The fact that the universe is made entirely out of matter, and contains no free anti-matter, has no physical explanation. The unknown process that created matter in the universe must violate a number of fundamental symmetries, including those that forbid the existence of certain electromagnetic moments of fundamental particles - moments which are amplified by the large internal fields in polar molecules. We discuss spectroscopic and theoretical investigations into polyatomic molecules that uniquely combine multiple desirable features for precision measurement, such as high polarizability through symmetry-lowering mechanical motions, laser-coolable electronic structures, and exotic nuclei.

Molecular spectroscopy is one of the leading tools to search for the manifestation of New Physics. It can also provide accurate information about the nucleus properties, such as its magnetic moment. The existence of interactions that violate the combined CP-symmetry of fundamental interactions inside the nucleus can lead to a non-zero Schiff moment that corresponds to the electric field directed along with the nuclear spin. This moment is strongly enhanced in deformed nuclei. In molecules, an additional enhancement with respect to atoms occurs due to the existence of closely-lying opposite parity states. Using a combination of direct and two-step theoretical relativistic approaches, we study the electronic structure of heavy-atom molecules. We predict Schiff moment enhancement and other properties of ²²⁷AcF, ²²⁷AcN, ²²⁷AcO⁺, ²²⁹ThO, ¹⁵³EuO⁺, and ¹⁵³EuN molecules containing f-elements with deformed nuclei as well as the TlF molecule. It is shown that experiments with these molecules should be very sensitive to New Physics [1]. The developed theoretical methods are applied to related problems. One of them is the test of theoretical predictions of the molecular parameters used to interpret experiments to measure the electron electric dipole moment. For this, we study a hyperfine structure of a molecule. In this study, we consider the effect of the finite nuclear magnetization distribution. Usually, this effect is considered only in atoms, but it is demonstrated that it should be treated in precise studies of molecules [2]. Finally, we show how accurate molecular electronic structure's description can be used to solve the discrepancy between the theoretical and experimental data on the hyperfine structure of highly charged ions [3,4]. Research has been supported by the Russian Science Foundation Grant No. 19-72-10019.
1. L.V. Skripnikov, N.S. Mosyagin, A.V. Titov, V.V. Flambaum, Phys. Chem. Chem. Phys., 22, 18374 (2020).
2. L.V. Skripnikov, J. Chem. Phys. 153, 114114 (2020).
3. L.V. Skripnikov, S. Schmidt, J. Ullmann, et al, Phys. Rev. Lett., 120, 093001 (2018).
4. V. Fella, L.V. Skripnikov, W. Nörtershäuser, et al, M. Vogel, Phys. Rev. Res. 2, 013368 (2020).

The Standard Model of particle physics (SM) is the most complete theory nowadays; this model predicts all known fundamental particles and explains their interactions unifying three of the four fundamental forces. There are still many open questions that cannot be explained by the SM, such as the matter-antimatter asymmetry. The electron electric dipole moment (eEDM) is one of the most sought-after phenomena as a non-zero value violates Parity and Time Reversal Symmetries and could provide a clue to the origin of the matter-antimatter assymetry. Experiments searching for the eEDM have been performed over the last 50 years and the latest upper limit was determined on ThO moleculeAndreev V. et al. Nature, 562, 355-360, 2018. Spectroscopy with high resolution and high sensitivity has developed enormously over the past years, enabling the observation of tiny optical effects induced by novel interactions. Now the focus of interest is shifting to polyatomic molecules. In this work we perform computational investigations of polyatomic molecules in the context of the search for the eEDM, using as the example AcOH⁺ and AcOCH₃⁺. The aim of this work is to provide values of effective electric field (E_eff- system-dependent relativistic enhancement factor that describes the interaction of the EDM of the unpaired electron with the molecular internal electric field) of AcOH⁺ and AcOCH₃⁺ on the highest level of theory currently available for heavy many-electron systems. Additionally we performed investigation of the influence of various computational parameters on the results. We analyzed the influence of the basis setsDyall K.G. The Journal of Phys. Chem. A. 113, 12638-12644, 2009.y checking the description of the valence and core regions and varying amount of diffuse or tight functions. Separately we investigated the effects of the electron correlation, like limiting number of active and virtual orbitals and the influence of perturbative triple excitations. Based on these calculations we are able to assign uncertainties on our predictions. Andreev V. et al. Nature, 562, 355-360, 2018.. Dyall K.G. The Journal of Phys. Chem. A. 113, 12638-12644, 2009.b

