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REVIEW 4 major objections 5 minor 72 references

Electronic Bridge processes in $^{229}$Th-doped LiCAF and LiSAF

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Laser-assisted electronic bridges can drive the 229Th nuclear clock transition orders of magnitude faster than direct VUV excitation in doped LiCAF and LiSAF crystals.

desk verdict A solid, honest extension of the electronic bridge formalism to Th:LiCAF/LiSAF whose headline enhancement is conditional on unmeasured defect-level energies. read the letter →

arxiv 2507.05070 v1 pith:4JZN32RW submitted 2025-07-07 physics.atom-ph cond-mat.mtrl-scinucl-ex

Tobias Kirschbaum , Martin Pimon , Andreas Grüneis , Thorsten Schumm , Adriana Pálffy This is my paper
classification physics.atom-phcond-mat.mtrl-scinucl-ex
keywords electronicbridgethorium-229isomernuclearclockLiCAFSAFchargecompensationdefectstateslaser-assistedexcitation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that laser-assisted electronic bridge processes in 229Th-doped LiCAF and LiSAF crystals can drive the 8.36 eV nuclear clock transition much faster than direct VUV laser excitation. Doping thorium into these hosts creates defect states in the electronic band gap, and these states can mediate nuclear excitation or deexcitation with the help of an infrared-to-UV laser. For the most favorable charge compensation structures, the calculated excitation enhancement exceeds two to three orders of magnitude, and the same mechanism can quench the long-lived isomer far faster than its radiative decay. The authors caution that these gains depend on the still-unmeasured energies of the thorium-localized defect states, which density-functional theory cannot yet pin down reliably.

What carries the argument

The machinery is the third-order electronic-bridge matrix element of Eq. (2): a product of the E1 photon-emission dipole operator $Q_{E1}$, the hyperfine operators $T_{\lambda K,q}$ for M1 and E2 electron-nucleus coupling, and the nuclear transition operator $M_{\lambda K,-q}$, summed over intermediate crystal states $|k\rangle$. Laser assistance enters through the stimulated-emission relation that converts the spontaneous bridge rate into the driven rate, and the paper measures the payoff with two dimensionless coefficients: $\beta_\ell$, the ratio of driven bridge excitation to direct VUV nuclear excitation, and $\alpha_{\rm qu}$, the ratio of laser-assisted quenching to the medium-corrected radiative decay rate.

What would settle it

Measure the defect-state spectrum of $^{229}$Th:LiCAF and $^{229}$Th:LiSAF by VUV absorption or fluorescence spectroscopy: if no thorium-localized defect state sits within about an electron-volt of the $8.36$ eV isomer energy in the favorable compensation structures, the claimed $10^3$-fold enhancements cannot occur. A second check is the proposed two-laser protocol: scanning the assisting laser across predicted bridge resonances should produce VUV fluorescence and an $\alpha_{\rm qu}$ around unity, and the absence of both would falsify the predicted laser-assisted electronic bridge channel.

Watch

Extended reading notes

Core claim

An electronic bridge is a third-order process in which the thorium nucleus flips between ground and isomeric state through a virtual electronic excitation, with a real photon making up the energy difference between the nuclear and electronic transitions. The paper adapts this mechanism to the periodic crystal environment of $^{229}$Th:LiCAF and $^{229}$Th:LiSAF, using Kohn-Sham wave functions from DFT supercells and summing over roughly two thousand unoccupied conduction and defect states. Its central result is that laser-assisted bridge excitation and quenching outperform both direct VUV driving of the nucleus and spontaneous radiative decay. For the best charge compensation structures, excitation coefficients $\beta_\ell$ exceed $10^3$ relative to direct excitation, and quenching coefficients $\alpha_{\rm qu}$ reach the same order relative to the bare radiative decay rate. Spontaneous bridge rates, by contrast, stay between $10^{-13}$ and $10^{-6}\ \mathrm{s}^{-1}$ and are judged irrelevant for clock operation.

Load-bearing premise

The load-bearing premise is that the true energies of the thorium-localized defect states lie close to the $8.36$ eV isomer energy after the DFT band-gap correction, so that favorable bridge resonances are actually reached; the paper itself shows rates swing by orders of magnitude when these energies are shifted.

