The nucleus 229Th has an anomalously low first-excited (isomeric) state, now measured at 8.3557 eV (wavelength 148.3821(5) nm), uniquely placing a nuclear transition within reach of vacuum-ultraviolet lasers. Tkalya (Phys. Rev. Lett. 106, 162501 (2011)) proved theoretically that stimulated amplification of this nuclear gamma radiation is possible in principle in a wide-bandgap dielectric host doped with 229Th, and identified the experimentally unresolved ingredients: the isomer energy (then 7.6 +/- 0.5 eV), the nuclear spin-lattice relaxation time T1T_1 at millikelvin temperature, the electric field gradient and Sternheimer antishielding (hence the quadrupole splitting) at the Th site, a suitable vacuum-ultraviolet pump laser, and experimental validation of metal-cover-assisted relaxation. The isomer energy, the pump source, and the radiative lifetime/internal-conversion suppression have since been measured or demonstrated, and electric-field-gradient data exist for Th:CaF2. The surviving open core is the laser itself: creating a population inversion between 229Th nuclear sublevels in a solid, measuring the still-unknown T1T_1 at millikelvin temperature, characterizing the quadrupole/site structure in candidate hosts, validating relaxation engineering, and demonstrating net stimulated-emission gain (positive amplification coefficient) on the isomer transition.

Background

A nuclear isomer is a long-lived excited state of a nucleus. The isomer of 229Th, denoted 229mTh, lies only about 8.36 eV above the ground state - the lowest nuclear excitation energy known - and decays to the ground state by a magnetic-dipole (M1) transition (spin-parity 3/2+ to 5/2+). Because the energy is in the vacuum ultraviolet (VUV; the 8.36 eV photon has wavelength 148.38 nm), this is the only nuclear transition directly accessible to table-top laser spectroscopy, which is why 229Th is the basis of the developing solid-state nuclear clock.

A nuclear (gamma-ray) laser - coherent amplification by stimulated emission on a nuclear transition - has been a standing challenge of modern physics since the 1970s; the classic review by Baldwin and Solem (Rev. Mod. Phys. 69, 1085 (1997)) identifies two basic obstacles: accumulating a sufficient density of isomeric nuclei, and narrowing the emission line to its natural radiative width. For low-energy nuclear transitions an additional killer is internal conversion, the decay channel in which the nuclear energy is transferred to an atomic electron instead of being emitted as a photon; for an 8 eV transition in a neutral atom or a narrow-gap solid, the radiative channel is suppressed by many orders of magnitude. A related higher-order channel is the electronic bridge, in which the nucleus transfers energy to an electronic transition.

Tkalya (2011) proposed a concrete route around these obstacles. He noted that in a dielectric crystal whose band gap (energy spacing between valence and conduction bands) exceeds the isomer energy, internal conversion is energetically forbidden and the electronic bridge is negligible, so the isomer decays essentially radiatively. Following Rellergert et al. (Phys. Rev. Lett. 104, 200802 (2010)), he took 229Th4+ doped into LiCaAlF6 (band gap about 10 eV) at density n0∼1018 cm−3n_0 \sim 10^{18}\ \mathrm{cm}^{-3}, where Th substitutes for Ca at a single lattice site. Emission and resonant absorption then occur without recoil (an optical-range analogue of the Moessbauer effect; the recoil energy is about 10^-10 eV, far below the Debye temperature, so the recoilless fraction is unity). The gain per unit length is χ=(λ2/2π)(Γrad/Δωtot)(1/(1+α))(nis−ngr/g)−κ\chi = (\lambda^2/2\pi)(\Gamma_{\mathrm{rad}}/\Delta\omega_{\mathrm{tot}})(1/(1+\alpha))(n_{\mathrm{is}} - n_{\mathrm{gr}}/g) - \kappa, where λ\lambda is the transition wavelength, Γrad\Gamma_{\mathrm{rad}} the radiative width, Δωtot\Delta\omega_{\mathrm{tot}} the total line width, α\alpha the internal-conversion coefficient, nisn_{\mathrm{is}} and ngrn_{\mathrm{gr}} the densities of nuclei in the isomeric and ground states, gg the ratio of spin degeneracies (g=(2Jgr+1)/(2Jis+1)=6/4=3/2g = (2J_{\mathrm{gr}}+1)/(2J_{\mathrm{is}}+1) = 6/4 = 3/2 here, with ground-state spin Jgr=5/2J_{\mathrm{gr}} = 5/2 and isomer spin Jis=3/2J_{\mathrm{is}} = 3/2), and κ\kappa the non-resonant absorption of the host. With Γrad\Gamma_{\mathrm{rad}} estimated from nuclear data (half-life about 25 min), line widths of order 1 kHz, and κ\kappa reduced to ~0.01 cm^-1, he obtained χ\chi of order 2 to 3 cm^-1.

