A permanent electric dipole moment (EDM) of an atom violates time-reversal symmetry and is a sensitive probe of CP violation beyond the Standard Model. In diamagnetic atoms such as 129Xe^{129}\mathrm{Xe} the observable is the nuclear Schiff moment SS, which induces an atomic EDM datom=αSMSd_{\mathrm{atom}}=\alpha_{\mathrm{SM}}S; a measured d(129Xe)d(^{129}\mathrm{Xe}) is interpreted through nuclear-structure calculations of SS in terms of CP-violating pion–nucleon couplings and quark chromo-EDMs. In 2014 the nuclear-spin-oscillator (active spin maser) program reported single-shot frequency precision of 9.3 nHz over 3×1043\times10^{4} s but identified open issues standing between that status and a competitive 129Xe^{129}\mathrm{Xe} EDM result: integration of a co-precessing 3He^{3}\mathrm{He} co-magnetometer and control of Xe–Rb and field-gradient systematics under electric-field reversals; the source also discusses the relation of the atomic EDM to the nuclear Schiff moment S(129Xe)S(^{129}\mathrm{Xe}) through which such a result is interpreted. The subsequent literature shows: a competitive measurement was delivered in 2019 by a different technique (free-precession 3He^{3}\mathrm{He}–129Xe^{129}\mathrm{Xe} comagnetometry with detection by SQUIDs, superconducting quantum interference devices), with the current best limit ∣d(129Xe)∣<8.3×10−28 e⋅cm|d(^{129}\mathrm{Xe})|<8.3\times10^{-28}\ e\cdot\mathrm{cm} (95% CL, 2021 reanalysis); the spin-oscillator route itself has published development work but no EDM result; atomic coefficients are now precise at the few-percent level while S(129Xe)S(^{129}\mathrm{Xe}) remains uncertain at the nuclear-model level. The open core is a measurement at the aimed 10−28 e⋅cm10^{-28}\ e\cdot\mathrm{cm} scale with fully characterized systematics, enabling its interpretation through S(129Xe)S(^{129}\mathrm{Xe}) in terms of fundamental CP violation.

Background

A permanent electric dipole moment (EDM) is a separation of positive and negative charge along the spin axis of a particle, atom, or molecule; because it must align with the spin, it changes sign under both parity (P) and time-reversal (T) transformations and can therefore be nonzero only if both symmetries are violated. Standard-Model EDM predictions lie far below current detectability, so any observed EDM would signal new CP-violating physics of the kind needed to explain the cosmic baryon asymmetry. Searches in diamagnetic atoms — atoms with closed electronic shells and nonzero nuclear spin — probe CP violation in the nucleon–nucleon interaction. In such atoms the nuclear EDM is screened by the electrons (the Schiff theorem), so the observable is the nuclear Schiff moment SS, the leading unscreened P,T-odd moment of the nuclear charge distribution. The atomic EDM is then datom=αSMSd_{\mathrm{atom}}=\alpha_{\mathrm{SM}}S, where the atomic coefficient αSM\alpha_{\mathrm{SM}} is computed with relativistic many-body atomic theory, while SS itself is computed from nuclear-structure models with CP-violating pion–nucleon couplings as input; these in turn connect to quark-level CP-violating parameters such as the quark chromo-EDMs (the EDM of a quark generated by its coupling to the gluon field).

The isotope 129Xe^{129}\mathrm{Xe} (nuclear spin 1/21/2, a noble gas) is attractive for EDM searches because it can be highly polarized by spin-exchange optical pumping with rubidium vapor and has long spin-coherence times. The measurement principle is to polarize the atoms, let them precess in parallel magnetic and electric fields, and search for a change of the precession frequency when the electric field is reversed: an EDM produces a frequency shift proportional to the applied field. Because magnetic-field drifts mimic this signal, a comagnetometer — a second spin species co-located in the same cell, here 3He^{3}\mathrm{He} or 131Xe^{131}\mathrm{Xe} — continuously measures and cancels the magnetic-field fluctuations. The nuclear spin oscillator (also called an active nuclear spin maser) is a technique in which optically detected nuclear spin precession is sustained indefinitely by feedback magnetic fields transverse to the static field, so the precession phase can be integrated over very long times, in principle reaching nHz-level frequency resolution. By 2014 the Tokyo/RIKEN collaboration had achieved 9.3 nHz single-shot frequency precision over 3×1043\times10^{4} s with this technique and had incorporated a 3He^{3}\mathrm{He} comagnetometer, but the 3He^{3}\mathrm{He} polarization in the EDM measurement cell was insufficient for concurrent maser operation, so the first EDM run combined 129Xe^{129}\mathrm{Xe} maser oscillation with 3He^{3}\mathrm{He} free-induction decay. Frequency shifts from the contact interaction between 129Xe^{129}\mathrm{Xe} and polarized Rb atoms — the dominant residual systematic, only partially removed by a double-cell geometry (a cell divided into a pumping part and a detection part to reduce Rb polarization where the signal is read out) — were reduced by more than a factor of ten but not eliminated. The then-current 129Xe^{129}\mathrm{Xe} limit was ∣d∣<6.6×10−27 e⋅cm|d|<6.6\times10^{-27}\ e\cdot\mathrm{cm} at 95% confidence level (Rosenberry and Chupp, 2001; the 2014 source quotes the more optimistic value 4.1×10−27 e⋅cm4.1\times10^{-27}\ e\cdot\mathrm{cm}), and the program aimed at ∣d∣∼10−28 e⋅cm|d|\sim10^{-28}\ e\cdot\mathrm{cm}, which requires roughly 1 nHz frequency precision under electric fields of order 10 kV/cm. Interpreting any measured d(129Xe)d(^{129}\mathrm{Xe}) requires the nuclear Schiff moment S(129Xe)S(^{129}\mathrm{Xe}), whose calculations in the nuclear shell model — the standard framework in which nucleons fill quantized single-particle orbitals and interact through an effective interaction — were at that time still unsettled. The open problem is what remains between that 2014 status and an authoritative 129Xe^{129}\mathrm{Xe} EDM result together with its interpretation in terms of fundamental CP violation.