Editorial extensions

If this is right

  • Excitation rates in the best LiCAF and LiSAF charge compensation schemes exceed direct VUV laser excitation by two to three orders of magnitude, shortening the time needed to interrogate the isomer.
  • The same laser-assisted bridge mechanism can quench the isomeric state much faster than its roughly 1800 s radiative lifetime, reducing dead time between clock interrogation cycles.
  • Because the lowest-energy charge compensation structure in Th:LiCAF can be favored by fluorine-rich growth conditions, crystal growth can be steered toward structures with higher bridge efficiency.
  • If bridge resonances are confirmed, the proposed two-laser protocol gives a direct way to measure the bridge rate from VUV fluorescence and from the quench-induced population drop.
  • Among recent unexplained observations, the quenching strength seen in Th:CaF2 is roughly compatible with the order-of-magnitude bridge estimates, while the fast 6.81 eV fluorescence in Th:LiSAF is more likely internal conversion than an electronic bridge.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: because the assisted-bridge rate scales linearly with the assisting laser's spectral intensity, even larger speed-ups than the quoted $10^3$ should be reachable by increasing that intensity, provided the crystal survives the average power.
  • Beyond the paper: the same quenching idea should be testable in other VUV-transparent hosts such as Th:CaF2, Th:MgF2, and ThF4 whenever analogous defect states exist, making host selection a knob for clock operation.
  • Beyond the paper: if the defect-state energies can be pinned down by higher-level electronic-structure methods or by the proposed spectroscopy, one could in principle pre-select growth conditions such as the fluorine chemical potential to realize the most favorable charge compensation structures.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript develops a theoretical treatment of spontaneous and laser-assisted electronic bridge (EB) processes in 229Th-doped LiCAF and LiSAF crystals, using Kohn-Sham states from PBE DFT calculations on large supercells with explicit charge-compensation defects. Spontaneous EB excitation rates are computed and found to be very small (roughly 10^-13–10^-6 s^-1). The central quantitative claims concern laser-assisted schemes: for selected charge-compensation structures, driven EB excitation coefficients β_ℓ and quenching coefficients α_qu are reported to exceed direct VUV laser excitation and radiative decay by up to three orders of magnitude under stated laser parameters. The paper also proposes a two-laser interrogation protocol intended to provide experimental evidence for EB excitation and quenching. The results are compared with recent experiments in Th:LiSAF and Th:CaF2, and the authors suggest that EB quenching may explain part of the quenching observations in Ref. [21].

Significance. If the central enhancement claim survives closer scrutiny, the paper would provide a concrete route to faster interrogation cycles in solid-state 229Th nuclear clocks, which is a timely and important goal. The work extends earlier EB calculations from Th:CaF2 to the technologically relevant LiCAF and LiSAF hosts, and it is genuinely useful that the authors supply explicit laser parameters, convergence checks, a sensitivity analysis with respect to defect-state energies, and a falsifiable experimental protocol. The main significance is therefore conditional: the claimed order-of-magnitude enhancements rest on defect-state energies that are currently unmeasured and that the paper itself shows can change the rates by many orders of magnitude under modest shifts.