Direct resonant pumping cannot invert the transition because g>1g > 1 and pump photons also stimulate re-emission; Tkalya therefore proposed a two-step scheme. A VUV laser first populates the isomer, and inversion is then created between magnetic (Zeeman) sublevels or quadrupole-split sublevels at millikelvin temperature, where the upper sublevels of the ground-state multiplet are emptied. Three variants were analyzed: (1) Zeeman ordering in a strong magnetic field, requiring the nuclear spin-lattice relaxation time T1T_1 (the time for the nuclear spins to reach thermal equilibrium with the crystal lattice) to be shorter than the isomer half-life; (2) quadrupole ordering driven by the electric field gradient (EFG, the second derivative of the crystal electric potential) at the Th nucleus, amplified by the Sternheimer antishielding factor γ∞\gamma_\infty (which describes how the electron cloud enhances an external field gradient at the nucleus), giving a uniform shift rather than broadening only if all Th nuclei sit at equivalent sites; and (3) the regime where the isomer half-life is much shorter than T1T_1, in which a non-superconducting metal cover (Au, Cu, Ag) provides spin relaxation through inelastic scattering of its conduction electrons, estimated to reduce the equilibration time to about 50 days, without quenching the 8 eV transition.

The field has since been transformed. The isomer energy is now precisely known (8.3557 eV), direct laser excitation of the isomer in Th:CaF2 has been achieved with a table-top tunable VUV laser and with a VUV frequency comb, the radiative decay has been observed directly (confirming a radiative fraction near unity in wide-gap hosts, i.e. α≈0\alpha \approx 0), and solid-state nuclear clocks comparing the nuclear transition to the 87Sr atomic clock are operating. None of this, however, constitutes population inversion or gain: current experiments work with tiny excited fractions and spontaneous (resonance fluorescence) emission. The laser objective, and the specific enabling quantities Tkalya flagged that remain unmeasured, define the open problem.

Problem Statement

Can a nuclear laser of optical range be realized on the 8.36 eV isomer transition of 229Th in a doped dielectric solid - that is, can a population inversion between the nuclear (Zeeman- or quadrupole-split) sublevels of 229Th be created and maintained in a wide-bandgap host, and net stimulated-emission gain - a positive amplification coefficient χ=(λ2/2π)(Γrad/Δωtot)(1/(1+α))(nis−ngr/g)−κ\chi = (\lambda^2/2\pi)(\Gamma_{\mathrm{rad}}/\Delta\omega_{\mathrm{tot}})(1/(1+\alpha))(n_{\mathrm{is}} - n_{\mathrm{gr}}/g) - \kappa at the 148.38 nm transition - be demonstrated? The isomer energy, a suitable VUV pump source, and the radiative lifetime/internal-conversion suppression that the analysis of Tkalya (Phys. Rev. Lett. 106, 162501 (2011)) left unresolved have since been settled, so the question now stands on the remaining open components, each of which bears on whether the isomer transition can lase: (i) the nuclear spin-lattice relaxation time T1T_1 of Th-doped wide-bandgap crystals at millikelvin temperature, whose magnitude decides which inversion scheme (Zeeman ordering, quadrupole ordering, or relaxation-assisted pumping in the regime where T1T_1 much exceeds the isomer half-life) is practical; (ii) experimental determination of the electric field gradient, Sternheimer antishielding and resulting quadrupole splitting and doping-site structure in candidate hosts - known for Th:CaF2 (four inequivalent sites), unknown for the originally proposed LiCaAlF6 and for ultrawide-bandgap thorium compounds - since a uniform, single-site shift is required to avoid inhomogeneous broadening of the roughly 1 kHz line; (iii) experimental validation of relaxation engineering, such as a metallic covering whose conduction electrons shorten T1T_1 without quenching the isomer or opening loss channels; and (iv) a pumping scheme that actually reaches inversion, whether Tkalya's two-step schemes or alternatives such as two-photon optonuclear pumping. The common scientific objective is the demonstration (or rigorous exclusion) of stimulated-emission amplification on a nuclear transition; these components represent the currently open landscape bearing on that objective rather than separately required results, and none of them has been demonstrated.

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