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Register a new userMethods, Analysis, and the Treatment of Systematic Errors for the Electron Electric Dipole Moment Search in Thorium Monoxide
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We recently set a new limit on the electric dipole moment of the electron (eEDM) (J. Baron et al., ACME collaboration, Science 343 (2014), 269-272), which represented an order-of-magnitude improvement on the previous limit and placed more stringent constraints on many CP-violating extensions to the Standard Model. In this paper we discuss the measurement in detail. The experimental method and associated apparatus are described, together with the techniques used to isolate the eEDM signal. In particular, we detail the way experimental switches were used to suppress effects that can mimic the signal of interest. The methods used to search for systematic errors, and models explaining observed systematic errors, are also described. We briefly discuss possible improvements to the experiment.
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We present an updated EDM effective electric field of $E_{text{eff}} = 75.2left[frac{rm GV}{rm cm}right]$ and the electron-nucleon scalar-pseudoscalar interaction constant $W_S=107.8$ [kHz] for the ${^3Delta}_1$ science state of ThO. The criticisms made in reference [J. Chem. Phys. 142, 024301 (2015)] are addressed and largely found to be unsubstantiated within the framework of our approach.
The energy splitings for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the $^3Delta_1$ electronic state of $^{180}$Hf$^{19}$F$^+$ ion are calculated as functions of the external variable electric and magnetic fields within two approaches. In the first one transition to the rotating frame is performed, whereas in the second approach the quantization of rotating electromagnetic field is performed. Calculations are required for understanding possible systematic errors in the experiment to search for electron electric dipole moment (eEDM) on $^{180}$Hf$^{19}$F$^+$ ion.
Polyatomic polar molecules are promising systems for future experiments that search for violation of time-reversal and parity symmetries due to their advantageous electronic and vibrational structure, which allows laser cooling, full polarisation of the molecule, and reduction of systematic effects [I. Kozyryev and N.R. Hutzler, Phys, Rev. Lett. {bf 119}, 133002 (2017)]. In this work we investigate the enhancement factor of the electric dipole moment of the electron ($E_text{eff}$) in the triatomic monohydroxide molecules BaOH and YbOH within the high-accuracy relativistic coupled cluster method. The recommended $E_text{eff}$ values of the two systems are 6.65 $pm$ 0.15 GV/cm and 23.4 $pm$ 1.0 GV/cm, respectively. We compare our results with similar calculations for the isoelectronic diatomic molecules BaF and YbF, which are currently used in experimental search for $P,T$-odd effects in molecules. The $E_text{eff}$ values prove to be very close, within about 1.5 $%$ difference in magnitude between the diatomic and the triatomic compounds. Thus, BaOH and YbOH have a similar enhancement of the electron electric dipole moment, while benefiting from experimental advantages, and can serve as excellent candidates for next-generation experiments.
We report the theoretical investigation of the suppression of magnetic systematic effects in HfF$^+$ cation for the experiment to search for the electron electric dipole moment. The g-factors for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the $^3Delta_1$ state are calculated as functions of the external electric field. The lowest value for the difference between the g-factors of $Omega$-doublet levels, $Delta g = 3 times 10^{-6}$, is attained at the electric field 7 V/cm. The body-fixed g-factor, $G_{parallel}$, was obtained both within the electronic structure calculations and with our fit of the experimental data from [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science {bf 342}, 1220 (2013)]. For the electronic structure calculations we used a combined scheme to perform correlation calculations of HfF$^+$ which includes both the direct 4-component all-electron and generalized relativistic effective core potential approaches. The electron correlation effects were treated using the coupled cluster methods. The calculated value $G_{parallel}=0.0115$ agrees very well with the $G_{parallel}=0.0118$ obtained in the our fitting procedure. The calculated value $D_{parallel}=-1.53$ a.u. of the molecule frame dipole moment (with the origin in the center of mass) is in agreement with the experimental value $D_{parallel}=-1.54(1)$ a.u. [H. Loh, Ph.D. thesis, Massachusetts Institute of Technology (2006)].
We investigate the merits of a measurement of the permanent electric dipole moment of the electron ($e$EDM) with barium monofluoride molecules, thereby searching for phenomena of CP violation beyond those incorporated in the Standard Model of particle physics. Although the BaF molecule has a smaller enhancement factor in terms of the effective electric field than other molecules used in current studies (YbF, ThO and ThF$^+$), we show that a competitive measurement is possible by combining Stark-deceleration, laser-cooling and an intense primary cold source of BaF molecules. With the long coherent interaction times obtainable in a cold beam of BaF, a sensitivity of $5times10^{-30}$ e$cdot$cm for an $e$EDM is feasible. We describe the rationale, the challenges and the experimental methods envisioned to achieve this target.
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