major comments (4)
  1. [§IV C and Table I] The central claim of two-to-three-order-of-magnitude enhancement is not robust to the presently unknown defect-state energies. The manuscript states in §IV that DFT one-electron energies cannot reliably determine whether defect states lie above or below the isomer energy, and Fig. 5 shows α_qu varying by many orders of magnitude for ~1 eV shifts of the final defect state. Yet Table I reports maximum coefficients β_ℓ up to 2.9×10^3 and α_qu up to 2.1×10^3 as if they were representative values, based only on PBE energies shifted by the pristine band-gap error. The stress-test concern therefore lands. The authors should either (a) quantify the plausible error in the defect-state positions and report the range of β_ℓ and α_qu across that range for all four structures, or (b) explicitly reframe the abstract and conclusion as conditional on the defect energies taking the predicted values. Without this, the abstract's 'significantly more efficient' claim overstates what the calculation establishes.
  2. [Eq. (2) and Fig. 5] The denominators in Eq. (2) omit the imaginary parts associated with intermediate-state widths, and the paper acknowledges in §IV C that this leads to divergent terms when a real electronic state approaches the virtual state. This omission is load-bearing for two reasons. First, the largest peaks in Fig. 5 are unphysical: a true resonance would be cut off by the finite lifetime of the intermediate state, and the limiting value is not estimated. Second, the comparison with the CaF2 quenching data in §V scales α_qu values taken from these spectra, so the quantitative compatibility argument inherits the divergence problem. The authors should include at least a lifetime-broadening regularization of the resonant denominators, or provide an upper-bound estimate of the enhancement set by the intermediate-state widths.
  3. [§IV B and Table I] The claimed maximum enhancements rely on an extrapolation of laser performance beyond the demonstrated tunability range. The pulsed four-wave-mixing VUV laser cited in Refs. [20,21,70] is stated to be tunable only between 7.4 eV and 10.2 eV, but several of the highest coefficients in Table I occur for defect states at 11–12 eV (e.g., LiCAF 0¯2001 at 11.12 eV and ¯10¯101 at 11.98 eV). The paper assumes, as a crude approximation, that the same laser performance extends above 12 eV. Because β_ℓ and α_qu scale linearly with the spectral intensity and with the defect-state population ρ_d, this assumption directly affects the numerical values of the headline enhancement. The authors should either use only states within the demonstrated tunability range for the central claim, or add an explicit sensitivity study showing how β_ℓ and α_qu change under a conservative degradation of laser intensity above 10.2 eV.
  4. [§V and Fig. 6] The proposed experimental protocol is a useful addition, but its practicality depends on the availability of a laser resonant with the defect transition and on prior knowledge of the defect-state energy. The manuscript states that this energy must be determined in advance, either spectroscopically or by 'high precision electronic structure calculations', citing a related calculation. Given that the present DFT calculations are the source of the energy uncertainty identified in §IV C, the protocol would be more convincing if it included a concrete scanning strategy over the unknown defect energy, or if the authors specified what accuracy in the defect energy is required to make the protocol feasible. As written, the protocol assumes the very information that the paper shows is missing.
minor comments (5)
  1. [Abstract and §I] In the introduction, the isomer is described as having a 'radiative lifetime of O(10^3 s^{-1})'; the units appear to be inverted or a typo, since a lifetime should be in seconds. Please correct.
  2. [Fig. 4 caption] The caption contains the fragment 'for to the four lowest energy charge compensation schemes'; the word 'for' should be removed.
  3. [§VI] In the conclusion, 'flourine' should be 'fluorine'.
  4. [Eq. (14)] The symbols Γ, Γ̃, Γ_dec, and Δ are introduced in quick succession; the decoherence rate Γ_dec is never defined explicitly beyond the parenthetical '(e.g. phonon scattering)' and should be stated more precisely for the numerical calculations.
  5. [Table I] The table format, with paired β and α columns and interleaved energy and relaxation-rate columns, is difficult to read; separating the β_ℓ and α_qu data into two tables, or adding explicit column headers for each crystal and structure, would substantially improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted EB enhancements are compared against external experimental benchmarks and explicitly flagged as conditional on unmeasured defect energies.

full rationale

The derivation chain is not circular. The laser-assisted enhancement coefficients βℓ (Eq. 10) and αqu (Eq. 11) are ratios whose denominators are external experimental quantities: Γex ≈ 3×10−7 s−1 from a pulsed VUV laser and n3Γγ = 1.8×10−3 s−1 derived from the measured radiative lifetime τ = 1800 s and refractive index n = 1.49. The numerators are computed from the EB matrix element in Eq. (2), whose inputs are DFT wave functions and energies; no parameter is fitted to the resulting EB rates or to the claimed enhancement. The only calibration applied, the rigid shift Δr, is fixed by the measured pristine band gaps (11.07 eV for LiCAF, 10.69 eV for LiSAF), an independent external benchmark that does not encode the target rates. The paper's own Section IV C is a limitation statement rather than a hidden fit: it artificially varies defect-state energies and shows order-of-magnitude sensitivity, explicitly stating that the true rate “will be just one point ... somewhere on the calculated lines” and that experimental determination of defect energies is “paramount.” This makes the central claim conditional, not circular. Self-citations to Refs. [36,37] for EB formalism and Ref. [50] for electronic structure are reused inputs, but the formalism is restated in the paper's equations and the DFT calculations are described, so the load does not reduce to an unverified self-citation. The neglect of imaginary parts in Eq. (2) is a correctness and divergence caveat, not a circularity.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new particles, fields, forces, or conserved quantities. The defect electronic states are predictions of the DFT model, not independently postulated entities. The central claim rests on unmeasured defect-state energies, external nuclear transition probabilities, and a set of chosen laser parameters, all of which are counted as free parameters or domain assumptions above.

