A 2024 proposal identified the diatomic molecules AuX (X = C, Si, Ge, Sn, Pb) as a rare combination of laser-accessible optical-cycling transitions with nearly diagonal Franck–Condon factors, parity-doubled X²Π₁/₂ ground states with near-zero magnetic moments, and effective electric fields of 10–30 GV/cm for electron electric dipole moment (eEDM) searches, projecting a statistical sensitivity of order 8×10⁻³² e·cm with trapped AuPb. Realizing this proposal requires four linked developments that the proposal itself left open: (i) high-resolution spectroscopic validation of the predicted term energies, Λ-doublet splittings (typically ~0.5 GHz), hyperfine structure (~100–1000 MHz), and rotational structure; (ii) quantification of the spin–orbit coupling between the A²Σ⁺ state and the nearby a⁴Σ⁻ quartet state as a possible loss channel from the optical cycle; (iii) ab initio extension of the sensitivity survey to other symmetry-violating electromagnetic moments, such as the nuclear magnetic quadrupole moment, and to the coinage-metal plumbides CuPb and AgPb; and (iv) trapping, cooling, and coherence-preservation protocols, including whether few-photon (Zeeman–Sisyphus) techniques can be applied to ground-state parity doublets. As of 2026 only the first item has begun: AuC has been observed for the first time, confirming the diagonal Franck–Condon factors and the parity-doubled ground state, but leaving rotational, hyperfine, and Λ-doublet structure unmeasured, while the other items are untouched. The problem remains open.

Background

The electron electric dipole moment (eEDM) is a hypothetical permanent dipole moment of the electron that violates both time-reversal (T) and parity (P) symmetry. The Standard Model predicts an eEDM many orders of magnitude below current experiments, so detecting one would reveal new physics, and every improved upper bound constrains broad classes of beyond-Standard-Model theories. Polar molecules are enhanced eEDM probes because their enormous internal electric fields, conventionally summarized by an effective electric field ε_eff acting on the electron spin, far exceed anything achievable in the laboratory; the eEDM energy shift is proportional to ε_eff, which favors molecules with large spin density on a high-Z nucleus. A second valuable feature is a ground-state parity doublet: a pair of nearly degenerate levels of opposite parity, such as the Λ-doublet of a ²Π molecular electronic state (in the standard term notation for diatomic molecules, the superscript 2 gives the spin multiplicity and the Greek letter labels the projection of the electronic orbital angular momentum onto the internuclear axis; the Λ-doublet arises because that orbital angular momentum can point along either direction of the internuclear axis). Parity doublets allow a molecule to be fully polarized by modest laboratory fields and enable internal comagnetometry, in which the sign of the eEDM interaction is reversed by switching between the doublet partners without changing laboratory fields, a powerful systematic-error control. The most stringent published eEDM limits come from molecular ThO (the ACME beam experiments, named for the Advanced Cold Molecule Electron EDM collaboration) and the trapped HfF⁺ ion measurement of Roussy et al. (Science 381, 46 (2023)), which defines the "current limit" used below. It has proven difficult to find molecules that combine large ε_eff, ground-state parity doublets, and optical cycling, where optical cycling means repeated laser excitation and spontaneous emission on a nearly closed electronic transition; it requires nearly diagonal Franck–Condon factors (the overlaps between vibrational wavefunctions of the two electronic states, which determine the vibrational branching ratios of fluorescence), so that many photons can be scattered without losing the molecule to unaddressed vibrational levels, typically using a handful of repumping lasers. In Phys. Rev. A 110, 042807 (2024), Stuntz, Rice, Cheng and Augenbraun proposed the class of diatomic molecules AuX (X = C, Si, Ge, Sn, Pb) as simultaneously possessing all of these features. Their relativistic coupled-cluster calculations (coupled cluster being the quantum-chemical method hierarchy that systematically accounts for electron correlation, here including relativistic effects for the heavy Au and Pb atoms) predicted ε_eff of 10–30 GV/cm; a parity-doubled X²Π₁/₂ absolute ground state whose g-factor, the dimensionless constant relating a state's magnetic moment to its angular momentum, is at least 50 times smaller than that of a ²Σ state, a term with zero electronic orbital angular momentum along the internuclear axis (strongly suppressing magnetic-field systematics); typical Λ-doublet splittings of about 0.5 GHz, which with dipole moments around 2 D allow full polarization in laboratory fields below 1 kV/cm; hyperfine splittings of order 100–1000 MHz (requiring frequency sidebands in any repumping scheme); and vibrational branching fractions permitting photon closure with 6–10 repumping lasers (14 for AuSn). They estimated that an experiment with 10⁴ trapped AuPb molecules and 2 s coherence time could reach a statistical sensitivity of roughly 8×10⁻³² e·cm in one week of averaging, nearly two orders of magnitude beyond the current limit. The proposal itself, however, identified the unresolved issues that stand between these predictions and a real experiment, and these constitute the present problem: the predicted structure (term energies, Λ-doublet, hyperfine, and rotational structure) was unvalidated by any spectroscopy; the spin–orbit coupling between the optically excited A²Σ⁺ state and the nearby a⁴Σ⁻ quartet state, a possible loss channel from the optical cycle (direct decays being spin- and symmetry-forbidden and the small energy gap suppressing spontaneous emission), was unquantified; the sensitivity of AuX to other symmetry-violating moments, such as the nuclear magnetic quadrupole moment (NMQM, a P,T-violating moment of a nucleus with spin ≥ 1 that couples to electronic structure analogously to the eEDM), and the properties of related coinage-metal plumbides (CuPb, AgPb) were unexplored; and no trapping, cooling, or coherence-preservation protocol existed for these molecules, including the open question of whether recent few-photon techniques, i.e. Zeeman–Sisyphus deceleration and cooling schemes in which each scattered photon removes a large energy increment, can be applied to molecules with ground-state parity doublets.