We report an analytic scheme for relativistic exact two-component coupled-cluster singles and doubles with a noniterative triples [X2C-CCSD(T)] calculations of electric effective field, ε_\texteff, a time-reversal symmetry-violating parameter that plays a key role in the interpretation of experimental precision measurement of paramagnetic atoms and molecules for electron electric dipole moment (eEDM) search. Benchmark X2C-CCSD(T) calculations for the ε_\texteff values of twenty-one heavy-metal containing small molecules demonstrate the efficacy and accuracy of the present scheme. The computational results show that metal methoxides including BaOCH₃, YbOCH₃, and RaOCH₃ possess large ε_\texteff values similar to those of the corresponding fluorides and hydroxides, supporting the recent proposal of using nearly degenerate rotational states of these symmetric-top molecules to enhance the sensitivity of eEDM measurement. The present analytic scheme enables fast and reliable initial screening of candidate molecules for the eEDM search.

One of the great mysteries of modern cosmology is the unknown nature of dark matter. A popular candidate for the dark matter component is the axion – the hypothetical pseudoscalar particle. Despite numerous attempts, the axion or axionlike particles have not been reliably detected. We study axion-mediated exchange between the atomic nucleus and electrons, which can induce a permanent electric dipole moment of the whole molecule. Therefore, axion properties can be measured indirectly in the experiments, which are aiming to search for the electron electric dipole moment (eEDM) and other spatial and time-invariance violation effects. We consider the ytterbium monohydroxide molecule (YbOH) and calculate the corresponding electronic structure parameter, which is necessary for the interpretation of experimental data. The dependence of the axionlike particle mass is studied extensively. We estimate the expected energy shift due to this interaction; it is shown that it is the same order of magnitude as eEDM contribution, so, these effects should be taken into account simultaneously. Electronic structure calculations have been supported by the Russian Science Foundation Grant No. 19-72-10019. Calculations of the interaction potential matrix elements were supported by the foundation for the advancement of theoretical physics and mathematics “BASIS” grant according to Project No. 20-1-5-76-1. Calculation of the Gaunt contribution has been supported by the Russian Foundation for Basic Research Grant No. 20-32-70177.

We are building a new-generation mid-infrared spectrometer specifically designed for precision vibrational spectroscopy of cold complex polyatomic molecules in the gas phase. The proposed technology is at the forefront of cold molecule research and frequency metrology, and opens possibilities for using polyatomic molecules to perform tests of fundamental physics and explore the limits of the standard model. The apparatus will be used in the first place for parity violation (PV) measurements in chiral molecules, i.e. for measuring the tiny energy difference between enantiomers induced by electroweak interactions. We will present our ongoing work towards developing the technologies needed for measuring PV in chiral molecules via Ramsey interferometry in the mid-infraredA. Cournol et al, Quantum Electron. 49, 288 (2019) This includes amongst other things developing frequency stabilised quantum cascade lasers calibrated to some of the world’s best frequency standardsR. Santagata et al, Optica 6, 411 (2019)B. Argence et al, Nature Photon. 9, 456 (2015) and producing gases of organo-metallic species cooled to a few kelvin in cryogenic buffer-gas cellsS.K. Tokunaga et al, New J. Phys. 19, 053006 (2017) We will also present the results of preliminary investigations conducted on various promising heavy metal complexes exhibiting intense signatures in different regions of the mid-infraredP. Asselin et al, Phys. Chem. Chem. Phys. 19, 4576 (2017)N. Saleh et al, Chirality 30, 147 (2018).

