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arXiv:1308.1125

Creation of the inverse population in the $^{229}$Th ground-state doublet

Evgenii V. Tkalya, Леонід Петрович Яценко

Published Aug 5, 2013• 0 citations
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Abstract

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 $^{229}$Th 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 $^{229}$Th 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 $^{229}$Th (a) in crystals with isovalent substitution of host ions (eg 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.

DOI
10.48550/arxiv.1308.1125

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Creation of the inverse population in the 229^{229}229Th ground-state doublet
A new method for obtaining of inverse population between quadrupole sublevels of the ground state 5/2+(0.0)5/2^+(0.0)5/2+(0.0) and the isomeric state 3/2+(7.63/2^+(7.63/2+(7.6 eV) of the 229^{229}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 229^{229}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 229^{229}229Th (a) in crystals with isovalent substitution of host ions (eg Si4+^{4+}4+ ions in the SiO2_22​ crystal replaced by the 229^{229}229Th4+^{4+}4+ ions) and (b) in crystals such as Na2_22​ThF6_66​, 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.
The authors leverage the recently proposed optonuclear quadrupolar effect to develop a two-photon pumping scheme for the isomeric state of 229{}^{229}229Th, an exotic nucleus with an ultralow excitation energy of 8.3 eV. Additionally, the authors demonstrate that the lasing between nuclear states, which has been pursued for decades, may be realized based on the two-photon pumping scheme in ultrawide-band-gap compounds like ThF4{}_{4}4​, Na2{}_{2}2​ThF6{}_{6}6​, or K2{}_{2}2​ThF6{}_{6}6​.
This work concerns the demonstration of the feasibility of the tuning and perhaps even stimulation of nuclear radiation. Theory1–3 has indicated that anti-Stokes Raman up- conversion of intense but conventional long-wavelength sources of radiation produced by scattering from isomeric states of nuclear excitation could lead to significant sources of tunable γ radiation characterized by the natural Mossbauer width of the lines. This would result in lines with sub-angstrom wavelengths and widths of a few megahertz. Further computations4 have suggested that this type of coherent, as well as a new type of incoherent, optical pumping could even lead to appreciable levels of inversion of the population of nuclear levels that would be capable of supporting the growth of stimulated γ-ray intensity. Whether these processes can reach threshold depends on the resolution of basic issues lying in an interdisciplinary region between quantum electronics and nuclear physics that have not been previously addressed.
As a unique feature, the 229{}^{229}229Th nucleus has an isomeric transition in the vacuum ultraviolet that can be accessed by optical lasers. The interference effects occurring in the interaction between coherent optical light and an ensemble of 229{}^{229}229Th nuclei are investigated theoretically. We consider the scenario of nuclei doped in vacuum ultraviolet transparent crystals and take into account the effect of different doping sites and therefore different lattice fields that broaden the nuclear transition width. This effect is shown to come into interplay with interference effects due to the hyperfine splitting of the ground and isomeric nuclear states. We investigate possible experimentally available situations involving two-, three- and four-level schemes of quadrupole sublevels of the ground and isomeric nuclear states coupling to one or two coherent fields. Specific configurations which offer clear signatures of the isomer excitation advantageous for the more precise experimental determination of the transition energy are identified. Furthermore, it is shown that population trapping into the isomeric state can be achieved. This paves the way for further nuclear quantum optics applications with 229{}^{229}229Th such as nuclear coherent control.
A low-energy nuclear transition in the isotope thorium-229 has been excited in thorium-doped crystals with laser light. This opens the perspective towards a highly stable and robust solid-state optical nuclear clock. The required laser radiation at 148 nm wavelength has so far been produced using pulsed laser systems where only a small fraction of the incident photons has been resonant with the narrow nuclear transition. Here we show that the nuclear resonance can be excited with a continuous-wave narrow-bandwidth laser source with a power of less than 1 nW, and that the resonance signal can be detected in absorption rather than in fluorescence. This eliminates the slow nuclear fluorescence decay from the detection process and offers a considerable advantage for clock operation through fast signal acquisition. The VUV laser source is based on three sequential frequency doublings, starting from a diode laser at 1187 nm that is well suited for linewidth narrowing and for frequency comparisons with optical atomic clocks. We use absorption spectroscopy for the quantitative characterization of two different Th-centers in calcium fluoride crystal and measure the isomeric shift between them. One of the centers shows a very small static electric crystal field gradient 0.1 V/A˚2Å^2A˚2, to be compared to gradients in the range of 100 V/A˚2Å^2A˚2 observed earlier. This indicates a center with high symmetry of the ions surrounding the Th nucleus, promising nuclear resonance lines that are nearly independent of the lattice spacing.
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.