Problem Statement

Identify and analyse the open issues standing between the 2014 status of the nuclear-spin-oscillator program and an authoritative electric dipole moment result for the 129Xe^{129}\mathrm{Xe} atom at the program's targeted sensitivity, ∣d(129Xe)∣∼10−28 e⋅cm|d(^{129}\mathrm{Xe})|\sim10^{-28}\ e\cdot\mathrm{cm} — an improved result below the current best limit ∣d(129Xe)∣<8.3×10−28 e⋅cm|d(^{129}\mathrm{Xe})|<8.3\times10^{-28}\ e\cdot\mathrm{cm} (95% CL) — together with the interpretation of such a result in terms of fundamental CP-violating parameters. Per the source, an EDM search at this scale requires frequency precision at the 1 nHz level under an electric field of order 10 kV/cm. The analysis must address the measurement component of this goal:

A 129Xe^{129}\mathrm{Xe} EDM measurement in which a co-habiting co-magnetometer (3He^{3}\mathrm{He}, or co-located 131Xe^{131}\mathrm{Xe}) continuously measures and corrects magnetic-field fluctuations in the 129Xe^{129}\mathrm{Xe} volume; residual Xe–Rb interaction-induced frequency shifts, spatial field gradients, and long-term stability under repeated electric-field reversals are characterized and suppressed below the statistical sensitivity; and the frequency determination reaches the nHz level under electric fields of order 10 kV/cm, as needed to resolve an EDM of 10−28 e⋅cm10^{-28}\ e\cdot\mathrm{cm}. For the active-spin-maser route this means sustained maser oscillation with the co-magnetometer integrated in the measurement cell. The analysis must specify what a complete statistical and systematic uncertainty budget for such a measurement would have to contain.

The interpretation follows the chain the source discusses: through datom=αSMSd_{\mathrm{atom}}=\alpha_{\mathrm{SM}}S, the measured EDM is related to the nuclear Schiff moment S(129Xe)S(^{129}\mathrm{Xe}) and, via it, to CP-violating pion–nucleon couplings and quark chromo-EDMs. The remaining nuclear-model uncertainty of S(129Xe)S(^{129}\mathrm{Xe}) limits the precision of this interpretation and is a known difficulty of the problem rather than a separately deliverable result.