Problem Statement

Establish whether the AuX (X = C, Si, Ge, Sn, Pb) molecules can actually serve as the proposed optical-cycling platform for an improved electron electric dipole moment search, by resolving the four linked gaps that the 2024 proposal left open. The common objective uniting them is the validation and completion of the AuX proposal, so that its projected sensitivity (of order 8×10⁻³² e·cm with 10⁴ trapped AuPb molecules and 2 s coherence) rests on measured rather than purely computed properties. Specifically: (1) perform high-resolution experimental spectroscopy of the leading candidate AuX molecules, at minimum AuC and AuPb, to validate the predicted term energies, Λ-doublet splittings (typically ~0.5 GHz, including the nuclear-electric-quadrupole corrections expected for ¹⁹⁷Au), hyperfine structure (~100–1000 MHz), and rotational structure that the detailed laser repumping and sidebanding schemes require; (2) determine, theoretically and where possible experimentally, the magnitude and impact of the spin–orbit coupling between the A²Σ⁺ state and the nearby a⁴Σ⁻ quartet state, and quantify any resulting loss from the optical cycle; (3) extend the ab initio survey by computing the sensitivity of AuX species to other symmetry-violating electromagnetic moments (for example the nuclear magnetic quadrupole moment) and by determining whether the related coinage-metal plumbides CuPb and AgPb share the combination of diagonal Franck–Condon factors and large effective electric fields; and (4) design and experimentally validate trapping, cooling, and coherence-preservation protocols for these molecules, in particular whether recent few-photon (Zeeman–Sisyphus) techniques can be applied to molecules with ground-state parity doublets, which are prerequisites for realizing the projected statistical sensitivities. Deliverables (1)–(3) constitute the scientifically bounded core, completed when the measured spectra of the leading candidate molecules — at minimum AuC, which has been observed, and AuPb, the molecule on which the projected sensitivity rests — confirm or correct the predicted structure, the optical-cycle loss channels are quantified, and the symmetry-violation sensitivity landscape (including CuPb/AgPb) is mapped. Deliverable (4) is the enabling technology stage that the same objective depends on and is complete when a demonstrated protocol realizes cold, coherent AuX samples; the overall question is answered when all four are resolved, whether affirmatively or by identifying where the proposal fails.

References

  1. K. C. Stuntz, K. L. Rice, L. Cheng, and B. L. Augenbraun, "Optical cycling and sensitivity to the electron's electric dipole moment in gold-containing molecules", Phys. Rev. A 110, 042807 (2024), DOI: 10.1103/physreva.110.042807, https://doi.org/10.1103/physreva.110.042807 (preprint arXiv:2407.19372, https://arxiv.org/abs/2407.19372)
  2. R. M. Weldon, D. M. Darling, N. M. Albright, K. L. Rice, P. L. Salerno, K. C. Stuntz, and B. L. Augenbraun, "Elucidating Au–C bonding via laser spectroscopy of gold monocarbide", J. Chem. Phys. 164, 224302 (2026), DOI: 10.1063/5.0337427, https://doi.org/10.1063/5.0337427 (preprint arXiv:2604.04322, https://arxiv.org/abs/2604.04322)
  3. A. Frenett, D. Gan, N. Emtage, M. Fouad, S. Miki-Silva, and X. Wu, "Optical cycling on thorium monoxide (ThO) for an improved test of fundamental symmetries", arXiv:2605.28509 (2026), https://arxiv.org/abs/2605.28509
  4. Z. D. Lasner, A. T. Ohl, N. M. Albright, K. L. Rice, C. Peng, L. Cheng, J. M. Doyle, and B. L. Augenbraun, "Hyperfine-resolved spectroscopy of dysprosium monoxide (DyO) for precision measurements of the nuclear Schiff moment", arXiv:2511.11975 (2025), https://arxiv.org/abs/2511.11975
  5. X. Fan and L. Cheng, "Nuclear-electric-quadrupole-moment-induced parity doubling in molecules for symmetry-violation searches", Phys. Rev. A 112, 022823 (2025), DOI: 10.1103/tydw-3ksd, https://doi.org/10.1103/tydw-3ksd (preprint arXiv:2506.10904, https://arxiv.org/abs/2506.10904)
  6. T. S. Roussy, L. Caldwell, T. Wright, W. B. Cairncross, Y. Shagam, K. B. Ng, N. Schlossberger, S. Y. Park, A. Wang, J. Ye, and E. A. Cornell, "An improved bound on the electron's electric dipole moment", Science 381, 46–50 (2023), DOI: 10.1126/science.adg4084, https://doi.org/10.1126/science.adg4084