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A. Cournol et al, Quantum Electron. 49, 288 (2019). R. Santagata et al, Optica 6, 411 (2019)

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S.K. Tokunaga et al, New J. Phys. 19, 053006 (2017). P. Asselin et al, Phys. Chem. Chem. Phys. 19, 4576 (2017)

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Cooling atoms to the ultracold regime has allowed for studies of physics, ranging from many-body physics of quantum degenerate gases, quantum computing, precision measurements and tests of fundamental symmetries. Extending these experiments to polar molecules has the prospect of enhancing the sensitivity of such tests and of enabling novel studies, such as cold controlled chemistry. However, applying traditional laser cooling techniques to molecules is rendered difficult due their additional degrees of freedom which result in a limited photon scattering budget. Here we study aluminum monochloride (AlCl) as a promising candidate for laser cooling and trapping. The cooling transition at 261 nm (A¹ Π− X¹ Σ⁺) has a theoretical Franck-Condon factor of 99.88% which allows for scattering  800 photons with a single laser before the molecule enters an excited vibrational state. We use a frequency-tripled (SHG + SFG) Titanium-Sapphire laser and generate AlCl via laser ablation in a cryogenic helium buffer gas beam source. We will present our spectroscopy results on AlCl and the measured molecular constants of the A¹Π state and compare them with ab-initio calculations. We will also discuss our estimates on the Franck-Condon factors.

We describe a laser spectroscopic study of ytterbium monomethoxide, a species of interest to search for time-reversal symmetry violation using laser-cooled molecules. We have performed measurements of vibrational structure in the low-lying electronic states, vibrational branching ratios for several electronically excited vibronic states, and radiative lifetimes of low-lying electronic states. Both laser-induced fluorescence and dispersed fluorescence spectra have been recorded and analyzed. In addition, we have recorded the rotationally-resolved high-resolution excitation spectrum of the à²E_1/2 ← X̃ ²A₁ band. Ab initio calculations aided the assignment of vibronic emission bands and provide insight into the electronic and vibrational structure. We compare the structure of YbOCH₃ to the isoelectronic species YbF and YbOH, as well as to the previously studied alkaline-earth monomethoxides. Finally, we discuss how our results open a path to increased sensitivity to P- and/or T-violating physics in future measurements.

Aluminum monofluoride (AlF) is an excellent candidate for laser cooling on any Q-line of the A¹Π - X¹Σ transition and trapping at high densities.Truppe et al., Phys. Rev. A 100, 052513 (2019) In preparation for cooling and manipulation experiments, it is necessary to know the detailed energy structure of the involved states, as well as their lifetimes, dipole moments and the Franck-Condon factors of their transitions.
The metastable a³Π state is the ideal starting point for extensive spectroscopic investigations. Therefore, this presentation will focus on the a³Π← X¹Σ⁺ transition. The energy levels in the X¹Σ⁺, v"=0 state and within each Ω manifold of the a³Π, v′=0 state were determined with a relative accuracy of a few kHz, using laser-radio-frequency multiple resonance and ionization detection schemes in a jet-cooled, pulsed molecular beam. All spectroscopic parameters relevant for describing the rotational and hyperfine structure were determined by fitting the eigenvalues of the molecular Hamiltonian to the data.
With this knowledge, the measured hyperfine structure in the A¹Π state could be assigned. The dipole moments of the X¹Σ⁺, A¹Π and a³Π states were determined by recording cw excitation spectra in electric fields up to 150 kV/cm.
The A¹Π - a³Π band was observed for the first time. Measurements on the transition strength showed that it is no significant loss channel for the A¹Π - X¹Σ laser cooling transition.

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Truppe et al., Phys. Rev. A 100, 052513 (2019)

The aluminium monofluoride (AlF) molecule is a promising candidate for laser cooling and trapping experimentsTruppe et al., Phys. Rev. A 100, 052513 (2019)
Here, we describe experiments studying the hyperfine structure of the b³Σ⁺, v=0 stateDoppelbauer et al., Mol. Phys. 119:1-2, e1810351 (2020) We first determined its radiative lifetime in a pulsed excitation – delayed ionization scheme and measured the rotational structure using (1+2)-REMPI.
We recorded laser-induced fluorescence spectra of the b³Σ⁺, v′=0 ← X¹Σ⁺, v"=1 transition of AlF molecules from a bright buffer gas source. The fluorescence detection works background-free because visible photons are emitted after UV excitation. From the obtained line positions, we determined the relevant fine- and hyperfine structure parameters. In a next step, laser-induced fluorescence spectra were recorded after excitation on the b³Σ⁺, v′=0 ← a³Π_Ω, v"=0 transition; we use all three spin-orbit (Ω = 0,1,2) manifolds of the a³Π state. These spectra were used to improve the uncertainty of our previous measurement of the spin-orbit coupling parameters in the a³Π, v=0 state by almost two orders of magnitude.
We observed the b³Σ⁺, v′=0 → X¹Σ⁺, v" bands, which are result of the spin–orbit coupling of the b³Σ⁺, v=0 state with the nearby A¹Π state.