free parameters (7)
  • Rigid band-gap shift Delta_r = 11.07 eV for LiCAF minus PBE gap; 10.69 eV for LiSAF minus PBE gap
    Shifts all unoccupied DFT states so the conduction band edge matches measured pristine band gaps; the central rates and state classification depend on these shifted energies.
  • Assisting laser spectral intensity I_omega = 5 W s/m^2
    Chosen as realistic for infrared to weak UV lasers; beta and alpha scale linearly with it, so the central enhancement factors are proportional to this choice.
  • cw-equivalent VUV pump intensity I_cw = 1.4e4 W/m^2
    Taken from the pulsed VUV laser in Refs [20,21,70]; used to populate defect states and to define Gamma_ex = 3e-7 s^-1 for comparison.
  • Laser linewidth Gamma_l = 2 pi x 10 GHz
    Sets decoherence in the defect population formula and the spectral intensity; assumed to be the dominant decoherence source.
  • Isomer radiative lifetime tau = 1800 s
    Used to convert the bare radiative decay rate into n^3 Gamma_gamma = 1.8e-3 s^-1 for the quenching coefficient.
  • Localization threshold = norm >= 0.4 classified as thorium-localized
    Defines which defect states are included as initial or final states in the EB rate calculation; the threshold is arbitrary and affects the set of rates shown in Figs 3-4.
  • Variable energy shift in Sec IV C = Final defect state energy varied over roughly 7 to 10.5 eV
    Not a fit; used to illustrate sensitivity of the quenching coefficient to the unknown defect energy position.
assumptions (6)
  • domain assumption DFT Kohn-Sham single-particle wave functions from VASP provide adequate electronic states and matrix elements for EB rates.
    Section III uses PBE, scalar relativistic approximation, and a thorium-centered spherical grid to compute hyperfine and dipole matrix elements; there is no validation against correlated electronic structure methods.
  • ad hoc to paper A rigid shift of unoccupied DFT states by the pristine band-gap error applies to defect states.
    Section IV A/B sets Delta_r = E_exp_g - E_DFT_g; the authors acknowledge DFT errors may differ for localized and delocalized states and add a variable shift in Section IV C.
  • domain assumption Valence band holes relax to the Fermi level faster than the electronic bridge time scale.
    Section IV treats the Fermi level as the electronic ground state because a hole is expected to relax faster than the bridge process, citing Ref [22].
  • domain assumption The 229Th isomer transition is pure M1+E2 with B_down(M1) = 0.022 W.u. and B_down(E2) = 27.04 W.u.
    These external reduced transition probabilities, from Refs [21,34,46], set the overall scale of the nuclear matrix elements in Eq (2).
  • standard math Third-order perturbation theory with neglect of intermediate state widths is valid away from resonance.
    The EB matrix element in Eq (2) omits imaginary parts of denominators; the authors note this avoids divergences when a real state coincides with the virtual state.
  • domain assumption A steady-state two-level formula describes the defect-state population under the driving laser.
    Equation (14) with Gamma_tilde approximately Gamma_l/2 assumes the laser linewidth dominates decoherence and that other relaxation channels are subdominant.

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Cite this review

Pith. "Pith review of Electronic Bridge processes in $^{229}$Th-doped LiCAF and LiSAF." pith.science (2026). https://pith.science/paper/4JZN32RW

@misc{pith2026250705070,
  author       = {Pith},
  title        = {Pith review of: Electronic Bridge processes in $^229$Th-doped LiCAF and LiSAF},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4JZN32RW}},
  note         = {Machine review of arXiv:2507.05070}
}
abstract

Electronic bridge mechanisms driving the $^{229}$Th nuclear clock transition in the vacuum-ultraviolet-transparent crystals $^{229}$Th:LiCAF (LiCaAlF$_6$) and $^{229}$Th:LiSAF (LiSrAlF$_6$) are investigated theoretically. Due to doping-induced symmetry breaking within the host crystal, electronic defect states emerge around the thorium nucleus and can facilitate nuclear (de)excitation via laser-assisted electronic bridge mechanisms. We investigate spontaneous and laser-assisted electronic bridge schemes for different charge compensation mechanisms. While the calculated spontaneous electronic bridge rates are very small, laser-assisted electronic bridge schemes for nuclear (de)excitation turn out to be significantly more efficient than both spontaneous nuclear decay and direct laser excitation, offering promising prospects for the future clock operation.

Figures

Figures reproduced from arXiv: 2507.05070 by the authors.