References

  1. K. Asahi, Y. Ichikawa, M. Chikamori, Y. Ohtomo, E. Hikota, T. Suzuki, T. Inoue, T. Furukawa, A. Yoshimi, K. Suzuki, T. Nanao, H. Miyatake, M. Tsuchiya, N. Yoshida, H. Shirai, T. Ino, H. Ueno, Y. Matsuo, T. Fukuyama, 'Search for electric dipole moment in 129Xe atom using a nuclear spin oscillator', Physics of Particles and Nuclei 45, 199-201 (2014). DOI: 10.1134/S1063779614010080, https://doi.org/10.1134/S1063779614010080
  2. Y. Ichikawa, M. Chikamori, Y. Ohtomo, E. Hikota, Y. Sakamoto, T. Suzuki, C. P. Bidinosti, T. Inoue, T. Furukawa, A. Yoshimi, K. Suzuki, T. Nanao, H. Miyatake, M. Tsuchiya, N. Yoshida, H. Shirai, T. Ino, H. Ueno, Y. Matsuo, T. Fukuyama, K. Asahi, 'Search for electric dipole moment in 129Xe atom using active nuclear spin maser', EPJ Web of Conferences 66, 05007 (2014). DOI: 10.1051/epjconf/20146605007, https://doi.org/10.1051/epjconf/20146605007
  3. M. A. Rosenberry, T. E. Chupp, 'Atomic Electric Dipole Moment Measurement Using Spin Exchange Pumped Masers of 129Xe and 3He', Physical Review Letters 86, 22-25 (2001). DOI: 10.1103/PhysRevLett.86.22, https://doi.org/10.1103/PhysRevLett.86.22
  4. N. Sachdeva, I. Fan, E. Babcock, M. Burghoff, T. E. Chupp, S. Degenkolb, P. Fierlinger, S. Haude, E. Kraegeloh, W. Kilian, S. Knappe-Grüneberg, F. Kuchler, T. Liu, M. Marino, J. Meinel, K. Rolfs, Z. Salhi, A. Schnabel, J. T. Singh, S. Stuiber, W. A. Terrano, L. Trahms, J. Voigt, 'New Limit on the Permanent Electric Dipole Moment of 129Xe using 3He Comagnetometry and SQUID Detection', Physical Review Letters 123, 143003 (2019). DOI: 10.1103/PhysRevLett.123.143003, https://doi.org/10.1103/PhysRevLett.123.143003 (arXiv:1902.02864)
  5. T. Liu, K. Rolfs, I. Fan, S. Haude, W. Kilian, L. Li, A. Schnabel, J. Voigt, L. Trahms, 'Revisiting 129Xe electric dipole moment measurements applying a new global phase fitting approach', New Journal of Physics 23, 063076 (2021). DOI: 10.1088/1367-2630/ac09ca, https://doi.org/10.1088/1367-2630/ac09ca (arXiv:2103.16221)
  6. T. Sato, Y. Ichikawa, S. Kojima, C. Funayama, S. Tanaka, T. Inoue, A. Uchiyama, A. Gladkov, A. Takamine, Y. Sakamoto, Y. Ohtomo, C. Hirao, M. Chikamori, E. Hikota, T. Suzuki, M. Tsuchiya, T. Furukawa, A. Yoshimi, C. P. Bidinosti, T. Ino, H. Ueno, Y. Matsuo, T. Fukuyama, N. Yoshinaga, Y. Sakemi, K. Asahi, 'Development of co-located 129Xe and 131Xe nuclear spin masers with external feedback scheme', Physics Letters A 382, 588-594 (2018). DOI: 10.1016/j.physleta.2017.12.003, https://doi.org/10.1016/j.physleta.2017.12.003 (arXiv:1803.06821)
  7. T. Sato, Y. Ichikawa, S. Kojima, C. Funayama, S. Tanaka, Y. Sakamoto, Y. Ohtomo, C. Hirao, M. Chikamori, E. Hikota, T. Furukawa, A. Yoshimi, C. P. Bidinosti, T. Ino, H. Ueno, Y. Matsuo, T. Fukuyama, K. Asahi, 'Development of 131Xe Co-magnetometry For Xe Atomic EDM Search', PoS(INPC2016), 174 (2017). DOI: 10.22323/1.281.0174, https://doi.org/10.22323/1.281.0174
  8. A. Sakurai, B. K. Sahoo, K. Asahi, B. P. Das, 'Relativistic many-body theory of the electric dipole moment of 129Xe and its implications for probing new physics beyond the standard model', Physical Review A 100, 020502(R) (2019). DOI: 10.1103/PhysRevA.100.020502, https://doi.org/10.1103/PhysRevA.100.020502
  9. M. Hubert, T. Fleig, 'Electric dipole moments generated by nuclear Schiff moment interactions: A reassessment of the atoms 129Xe and 199Hg and the molecule 205TlF', Physical Review A 106, 022817 (2022). DOI: 10.1103/PhysRevA.106.022817, https://doi.org/10.1103/PhysRevA.106.022817 (arXiv:2203.04618)
  10. T. Fleig, M. Jung, 'P,T-odd interactions in atomic 129Xe and phenomenological applications', Physical Review A 103, 012807 (2021). DOI: 10.1103/PhysRevA.103.012807, https://doi.org/10.1103/PhysRevA.103.012807
  11. N. Yoshinaga, K. Higashiyama, R. Arai, E. Teruya, 'Nuclear Schiff moments for the lowest 1/2+ states in Xe isotopes', Physical Review C 87, 044332 (2013). DOI: 10.1103/PhysRevC.87.044332, https://doi.org/10.1103/PhysRevC.87.044332
  12. K. Yanase, N. Shimizu, 'Large-scale shell-model calculations of nuclear Schiff moments of 129Xe and 199Hg', Physical Review C 102, 065502 (2020). DOI: 10.1103/PhysRevC.102.065502, https://doi.org/10.1103/PhysRevC.102.065502
  13. B. K. Sahoo, N. Yamanaka, K. Yanase, 'Revisiting theoretical analysis of the electric dipole moment of 129Xe', Physical Review A 108, 042811 (2023). DOI: 10.1103/PhysRevA.108.042811, https://doi.org/10.1103/PhysRevA.108.042811
  14. S. Degenkolb, N. Elmer, T. Modak, M. Mühlleitner, T. Plehn, 'A global view of the EDM landscape', SciPost Physics 20, 151 (2026). DOI: 10.21468/SciPostPhys.20.6.151, https://doi.org/10.21468/SciPostPhys.20.6.151