Expected IC signal
The incident VUV flux is attenuated, so that it follows φ 0 e−αz, in which α is the VUV attenuation coefficient. The number of excited 229Th nuclei in a target of length L should go as57
$${N}_{{\rm{e}}}\approx \frac{4}{6}\frac{{\lambda }^{2}}{2{\rm{\pi }}}\frac{{n}_{{\rm{Th}}}}{{\varGamma }_{{\rm{L}}}}\frac{T|\widetilde{n}{|}^{2}}{{\rm{Re}}[\widetilde{n}]}\frac{{\varphi }_{0}(1-{{\rm{e}}}^{-\alpha L})}{\alpha }\times \frac{1}{1+4{\left(\frac{\delta }{{\varGamma }_{{\rm{L}}}}\right)}^{2}}\times \left(\frac{{t}_{{\rm{e}}}}{{\tau }_{{\rm{rad}}}}\right),$$ (2)
in which λ is the vacuum transition wavelength, n Th is the density of 229Th in the 229ThO 2 target, Γ rad = 1/τ rad is the vacuum radiative decay rate, Γ L is the VUV laser bandwidth, Γ IC = 1/τ IC is the IC decay rate, δ is the laser detuning, φ 0 is the incident laser photon flux, L is the target thickness, T is the transmission of the VUV laser into the target and \(\widetilde{n}=n-{\rm{i}}\kappa \) is the complex index of refraction with κ = λα/4π. The target was produced using a 0.75:0.25 229Th:232Th isotope mix from Oak Ridge National Laboratory, leading to an effective 229Th density of n Th = 0.75 × 2.28 × 1022 cm−3 (ref. 47).
From the number of excited 229Th nuclei, the number of detected IC electrons is given by
$${N}_{\det }={\eta }_{{\rm{e}}}{\eta }_{{\rm{c}}}{N}_{{\rm{e}}}\times {{\rm{e}}}^{-{t}_{{\rm{i}}}/{\tau }_{{\rm{IC}}}}$$ (3)
in which η e is the extraction efficiency from the 229ThO 2 target, η c is the collection efficiency and t i is the start of the acquisition time window. The extraction efficiency represents the probability that an IC electron is able to leave the 229ThO 2 target and combines many physical processes, such as whether the electron is promoted high enough into the conduction band to overcome the ionization energy barrier (either by being in a state above the ionization energy or tunnelling), whether the electron inelastically scatters, whether surface conditions are favourable and so on. Owing to all of these confounding factors, theoretical calculation of η e is difficult and it must be estimated from experiments. To do this, we make the assumption that the probability for a photoelectron promoted by a VUV photon to leave the target is the same as an IC electron promoted by an excited 229Th nucleus. By making this assumption, we are able to use the efficiency with which photoelectrons are generated by our VUV laser system to obtain an estimate of Tη e . The collection efficiency η c is simply the efficiency with which electrons that leave the target are detected on the MCP given the voltage biasing and magnetic field configuration used in the experiment. This can be readily determined by measuring the ratio of the number of photoelectrons collected on the MCP front plate relative to the number of photoelectrons leaving the target.
Using the values listed in Extended Data Table 1, the expected on-resonance IC signal was estimated to be \({N}_{{\rm{\det }}}/(\hbar {\omega }_{0}{\varphi }_{0}{t}_{{\rm{e}}})\,=\) \(0.1{5}_{-0.09}^{+0.25}\,{{\rm{e}}}^{-}\,{{\rm{\mu }}{\rm{J}}}^{-1}\) per shot.
Quenching of ASE in Xe four-wave mixing
The four-wave mixing process can produce a beam of ASE along the beam axis, complicating detection. The origin of the ASE is resonant excitation by the 249.6-nm laser of the \(5{{\rm{p}}}^{6}\,\genfrac{}{}{0ex}{}{1}{}{S}_{0}\to 5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{p}}}^{2}\,{[1/2]}_{0}\) transition. Any Xe population not participating in the four-wave mixing process will be left in the excited two-photon state. This \(5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{p}}}^{2}\,{[1/2]}_{0}\) (abbreviated as 6p2 [1/2] 0 ) state will then decay to the \(5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\) (abbreviated as \(6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\)) state by 828-nm emission in about 30 ns and the \(6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\) state will decay to the 1S 0 ground state by emission of a 147-nm photon in about 3.7 ns. If the Xe pressure is in the several hundred Pa range, as it is for efficient four-wave mixing, there are enough nearby Xe atoms that they may reabsorb these 828-nm and 147-nm photons. Effectively, this leads to radiation trapping, which extends the effective fluorescence lifetime of the Xe spontaneous emission58. At the same time, the 828-nm/147-nm spontaneous emission will experience gain as it stimulates Xe in the excited 6p2 [1/2] 0 and \(6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\) to emit, yielding ASE. This gain will be highly directional, as the excited Xe will essentially lie in a column defined by the propagation of the 249.6-nm pulse of the pump laser. This interplay between radiation trapping and ASE will then yield bidirectional emission from the Xe cell along the pumping axis, which will have a timescale much longer than the spontaneous emission lifetime of the excited states59.
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