Figure 1
Figure 1. FIG. 1: Spontaneous EB schemes: (a), (b) isomer excitation [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Laser-assisted EB schemes. (a) Driven EB schemes [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Spontaneous EB nuclear excitation rates Γ [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Dimensionless enhancement coefficients [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Quenching coefficient as a function of artificially var [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Quantum dynamical protocol to prove the existence [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Spontaneous EB rate as a function of number of intermediate electronic states [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: (a) Dipole matrix (in arbitrary units) for [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Effective hyperfine strength (in arbitrary units) as a function of initial state. In all cases, the Fermi level [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]

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Works this paper leans on

72 extracted references · 55 canonical work pages

  1. [21]

    Dessovic, P

    P. Dessovic, P. Mohn, R. Jackson, G. Winkler, M. Schre- itl, G. Kazakov, and T. Schumm, Journal of Physics: Condensed Matter 26, 105402 (2014)

    work page 2014

  2. [1]

    [22] 229Th was excited in the host crystal LiSAF

    In Ref. [22] 229Th was excited in the host crystal LiSAF. Two relevant spectroscopic features are re- ported. The first one was assigned to the radiative decay of the nuclear isomer. The second feature is a broad line at ∼ 6.81 eV which decays within a few seconds. This feature apparently stems from the deexcitation of 229Th in the crystal environment. Ou...

    work page

  3. [2]

    [23] laser assisted quenching was demon- strated in 229Th:LiSAF

    In Ref. [23] laser assisted quenching was demon- strated in 229Th:LiSAF. Here, the VUV laser was shifted by 100 GHz from the thorium resonance af- ter the excitation cycle. The authors then observed that the nuclear excited state population could be depleted. From these measurements, a quenching cross section was extracted. This cross section cor- respond...

    work page

  4. [3]

    [21], quenching at various laser wavelengths and powers, and sample temperatures was investi- gated in 229Th:CaF2

    In Ref. [21], quenching at various laser wavelengths and powers, and sample temperatures was investi- gated in 229Th:CaF2. In the following, we will fo- cus on the room temperature results, because they are of greater reliability. Quenching strengths were measured across a broad spectral range from VUV to IR. In particular, all lasers except the IR lasers...

  5. [4]

    Peik and C

    E. Peik and C. Tamm, Europhysics Letters 61, 181 (2003)

    2003

  6. [5]

    Peik and M

    E. Peik and M. Okhapkin, Comptes Rendus Physique 16, 516 (2015)

    work page 2015

  7. [6]

    E. Peik, T. Schumm, M. Safronova, A. Palffy, J. Weiten- berg, and P. G. Thirolf, Quantum Science and Technol- ogy 6, 034002 (2021)

    work page 2021

  8. [7]

    P. G. Thirolf, S. Kraemer, D. Moritz, and K. Scharl, The European Physical Journal Special Topics 233, 1113 (2024)

    work page 2024

Show all 72 references
  1. [8]

    Kraemer, J

    S. Kraemer, J. Moens, M. Athanasakis-Kaklamanakis, S. Bara, K. Beeks, P. Chhetri, K. Chrysalidis, A. Claessens, T. E. Cocolios, J. G. Correia, et al., Nature 617, 706 (2023)

    2023

  2. [9]

    Zhang, T

    C. Zhang, T. Ooi, J. S. Higgins, J. F. Doyle, L. von der Wense, K. Beeks, A. Leitner, G. A. Kazakov, P. Li, P. G. Thirolf, et al., Nature 633, 63 (2024)

    2024

  3. [10]

    Dzuba, V

    V. Dzuba, V. Flambaum, and E. Peik, arXiv preprint arXiv:2503.04081 (2025)

    2025 arXiv

  4. [11]

    V. V. Flambaum, Phys. Rev. Lett. 97, 092502 (2006), URL https://link.aps.org/doi/10.1103/ PhysRevLett.97.092502

    2006

  5. [12]

    Fadeev, J

    P. Fadeev, J. C. Berengut, and V. V. Flambaum, Phys. Rev. A 102, 052833 (2020), URL https://link.aps. org/doi/10.1103/PhysRevA.102.052833

    2020 doi

  6. [13]

    Beeks, G

    K. Beeks, G. A. Kazakov, F. Schaden, I. Morawetz, L. T. de Col, T. Riebner, M. Bartokos, T. Siko- rsky, T. Schumm, C. Zhang, et al., arXiv preprint arXiv:2407.17300 (2024)

    2024 arXiv

  7. [14]

    Y.-D. Tsai, J. Eby, and M. S. Safronova, Nature Astron- omy 7, 113 (2023)

