of ^{229}Th^{3+} ions. This approach considers both the hyperfine structure and atomic decay through dressed hyperfine state and quantum master equation techniques. Numerical results show that the isomeric steady-state population of the time-independent scheme is constrained by atomic decay to a maximum of only 27.9%. By leveraging the dark state, however, the (time-dependent) stimulated Raman adiabatic passage method theoretically reaches a remarkable 99.7% isomeric population transfer and demonstrates a potential nuclear-laser scheme via the EB mechanism. Our quantum-optical approach exhibits a large flexibility and paves a promising avenue for utilizing advanced quantum-control technologies to design and optimize experimental schemes of EB excitation.
Shortcut to Adiabatic Isomeric Population Transfer of the 229Th Nucleus via Hyperfine Electronic Bridge
The 229Th nucleus is well known for its exceptionally low-lying nuclear isomeric level, which provides a unique platform for exploring electron-nucleus interactions and gives rise to a variety of rich physical phenomena. One such phenomenon is the hyperfine electronic bridge, which has recently been shown to enable efficient and precise manipulation of the nuclear isomeric levels of 229Th [W. Wang etal., Phys. Rev. Lett. \textbf{133}, 223001 (2024)]. However, that study used the stimulated Raman adiabatic passage method, which requires relatively long operation times. In this work, we employ the stimulated Raman shortcut-to-adiabatic passage method, which dramatically shortens the operation time from the order of hundreds of milliseconds to hundreds of microseconds while maintaining a transfer efficiency of about 79.38%.
Hyperfine-resolved laser excitation and detection of nuclear isomer in trapped 229Th3+ ions
We present a comprehensive theoretical investigation of hyperfine-resolved excitation and detection of the low-energy isomeric state of 229Th in trapped 229Th3+ ions. Using a quantum master equation approach, we quantitatively analyze the dependence of the isomeric population on laser linewidth, detuning, and irradiation time, showing that their proper matching is essential for efficient excitation. Going beyond earlier conceptual discussions of electronic-fluorescence-based nuclear-state detection, we propose two concrete nuclear-state detection schemes based on three hyperfine-resolved electronic fluorescence channels at 690, 984, and 1088 nm. Our quantitative analysis shows that, for 50 ions, the 690- and 984-nm scheme yields detectable photon count rates on the order of 103s−1 at 690 nm and 104s−1 at 984 nm, whereas the 1088-nm scheme achieves a detectable photon rate on the order of 103s−1. By quantifying the trade-off between irradiation time and scan-step size, we show that the nuclear transition can be located within one month for a 100-MHz uncertainty using currently available vacuum-ultraviolet laser technology. These results provide practical guidance for trapped-ion 229Th spectroscopy and the development of nuclear clocks.
Nuclear coherent population transfer to the 229mTh isomer using x-ray pulses
Population of the 8 eV 229mTh isomer via the second nuclear excited state at 29.19 keV by means of coherent x-ray pulses is investigated theoretically. We focus on two nuclear coherent population transfer schemes using partially overlapping x-ray pulses known from quantum optics: stimulated Raman adiabatic passage (STIRAP), and successive π pulses. Numerical results are presented for three possible experimental setups. Our results identify the Gamma Factory as the most promising scenario, where two ultraviolet pulses combined with relativistically accelerated ions deliver the required intensities for efficient isomer population. Our simulations require knowledge of the in-band and cross-band nuclear transition probabilities. We give theoretically predicted values for the latter and discuss them in the context of recent experiments.
The Th-229 nuclear isomeric state has the lowest energy of all known nuclear excited states, placing it within the reach of current table-top laser technology. This extraordinary property has made this nuclear isomer an attractive candidate for a nuclear optical clock of incredibly high precision and accuracy, both as isolated trapped Th-229 ions and embedded into solid-state platforms. Activity around Th-229 has surged in recent years, driven by breakthroughs in its direct laser excitation. The underlying nuclear physics that gives rise to this unique isomer will be elucidated, as well as the nearly half-century of efforts that led to its direct excitation. The design and systematics of a Th-229 nuclear clock will be discussed, both in ion traps and in the solid-state. These systematics, such as frequency shifts and quenching channels, can be leveraged both to probe the local chemical environment, and as a control knob during clock operation. Finally, the nuclear clock's high sensitivity to the variations of fundamental constants will be discussed.
Creation of the inverse population in the 229Th ground-state doublet
A new method for obtaining of inverse population between quadrupole sublevels of the ground state 5/2+(0.0) and the isomeric state 3/2+(7.6 eV) of the 229Th nucleus in a dielectric crystal with a large band gap by means of external source of the VUV radiation is proposed. The method is based on an efficient depopulation of the upper sublevels of the ground state of 229Th by resonant photons from narrowband laser or broader tunable free electron laser. Sublevels of the isomeric state play the role of intermediate states. In addition, we have considered a case of excitation of the isomeric state (without creation of inverse population) by broadband source of light with the anti-Stokes scattering. The proposed scheme of optical pumping results in (1) inverse population of nuclear sublevels without using extremely low temperatures, and (2) shows a new way for the creation of the gamma-ray laser of optical range at the nuclear transition in 229Th (a) in crystals with isovalent substitution of host ions (eg Si4+ ions in the SiO2 crystal replaced by the 229Th4+ ions) and (b) in crystals such as Na2ThF6, where the substitution is not necessary.
A new method for obtaining inverse population between quadrupole sublevels of the ground state 5/2 + (0.0) and the isomeric state 3/2 + (7.6 eV) of the 229 Th nucleus in a dielectric crystal with a large band gap by means of an external source of VUV radiation is proposed. The method is based on an efficient depopulation of the upper sublevels of the ground state of 229 Th by resonant photons from a narrowband laser or a broader tunable free electron laser. The sublevels of the isomeric state play the role of intermediate states. The proposed scheme of optical pumping (1) results in inverse population of nuclear sublevels without using extremely low temperatures, and (2) shows a new means of creating a gamma-ray laser of optical range at the nuclear transition in 229 Th (a) in crystals with isovalent substitution of host ions (e.g. Si 4+ ions in the SiO 2 crystal replaced by the 229 Th 4+ ions) and (b) in crystals such as Na 2 ThF 6 , where the substitution is not necessary.