Optical Mass Spectrometry of Cold RaOH^{+} and RaOCH_{3}^{+}

Experimental perspectives on the matter-antimatter asymmetry puzzle: developments in electron EDM and [Formula: see text] experiments

In the search for clues to the matter-antimatter puzzle, experiments with atoms or molecules play a particular role. These systems allow measurements with very high precision, as demonstrated by the unprecedented limits down to [Formula: see text] e cm on electron EDM using molecular ions, and relative measurements at the level of [Formula: see text] in spectroscopy of antihydrogen atoms. Building on these impressive measurements, new experimental directions offer potential for drastic improvements. We review here some of the new perspectives in those fields and their associated prospects for new physics searches. This article is part of the theme issue 'The particle-gravity frontier'.

Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method

A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.

Relativistic coupled-cluster calculations of RaOH pertinent to spectroscopic detection and laser cooling

A relativistic coupled-cluster study of the low-lying electronic states in the radium monohydroxide molecule (RaOH), a radioactive polyatomic molecule of interest to laser cooling and to the search of new physics beyond the Standard Model, is reported. The level positions of the A2Π1/2 and C2Σ states have been computed with an accuracy of around 200 cm-1 to facilitate spectroscopic observation of RaOH using laser induced fluorescence spectroscopy, thereby exploiting the systematic convergence of electron-correlation and basis-set effects in relativistic coupled-cluster calculations. The energy level for the B2Δ3/2 state has also been calculated accurately to conclude that the B2Δ3/2 state lies above the A2Π1/2 state. This confirms X2Σ ↔ A2Π1/2 as a promising optical cycling transition for laser cooling RaOH.

Quantum-Enhanced Metrology for Molecular Symmetry Violation Using Decoherence-Free Subspaces

We propose a method to measure time-reversal symmetry violation in molecules that overcomes the standard quantum limit while leveraging decoherence-free subspaces to mitigate sensitivity to classical noise. The protocol does not require an external electric field, and the entangled states have no first-order sensitivity to static electromagnetic fields as they involve superpositions with zero average lab-frame projection of spins and dipoles. This protocol can be applied with trapped neutral or ionic species, and can be implemented using methods that have been demonstrated experimentally.

Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation

Parity non-conservation (PNC) due to the weak interaction is predicted to give rise to enantiomer dependent vibrational constants in chiral molecules, but the phenomenon has so far eluded experimental observation. The enhanced sensitivity of molecules to physics beyond the Standard Model (BSM) has led to substantial advances in molecular precision spectroscopy, and these may be applied to PNC searches as well. Specifically, trapped molecular ion experiments leverage the universality of trapping charged particles to optimize the molecular ion species studied toward BSM searches, but in searches for PNC, only a few chiral molecular ion candidates have been proposed so far. Importantly, viable candidates need to be internally cold, and their internal state populations should be detectable with high quantum efficiency. To this end, we focus on molecular ions that can be created by near threshold resonant two-photon ionization and detected via state-selective photo-dissociation. Such candidates need to be stable in both charged and neutral chiral versions to be amenable to these methods. Here, we present a collection of suitable chiral molecular ion candidates we have found, including CHDBrI+ and CHCaBrI+, that fulfill these conditions according to our ab initio calculations. We find that organo-metallic species have low ionization energy as neutrals and relatively high dissociation thresholds. Finally, we compute the magnitude of the PNC values for vibrational transitions for some of these candidates. An experimental demonstration of state preparation and readout for these candidates will be an important milestone toward measuring PNC in chiral molecules for the first time.

Single molecule infrared spectroscopy in the gas phase

Spectroscopy is a key analytical tool that provides valuable insight into molecular structure and is widely used to identify chemical samples. Tagging spectroscopy is a form of action spectroscopy in which the absorption of a single photon by a molecular ion is detected via the loss of a weakly attached, inert 'tag' particle (for example, He, Ne, N2)1-3. The absorption spectrum is derived from the tag loss rate as a function of incident radiation frequency. So far, all spectroscopy of gas phase polyatomic molecules has been restricted to large molecular ensembles, thus complicating spectral interpretation by the presence of multiple chemical and isomeric species. Here we present a novel tagging spectroscopic scheme to analyse the purest possible sample: a single gas phase molecule. We demonstrate this technique with the measurement of the infrared spectrum of a single gas phase tropylium (C7H7+) molecular ion. The high sensitivity of our method revealed spectral features not previously observed using traditional tagging methods4. Our approach, in principle, enables analysis of multicomponent mixtures by identifying constituent molecules one at a time. Single molecule sensitivity extends action spectroscopy to rare samples, such as those of extraterrestrial origin5,6, or to reactive reaction intermediates formed at number densities that are too low for traditional action methods.

Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory. The characterization is performed by using a frequency comb which probes rotational transitions in the molecular ion. With improved coherence of the comb laser, a fractional statistical uncertainty for a transition line center of as low as 4.6×10^{-13} was achieved.

Isotope Shifts of Radium Monofluoride Molecules

Isotope shifts of ^{223-226,228}Ra^{19}F were measured for different vibrational levels in the electronic transition A^{2}Π_{1/2}←X^{2}Σ^{+}. The observed isotope shifts demonstrate the particularly high sensitivity of radium monofluoride to nuclear size effects, offering a stringent test of models describing the electronic density within the radium nucleus. Ab initio quantum chemical calculations are in excellent agreement with experimental observations. These results highlight some of the unique opportunities that short-lived molecules could offer in nuclear structure and in fundamental symmetry studies.

Electronic spectroscopy of the A1̃2A''/A2̃2A'-X̃2A' transitions of jet-cooled calcium ethoxide radicals: Vibronic structure of alkaline earth monoalkoxide radicals of Cs symmetry

Laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down spectra of the A₁̃²A^''/A₂̃²A^'-X̃²A^' electronic transition of the calcium ethoxide (CaOC₂H₅) radical have been obtained under jet-cooled conditions. An essentially constant Ã₂-Ã₁ energy separation for different vibronic levels is observed in the LIF spectrum, which is attributed to both the spin-orbit (SO) interaction and non-relativistic effects. Electronic transition energies, vibrational frequencies, and spin-vibrational eigenfunctions calculated using the coupled-cluster method, along with results from previous complete active space self-consistent field calculations, have been used to predict the vibronic energy level structure and simulate the recorded LIF/DF spectra. Although the vibrational frequencies and Franck-Condon (FC) factors calculated under the Born-Oppenheimer approximation and the harmonic oscillator approximation reproduce the dominant spectral features well, the inclusion of the pseudo-Jahn-Teller (pJT) and SO interactions, especially those between the A₁̃²A^″/A₂̃²A^' and the B̃²A^' states, induces additional vibronic transitions and significantly improves the accuracy of the spectral simulations. Notably, the spin-vibronic interactions couple vibronic levels and alter transition intensities. The calculated FC matrix for the A₁̃²A^''/A₂̃²A^'-X̃²A^' transition contains a number of off-diagonal matrix elements that connect the vibrational ground levels to the levels of the ν₈ (CO stretch), ν₁₁ (OCC bending), ν₁₂ (CaO stretch), ν₁₃ (in-plane CaOC bending), and ν₂₁ (out-of-plane CaOC bending) modes, which are used for vibrational assignments. Transitions to the ν₂₁(a″) levels are allowed due to the pJT effect. Furthermore, when LIF transitions to the Ã-state levels of the CaOC-bending modes, ν₁₃ and ν₂₁, are pumped, A₁̃²A^''/A₂̃²A^'→X̃²A^' transitions to the combination levels of these two modes with the ν₈, ν₁₁, and ν₁₂ modes are also observed in the DF spectra due to the Duschinsky mixing. Implications of the present spectroscopic investigation to laser cooling of asymmetric-top molecules are discussed.

Probing Fundamental Symmetries of Deformed Nuclei in Symmetric Top Molecules

Precision measurements of Schiff moments in heavy, deformed nuclei are sensitive probes of beyond standard model T, P violation in the hadronic sector. While the most stringent limits on Schiff moments to date are set with diamagnetic atoms, polar polyatomic molecules can offer higher sensitivities with unique experimental advantages. In particular, symmetric top molecular ions possess K doublets of opposite parity with especially small splittings, leading to full polarization at low fields, internal comagnetometer states useful for rejection of systematic effects, and the ability to perform sensitive searches for T, P violation using a small number of trapped ions containing heavy exotic nuclei. We consider the symmetric top cation ^{225}RaOCH_{3}^{+} as a prototypical and candidate platform for performing sensitive nuclear Schiff measurements and characterize in detail its internal structure using relativistic ab initio methods. The combination of enhancements from a deformed nucleus, large polarizability, and unique molecular structure make this molecule a promising platform to search for fundamental symmetry violation even with a single trapped ion.