    2023

  8. [15]

    M. H. Zaheer, N. J. Matjelo, D. B. Hume, M. S. Safronova, and D. R. Leibrandt, Phys. Rev. A 111, 012601 (2025), URL https://link.aps.org/doi/10. 1103/PhysRevA.111.012601

    2025

  9. [16]

    C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A. Dzuba, V. V. Flambaum, and A. Derevianko, Physical review letters 108, 120802 (2012)

    2012

  10. [17]

    W. G. Rellergert, D. DeMille, R. R. Greco, M. P. Hehlen, J. R. Torgerson, and E. R. Hudson, Phys. Rev. Lett. 104, 200802 (2010), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.104.200802

    2010 doi

  11. [18]

    Kazakov, A

    G. Kazakov, A. Litvinov, V. Romanenko, L. Yatsenko, A. Romanenko, M. Schreitl, G. Winkler, and T. Schumm, New Journal of physics 14, 083019 (2012)

    2012

  12. [19]

    W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilli- gan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, Phys. Rev. A 47, 3554 (1993), URL https: //link.aps.org/doi/10.1103/PhysRevA.47.3554

    1993 doi

  13. [20]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Reviews of Modern Physics 87, 637 (2015)

    2015

  14. [22]

    Pimon, A

    M. Pimon, A. Gr¨ uneis, P. Mohn, and T. Schumm, Crys- tals 12, 1128 (2022)

    2022

  15. [23]

    Tiedau, M

    J. Tiedau, M. Okhapkin, K. Zhang, J. Thielk- ing, G. Zitzer, E. Peik, F. Schaden, T. Pronebner, I. Morawetz, L. T. De Col, et al., Physical Review Letters 132, 182501 (2024)

    2024

  16. [24]

    Schaden, T

    F. Schaden, T. Riebner, I. Morawetz, L. T. De Col, G. A. Kazakov, K. Beeks, T. Sikorsky, T. Schumm, K. Zhang, V. Lal, et al., Phys. Rev. Res. 7, L022036 (2025), URL https://link.aps.org/doi/10. 1103/PhysRevResearch.7.L022036

    2025

  17. [25]

    Elwell, C

    R. Elwell, C. Schneider, J. Jeet, J. Terhune, H. Morgan, A. Alexandrova, H. Tran Tan, A. Derevianko, and E. R. Hudson, Physical Review Letters 133, 013201 (2024)

    2024

  18. [26]

    Terhune, R

    J. Terhune, R. Elwell, H. Tan, U. Perera, H. Morgan, A. Alexandrova, A. Derevianko, and E. R. Hudson, arXiv preprint arXiv:2412.08998 (2024)

    2024 arXiv

  19. [27]

    Zhang, L

    C. Zhang, L. von der Wense, J. F. Doyle, J. S. Higgins, T. Ooi, H. U. Friebel, J. Ye, R. Elwell, J. E. S. Terhune, H. W. T. Morgan, et al., Nature 636, 603 (2024), URL https://doi.org/10.1038/s41586-024-08256-5

    2024 doi

  20. [28]

    J. S. Higgins, T. Ooi, J. F. Doyle, C. Zhang, J. Ye, K. Beeks, T. Sikorsky, and T. Schumm, Phys. Rev. Lett. 134, 113801 (2025), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.134.113801

    2025 doi

  21. [29]

    Pineda, P

    S. Pineda, P. Chhetri, S. Bara, Y. Elskens, S. Casci, A. Alexandrova, M. Au, M. Athanasakis-Kaklamanakis, M. Bartokos, K. Beeks, et al., Physical Review Research 7, 013052 (2025)

    2025

  22. [30]

    Hiraki, K

    T. Hiraki, K. Okai, M. Bartokos, K. Beeks, H. Fujimoto, Y. Fukunaga, H. Haba, Y. Kasamatsu, S. Kitao, A. Leit- ner, et al., Nature communications 15, 5536 (2024)

    2024

  23. [31]

    Strizhov and E

    V. Strizhov and E. Tkalya, Sov. Phys. JETP 72, 387 (1991)

    1991

  24. [32]

    Tkalya, Sov

    E. Tkalya, Sov. Phys. JETP 75, 200 (1992)

    1992

  25. [33]

    Porsev and V

    S. Porsev and V. Flambaum, Physical Review A—Atomic, Molecular, and Optical Physics 81, 032504 (2010)

    2010

  26. [34]

