WC

Electric Dipole Moments: A permanent electric dipole moment (EDM) of a fundamental particle, nucleus, atom, or molecule violates both parity (P) and time-reversal (T) symmetries. The Standard Model contains only enough CP-violation to generate tiny EDMs, however various extensions to the Standard Model [e.g. Supersymmetry (SUSY)] predict EDMs that are 10 orders of magnitude larger. The current experimental limit on the electron EDM, |de| < 1.6 x 10-27 e-cm [1], already constrains the minimal supersymmetric extension to the Standard Model (MSSM). Ongoing EDM searches strive to tighten constraints on SUSY and/or probe for physics beyond the Standard Model [2]. This research project searches for the electron EDM in a new system, the tungsten carbide (WC) molecule, using proven molecular beam resonance techniques developed by Ramsey [3].

WC has a 3Δ1 ground state with its two valance electrons in a σδ molecular orbital configuration [4-6]. With some generality, the JILA EDM Group has shown that a 3Δ1 molecular state arising from a σδ orbital configuration has several key benefits for an electron EDM search [7,8]:

  1. An electron EDM manifests itself as an energy splitting between spin-up and spin-down states that is proportional to an electric field. Laboratory electric fields are limited to 105 V/cm, however the effective electric field, Eeff, experienced by an electron inside a fully-polarized, heavy, diatomic molecule can exceed 1010 V/cm [9-13]. WC is expected to have |Eeff| ≈ 6 x 1010 V/cm [14].
  2. The Zeeman effect generates an energy splitting between electron spin-up and spin-down states, which can obscure an electron EDM signal. In order to mitigate this effect, a co-magnetometer must be used to continuously monitor the background magnetic field. The 3Δ1 ground state of WC comprises a pair of nearly degenerate J=1 manifolds arising from the Ω-doubling effect [12]. The Zeeman splitting between the m=+1 and m=-1 levels is identical in both J=1 manifolds, however an electron EDM would generate a splitting between m=+1 and m=-1 levels that changes sign between the two J=1 manifolds. Thus, taking the difference frequency between m=+1 ↔ m=-1 transitions in the upper and lower J=1 manifolds generates a result proportional to a potential electron EDM signal that is independent of the background magnetic field.
  3. The pair of J=1 Ω-doublet levels in the 3Δ1 state are closely separated in energy have opposite parity. As a result, WC is relatively easy to polarize, requiring modest laboratory electric fields of order 1 V/cm to fully mix the Ω-doublet parity eigenstates. This reduces systematic effects that are proportional to the applied laboratory electric field, which often plague EDM searches. Additionally, when the opposite parity states are fully mixed, the effective electric field experience by the valance electrons saturates to its maximal value, |Eeff| ≈ 6 x 1010 V/cm. This decouples true EDM signals, which will saturate as well, from false EDM signals, which are often proportional to the applied laboratory electric field.
  4. The 3Δ1 state of WC has a relatively small magnetic moment, μ ≈ μB(2Σ+Λ) << μB, because the electronic spin, |Σ|=1, and orbital, |Λ|=2, angular momenta have opposite projections along the molecular axis [13]. This limits the susceptibility of the experiment to uncontrolled and/or uncalibrated magnetic fields.

The minimum-sized electron EDM that can be experimentally resolved from zero is given by |de| ∼ h/4πEeffτ√N, where N molecules are interrogated for a duration τ. For WC, theoretical calculations suggest |Eeff| ≈ 60 GV/cm [14] and typical molecular beams deliver 106 molecules/sec with an interrogation time of order 1 ms. Under these conditions, we can expect to have the statistical sensitivity to detect an electron EDM of magnitude |de| ∼ 10-29 e-cm/√day, such that 1 day of data would provide a factor of 100 improvement on the current electron EDM limit.

References:

  1. B.C. Regan, E.D. Commins, C.J. Schmidt, and D. DeMille, Phys. Rev. Lett. 88, 071805 (2002).
  2. M. Pospelov and A. Ritz, Ann. Phys. 318, 119 (2005).
  3. N.F. Ramsey, Molecular Beams, Clarendon Press, Oxford (1956).
  4. X. Li, S.S. Liu, W. Chen, and L.-S. Wang, J. Chem. Phys. 111, 2464 (1999).
  5. K. Balasubramanian, J. Chem. Phys. 112, 7425 (2000).
  6. S.M. Sickafoose, A.W. Smith, and M.D. Morse, J. Chem. Phys. 116, 993 (2002).
  7. E.R. Meyer, J.L. Bohn, and M.P. Deskevich, Phys. Rev. A 73, 062108 (2006).
  8. http://jilawww.colorado.edu/bec/CornellGroup/
  9. P.G.H. Sandars, Phys. Rev. Lett. 19, 1396 (1967).
  10. P.G.H. Sandars, Atomic Physics 4, 71 (1975).
  11. J.J. Hudson, B.E. Sauer, M.R. Tarbutt, and E.A. Hinds, Phys. Rev. Lett. 89, 023003 (2002).
  12. D. Kawall, F. Bay, S. Bickman, Y. Jiang, and D. DeMille, Phys. Rev. Lett. 92, 133007 (2004).
  13. N.E. Shafer-Ray, Phys. Rev. A 73, 034102 (2006).
  14. E.R. Meyer and J.L. Bohn, private communication. Consistent with the sign convention and uncertainty estimate in Ref. [7], WC is expected to have Eeff ≈ -60 GV/cm to within a factor of 3.

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