An electron electric dipole moment search in the X³Δ₁ ground state of tungsten carbide molecules

Abstract

We identify the X ³Δ₁ electronic ground state of tungsten carbide (WC) as a candidate molecular system in which to search for a permanent electric dipole moment (EDM) of the electron. The valence electrons in tungsten carbide experience an effective electric field of order 54 GV cm⁻¹ when the molecule is placed in a laboratory electric field of just a few mV cm⁻¹. Currently, a continuous tungsten carbide molecular beam is under construction. Tungsten atoms are evaporated from a resistively heated tungsten filament and are entrained in a noble gas jet containing a small fraction of methane. Tungsten carbide molecules are formed through the reaction W + CH₄ → WC + 2H₂.

Keywords:

• precision measurement
• tungsten carbide
• electron electric dipole moment
• CP-violation
• supersymmetry

Acknowledgements

We thank the Physics of Quantum Electronics XXXIX organizing committee, Marlan O. Scully, M. Suhail Zubairy, and George R. Welch, for the invitation to present our research. Also, we acknowledge valuable insights and comments from T. Chupp, E. Cornell, L. Sinclair, and R. Stutz throughout the development of this work. This work was partially funded by the NSF.

Notes

Notes

1. There are solid state electron EDM searches that look for an induced magnetic field under an applied voltage 35 or an induced voltage under an applied magnetic field 36.

2. To our knowledge, there is one published calculation that disagrees with the ³Δ₁ assignment for the ground state of tungsten carbide 37.

3. All M levels of the J = 1 rotational ground state will mix with the corresponding M levels of the J = 2 rotationally excited state, however, this mixing will be minimal for sufficiently weak laboratory electric fields in the limit ΔE _Ω ≪ μ_eℰ ≪ hcB, where h is the Planck constant, c is the speed of light, and B is the rotational constant of the molecular state.

4. The average energy splitting for the singly-ionized atomic tungsten electronic ground state, (E[⁶ D _9/2] − E[⁶ D _1/2])/4 ≈ hc × 1537 cm⁻¹, was taken to be the relevant spin–orbit splitting since the tungsten carbide bond is fairly ionic, i.e. W⁺–C⁻. Using the average energy splitting for the neutral atomic tungsten electronic ground state, (E[⁵ D ₄] − E[⁵ D ₀])/4 ≈ hc × 1555 cm⁻¹ does not significantly modify the calculation.