    P. V. Bilous, E. Peik, and A. P´ alffy, New Journal of Physics 20, 013016 (2018)

    2018

  27. [35]

    P. V. Bilous, H. Bekker, J. C. Berengut, B. Seiferle, L. von der Wense, P. G. Thirolf, T. Pfeifer, J. R. C. L´ opez-Urrutia, and A. P´ alffy, Phys. Rev. Lett. 124, 192502 (2020), URL https://link.aps.org/doi/10. 1103/PhysRevLett.124.192502

    2020

  28. [36]

    Porsev, C

    S. Porsev, C. Cheung, and M. Safronova, Quantum Sci- ence and Technology 6, 034014 (2021)

    2021

  29. [37]

    W. Wang, F. Zou, S. Fritzsche, and Y. Li, Phys. Rev. Lett. 133, 223001 (2024), URL https://link.aps.org/ doi/10.1103/PhysRevLett.133.223001

    2024 doi

  30. [38]

    V. A. Dzuba and V. V. Flambaum, Phys. Rev. A 111, L041103 (2025), URL https://link.aps.org/doi/10. 1103/PhysRevA.111.L041103

    2025

  31. [39]

    B. S. Nickerson, M. Pimon, P. V. Bilous, J. Gugler, K. Beeks, T. Sikorsky, P. Mohn, T. Schumm, and A. P´ alffy, Physical Review Letters125, 032501 (2020)

    2020

  32. [40]

    B. S. Nickerson, M. Pimon, P. V. Bilous, J. Gugler, G. A. Kazakov, T. Sikorsky, K. Beeks, A. Gr¨ uneis, T. Schumm, and A. P´ alffy, Phys. Rev. A 103, 053120 (2021), URL https://link.aps.org/doi/10. 1103/PhysRevA.103.053120

    2021

  33. [41]

    Morgan, H

    H. Morgan, H. Tran Tan, R. Elwell, A. Alexandrova, E. R. Hudson, and A. Derevianko, Physical Review Let- ters 134, 253801 (2025)

    2025

  34. [42]

    M. O. Scully and M. S. Zubairy, Quantum optics (Cam- bridge university press, 1997)

    1997

  35. [43]

    Kirschbaum, T

    T. Kirschbaum, T. Schumm, and A. P´ alffy, Physical Re- view C 110, 064326 (2024). 17

    2024

  36. [44]

    Ditler, J

    E. Ditler, J. Mattiat, and S. Luber, Physical Chemistry Chemical Physics 25, 14672 (2023)

    2023

  37. [45]

    Abragam, The principles of nuclear magnetism, 32 (Oxford university press, 1961)

    A. Abragam, The principles of nuclear magnetism, 32 (Oxford university press, 1961)

    1961

  38. [46]

    B. H. Bransden and C. J. Joachain, Physics of atoms and molecules (Pearson Education India, 2006)

    2006

  39. [47]

    W. R. Johnson, Atomic structure theory(Springer, 2007)

    2007

  40. [48]

    A. R. Edmonds, Angular momentum in quantum me- chanics, vol. 4 (Princeton university press, 1996)

    1996

  41. [49]

    Minkov and A

    N. Minkov and A. P´ alffy, Phys. Rev. Lett. 118, 212501 (2017), URL https://link.aps.org/doi/10. 1103/PhysRevLett.118.212501

    2017

  42. [50]

    I. I. Sobelman, Atomic spectra and radiative transitions, vol. 12 (Springer Science & Business Media, 2012)

    2012

  43. [51]

    Tkalya, Journal of Experimental and Theoretical Physics Letters 71, 311 (2000)

    E. Tkalya, Journal of Experimental and Theoretical Physics Letters 71, 311 (2000)

    2000

  44. [52]

    E. V. Tkalya, A. N. Zherikhin, and V. I. Zhudov, Physical Review C 61, 064308 (2000)

    2000

  45. [53]

    Pimon, T

    M. Pimon, T. Kirschbaum, T. Schumm, A. P´ alffy, and A. Gr¨ uneis, in preparation (2025)

    2025

  46. [56]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Computational Ma- terials Science 6, 15 (1996), ISSN 0927-0256, URL https://www.sciencedirect.com/science/article/ pii/0927025696000080

    1996

  47. [57]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Phys. Rev. B 54, 11169 (1996), URL https://link.aps.org/doi/10. 1103/PhysRevB.54.11169

    1996

  48. [59]

