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Register a new userZeeman interaction in ThO $H^3Delta_1$ for the electron EDM search
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The current limit on the electrons electric dipole moment, $|d_mathrm{e}|<8.7times 10^{-29} e {cdotp} {rm cm}$ (90% confidence), was set using the molecule thorium monoxide (ThO) in the $J=1$ rotational level of its $H ^3Delta_1$ electronic state [Science $bf 343$, 269 (2014)]. This state in ThO is very robust against systematic errors related to magnetic fields or geometric phases, due in part to its $Omega$-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the $g$-factor difference between the $Omega$-doublets is minimized. We consider the $g$-factors of the ThO $H^3Delta_1$ state both experimentally and theoretically, including dependence on $Omega$-doublets, rotational level, and external electric field. The calculated and measured values are in good agreement. We find that the $g$-factor difference between $Omega$-doublets is smaller in $J=2$ than in $J=1$, and reaches zero at an experimentally accessible electric field. This means that the $H,J=2$ state should be even more robust against a number of systematic errors compared to $H,J=1$.
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A method and code for calculations of diatomic molecules in the external variable electromagnetic field have been developed. Code applied for calculation of systematics in the electrons electric dipole moment search experiment on ThO $H^3Delta_1$ state related to geometric phases, including dependence on $Omega$-doublet, rotational level, and external static electric field. It is found that systematics decrease cubically with respect to the frequency of the rotating transverse component of the electric field. Calculation confirms that experiment on ThO $H^3Delta_1$ state is very robust against systematic errors related to geometric phases.
Experimental searches for the electron electric dipole moment (EDM) probe new physics beyond the Standard Model. The current best EDM limit was set by the ACME Collaboration [Science textbf{343}, 269 (2014)], constraining time reversal symmetry ($T$) violating physics at the TeV energy scale. ACME used optical pumping to prepare a coherent superposition of ThO $H^3Delta_1$ states that have aligned electron spins. Spin precession due to the molecules internal electric field was measured to extract the EDM. We report here on an improved method for preparing this spin-aligned state of the electron by using STIRAP. We demonstrate a transfer efficiency of $75pm5%$, representing a significant gain in signal for a next generation EDM experiment. We discuss the particularities of implementing STIRAP in systems such as ours, where molecular ensembles with large phase-space distributions are transfered via weak molecular transitions with limited laser power and limited optical access.
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 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 best upper limit for the electron electric dipole moment was recently set by the ACME collaboration. This experiment measures an electron spin-precession in a cold beam of ThO molecules in their metastable $H~(^3Delta_1)$ state. Improvement in the statistical and systematic uncertainties is possible with more efficient use of molecules from the source and better magnetometry in the experiment, respectively. Here, we report measurements of several relevant properties of the long-lived $Q~(^3Delta_2)$ state of ThO, and show that this state is a very useful resource for both these purposes. The $Q$ state lifetime is long enough that its decay during the time of flight in the ACME beam experiment is negligible. The large electric dipole moment measured for the $Q$ state, giving rise to a large linear Stark shift, is ideal for an electrostatic lens that increases the fraction of molecules detected downstream. The measured magnetic moment of the $Q$ state is also large enough to be used as a sensitive co-magnetometer in ACME. Finally, we show that the $Q$ state has a large transition dipole moment to the $C~(^1Pi_1)$ state, which allows for efficient population transfer between the ground state $X~(^1Sigma^+)$ and the $Q$ state via $X-C-Q$ Stimulated Raman Adiabatic Passage (STIRAP). We demonstrate $90,$% STIRAP transfer efficiency. In the course of these measurements, we also determine the magnetic moment of $C$ state, the $Xrightarrow C$ transition dipole moment, and branching ratios of decays from the $C$ state.
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