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Truppe et al., Phys. Rev. A 100, 052513 (2019). Doppelbauer et al., Mol. Phys. 119:1-2, e1810351 (2020).

Aluminum monofluoride (AlF) is an excellent candidate for laser cooling.Truppe et al., Physical Review A 100, 052513 (2019)ll Q-lines of the strong A¹Π ← X¹Σ⁺ transition are rotationally closed and thereby suitable for the main cooling cycle, while the spin-forbidden a³Π ← X¹Σ⁺ transition can be used to achieve final temperatures in the μK range. In view of cooling and trapping experiments, it is essential to have a detailed insight into the energy structure of the directly and indirectly involved states. The A¹Π, v=6, J=1 and the b³Σ⁺, v=5, N=2 levels are very nearly iso-energetic and strongly interact.Barrow et al., Physica Scripta 10, 86 (1974)onsequently, these levels have a mixed singlet and triplet character. The triplet character of the A¹Π state causes a loss from the main laser cooling cycle that has been studied previously.Doppelbauer et al., Molecular Physics 119(1-2), e1810351 (2020)urthermore, these states with their mixed character are particularly suited as doorway states between the singlet and the triplet manifold for ultracold experiments on AlF. We completed an extensive rotationally resolved spectroscopic investigation of energy levels in this perturbed range using optical-optical double resonance ionization, followed by mass-selective ion detection. Subsequently, we performed hyperfine resolved excitation with a cw laser, using laser induced fluorescence for detection. Both measurement schemes were employed on a supersonic, pulsed molecular beam. The lifetimes of the perturbed levels cover two orders of magnitudes (about 2 − 200 ns), which requires different experimental techniques to determine their exact values. Lifetimes of selected levels have been measured using e.g. time delayed ionization and Lamb-dip experiments. The fine- and hyperfine structure parameters as well as the spin-orbit interaction parameter are determined from the experimental data.

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Truppe et al., Physical Review A 100, 052513 (2019)A Barrow et al., Physica Scripta 10, 86 (1974)C Doppelbauer et al., Molecular Physics 119(1-2), e1810351 (2020)F

The odd isotopologues of ytterbium monohydroxide, ^171,173YbOH, have been identified as promising molecules in which to measure parity (P) and time reversal (T) violating physics. We report on the prerequisite characterization of the òΠ_1/2(0,0,0)−X̃²Σ⁺(0,0,0) band near 577 nm for these odd isotopologues. Both laser-induced fluorescence (LIF) excitation spectra of a supersonic molecular beam sample and the absorption spectra of a cryogenic buffer-gas cooled sample were recorded. Additionally, a novel spectroscopic technique based on laser-enhanced chemical synthesis is demonstrated and utilized in the absorption measurements. This technique was critical as it enabled the disentangling of the congested isotopologue structure. An effective Hamiltonian model is used to extract the fine and hyperfine parameters for the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states. A comparison of the determined X̃²Σ⁺(0,0,0) parameters with recently predicted values M. Denis et al, J. Chem. Phys. 152, 084303 (2020), K. Gaul and R. Berger, Phys. Rev. A 101, 012508 (2020), J. Liu et al, J. Chem. Phys. 154, 064110 (2021)s made. The measured hyperfine parameters also provide experimental confirmation of the computational methods used to compute the P,T-violating coupling constants, W_d and W_M, theoretical constants needed to correlate the P,T-violating physics to the corresponding P,T-violating energy shifts in the molecule. The dependence of the fine and hyperfine parameters for both the even and odd isotopologues for both the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states for YbOH and isoelectronic YbF are discussed.This work was supported by the Heising-Simons Foundation, NSF CAREER, and NIST Precision Measurement Granthtml:<hr /><h3>Footnotes: M. Denis et al, J. Chem. Phys. 152, 084303 (2020), K. Gaul and R. Berger, Phys. Rev. A 101, 012508 (2020), J. Liu et al, J. Chem. Phys. 154, 064110 (2021)i This work was supported by the Heising-Simons Foundation, NSF CAREER, and NIST Precision Measurement Grant