    P. E. Bl¨ ochl, Physical Review B50, 17953 (1994), URL https://doi.org/10.1103/physrevb.50.17953

    1994 doi

  49. [60]

    D. D. Koelling and B. N. Harmon, Journal of Physics C: Solid State Physics 10, 3107 (1977), URL https://doi. org/10.1088/0022-3719/10/16/019

    1977 doi

  50. [61]

    Takeda, Zeitschrift f¨ ur Physik B Condensed Matter and Quanta 32, 43 (1978), URL https://doi.org/10

    T. Takeda, Zeitschrift f¨ ur Physik B Condensed Matter and Quanta 32, 43 (1978), URL https://doi.org/10. 1007/bf01322185

    1978

  51. [62]

    R. M. Feenstra, N. Srivastava, Q. Gao, M. Widom, B. Di- aconescu, T. Ohta, G. L. Kellogg, J. T. Robinson, and I. V. Vlassiouk, Physical Review B 87 (2013), URL https://doi.org/10.1103/physrevb.87.041406

    2013 doi

  52. [63]

    Wigner and F

    E. Wigner and F. Seitz, Phys. Rev. 43, 804 (1933), URL https://link.aps.org/doi/10.1103/PhysRev.43.804

    1933 doi

  53. [64]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Physical Re- view Letters 77, 3865 (1996), URL https://doi.org/ 10.1103/physrevlett.77.3865

    1996 doi

  54. [65]

    Kr¨ oger and H

    F. Kr¨ oger and H. Vink, Relations between the Con- centrations of Imperfections in Crystalline Solids(Else- vier, 1956), pp. 307–435, ISBN [’9780126077032’], URL https://doi.org/10.1016/s0081-1947(08)60135-6

    1956 doi

  55. [67]

    J. P. Perdew, International Journal of Quantum Chem- istry 28, 497 (2009), URL http://dx.doi.org/10.1002/ qua.560280846

    2009

  56. [68]

    Shimamura, S

    K. Shimamura, S. L. Baldochi, N. Mujilatu, K. Nakano, Z. Liu, N. Sarukura, and T. Fukuda, Journal of crystal growth 211, 302 (2000)

    2000

  57. [69]

    Sakai, Z

    M. Sakai, Z. Liu, H. Ohtake, N. Sarukura, Y. Segawa, T. Oba, K. Shimamura, S. L. Baldochi, K. Nakano, N. Mujilatu, et al., in Technical Digest. Summaries of papers presented at the Conference on Lasers and Electro-Optics. Postconference Edition. CLEO’99. Con- ference on Lasers...

    1999

  58. [70]

    Pimon, A

    M. Pimon, A. Gr¨ uneis, P. Mohn, and T. Schumm, Crys- tals 12 (2022), ISSN 2073-4352, URL https://www. mdpi.com/2073-4352/12/8/1128/htm

    2022

  59. [71]

    Elwell, J

    R. Elwell, J. E. Terhune, C. Schneider, H. W. Morgan, H. B. T. Tan, U. C. Perera, D. A. Rehn, M. C. Al- fonso, L. von der Wense, B. Seiferle, et al., arXiv preprint arXiv:2506.03018 (2025)

    2025

  60. [72]

    von der Wense, P

    L. von der Wense, P. V. Bilous, B. Seiferle, S. Stellmer, J. Weitenberg, P. G. Thirolf, A. P´ alffy, and G. Kazakov, The European Physical Journal A 56, 1 (2020)

    2020

  61. [73]

    Thielking, K

    J. Thielking, K. Zhang, J. Tiedau, J. Zander, G. Zitzer, M. Okhapkin, and E. Peik, New journal of physics 25, 083026 (2023)

    2023

  62. [74]

    B. W. Woods, S. A. Payne, J. E. Marion, R. S. Hughes, and L. E. Davis, Journal of the Optical Society of Amer- ica B 8, 970 (1991)

    1991

  63. [75]

    Jeet, Search for the low lying transition in the 229Th Nucleus (University of California, Los Angeles, 2018)

    J. Jeet, Search for the low lying transition in the 229Th Nucleus (University of California, Los Angeles, 2018)

    2018

  64. [76]

    Nalikowski, V

    K. Nalikowski, V. Veryazov, K. Beeks, T. Schumm, and M. Kro´ snicki, Phys. Rev. B 111, 115103 (2025), URL https://link.aps.org/doi/10.1103/PhysRevB. 111.115103

    2025 doi

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