ac Stark effect in ThOH3Δ1for the electron electric-dipole-moment search

Abstract

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 electron's electric dipole moment search experiment on ThO H 3 ∆1 state related to geometric phases, including dependence on Ω-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 3 ∆1 state is very robust against systematic errors related to geometric phases.The experimental measurement of a non-zero electron electric dipole moment (eEDM, d e ) would be a clear signature of physics beyond the Standard model [1-4]. The current limit for eEDM, |d e | < 9 × 10 −29 e·cm (90% confidence), was set with a buffer-gas cooled molecular beam [5][6][7] of thorium monoxide (ThO) molecules in the metastable electronic H 3 ∆ 1 state. It was shown that due to existence of closely-spaced levels of opposite parity of Ω-doublet the experiment on ThO is very robust against a number of systematic effects related to magnetic fields [8,9] or geometric phases [10]. However, the upper and lower Ω-doublet states have slightly different properties and systematic effects related to magnetic field imperfections and geometric phases can still manifest themselves as a false eEDM. The dependence of gfactors of the ThO H 3 ∆ 1 state on Ω-doublets and external electric field was considered in Ref. [9]. The aim of the present work is to consider geometric phase shifts.Following the computational scheme of [9,11], the energies of the rotational levels in the H 3 ∆ 1 electronic state of the 232 Th 16 O molecule in external static electric E = Eẑ and magnetic B = Bẑ fields are obtained by numerical diagonalization of the molecular Hamiltonian (Ĥ mol ) over the basis set of the electronic-rotational wavefunc-is the rotational wavefunction, α, β, γ are Euler angles, and M (Ω) is the projection of the molecule angular momentum J on the labẑ (internuclearn) axis. Detailed feature of the Hamiltonian is described in [9]. In the paper the M = ±1 states which represent interest for eEDM search experiment are considered. For electric field E = 20 − 200 V/cm, used in the experiment, lower rotational levels with M = 0 can be labeled by |J, M, Ω > quantum numbers. States |J, M =1, Ω=1 >, |J, M = − 1, Ω= − 1 > correspond to the upper and |J, M = − 1, Ω=1 >, |J, M =1, Ω= − 1 > to the lower Ω-doublet levels. External magnetic field removes the degeneracy between Ω-doublet components: , here E eff = 81.5GV/cm [12,14] is the effective internal electric field. However, there are systematic effects which can give additional energy shifts δ∆E l and δ∆E u for ∆E l and ∆E u which manifest as a false eEDM. This leads to a systematic error δd e (sys) =. It is also useful to consider systematic effectsδd e (sys) =4E eff related to one of the Ω-doublet component . One of the effect is the interaction with trans...

Rovibrational structure of the Ytterbium monohydroxide molecule and the $\mathcal{P}$,$\mathcal{T}$-violation searches

“…For now, the best experimental bound on the eEDM was obtained for diatomic molecule with closely spaced a) Electronic mail: zakharova.annet@gmail.com b) Electronic mail: igorkurchavov58@gmail.com c) Electronic mail: petrov an@pnpi.nrcki.ru Ω-doublets such as ThO [17][18][19][20][21][22] and HfF +23,24 . These experiments also put constraints on scalar-pseudoscalar nucleon-electron interaction 11,25,26 .…”