A search for the time-noninvariant (T-odd) interactions is one of the most fundamental not yet resolved problems in physics. The existence of the electric dipole moment (EDM) for any particle violates both P- and T-invariances (P is the space parity). The search for the EDMs continues for more than half a century without any success. The present constraint on the P- and T-violating effects is based on the observation of the electron-spin precession in an external electric field using the ThO molecule (ACME collaboration, USA). This experiment sets the upper bound for the electron EDM (eEDM) d_e < 1.1×10⁻²⁹ e cm (e is the electron charge)V. Andreev et al. (ACME collaboration), Nature 562, 355 (2018) An accurate evaluation of the eEDM within the standard model is still absent. The maximum estimated value is d_e  ∼ 10⁻³⁸ e cmM. Pospelov, I. Khriplovich, Sov.Nucl.Phys. 53, 638 (1991) No signs of "new physics" inside this gap between the theory and experiment have not yet been found. This encourages to suggest the new, more sensitive methods for observation of the eEDM in low-energy physics. We suggest considering the P, T-odd Faraday effect (rotation of the polarization plane for the light propagating through a medium in presence of an external electric field). The experiment is assumed to be performed with the modern intra-cavity/cavity-enhanced absorption spectroscopy techniques in combination with a molecular beam crossing the cavityD.V. Chubukov, L.V. Skripnikov, L.N. Labzowsky, JETP Letters 110, 382 (2019); D.V. Chubukov, L.V. Skripnikov, A.N. Petrov, V.N. Kutuzov, L.N. Labzowsky, PRA (2021) [Accepted, to be published; Preprint: arXiv:2102.05157] Theoretical simulations of the proposed experiment with the PbF and ThO molecular beams together with accurate molecular structure calculations show that the present constraint on the eEDM in principle can be improved by a few orders of magnitude. An advantage of the P, T-odd Faraday experiment is that the P, T-odd effect is cumulated on the light, while in the ACME-like experiment it is cumulated on the molecules. For the shot-noise limited measurement, it is much easier to have a larger number of photons than a larger number of molecules.

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Footnotes:

V. Andreev et al. (ACME collaboration), Nature 562, 355 (2018). M. Pospelov, I. Khriplovich, Sov.Nucl.Phys. 53, 638 (1991). D.V. Chubukov, L.V. Skripnikov, L.N. Labzowsky, JETP Letters 110, 382 (2019); D.V. Chubukov, L.V. Skripnikov, A.N. Petrov, V.N. Kutuzov, L.N. Labzowsky, PRA (2021) [Accepted, to be published; Preprint: arXiv:2102.05157].

l0pt Figure The jet-cooled molybdenum monoxide (MoO) molecule involving seven natural isotopologues from ⁹²MoO (14.5%), ⁹⁴MoO (9.2%), ⁹⁵MoO (15.8%), ⁹⁶MoO (16.7%), ⁹⁷MoO (9.6%), ⁹⁸MoO (24.4%), and ¹⁰⁰MoO (9.8%), have been investigated with the laser-induced fluorescence (LIF) excitation spectra and the single vibronic level (SVL) emission spectra in the energy range from 13 800 to 16 500 cm⁻¹. Four rotationally resolved transition bands near 14 107, 14 144, 14 237, and 15 034 cm⁻¹ have been observed, and exhibit extremely large isotope shifts, in which the largest shift is 53 cm⁻¹ for ν(⁹²MoO)−ν(¹⁰⁰MoO). By rotational analysis, the four bands all originate from the X ⁵Π₋₁ ground state, and are assigned as the 6−0, 7−0, 6−0, and 9−0 (v^′−v^′′) bands of the Ω^′=2←Ω^′′=−1 transition according to the vibrational isotope shift. In addition, the isotopologues-resolved SVL emission spectra have been obtained by fixing the excitation laser at Q-branch bandhead of the transition. The isotope shifts in the vibrational v^′′= 0, 1, 2, and 3 levels of the X⁵Π₋₁ ground state have been observed and show well agreement with the calculation from the model of harmonic vibration. The solid experimental results are consistent with the theoretical prediction, which indicates that the works on MoO are of great benchmark to reveal the role of the isotope shift in the vibrational levels of simple molecules.