Precision Measurement of the Electron's Electric Dipole Moment Using Trapped Molecular Ions

Approaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra+ by including quantum-electrodynamics effects

Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, ²²⁶RaF, and radium cation, ²²⁶Ra⁺, are reported. The considered transition X²Σ_1/2 → A²Π_1/2 in RaF is one of the main features of this molecule and can be used to laser-cool RaF for a subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions, we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. The effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is now implemented for molecules. It is shown that the inclusion of the QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the "chemical accuracy," 1 kcal/mol = 43 meV, that is usually considered as a guiding thread in theoretical molecular physics.

Experimental Constraint on Axionlike Particles over Seven Orders of Magnitude in Mass

We use our recent electric dipole moment (EDM) measurement data to constrain the possibility that the HfF^{+} EDM oscillates in time due to interactions with candidate dark matter axionlike particles (ALPs). We employ a Bayesian analysis method which accounts for both the look-elsewhere effect and the uncertainties associated with stochastic density fluctuations in the ALP field. We find no evidence of an oscillating EDM over a range spanning from 27 nHz to 400 mHz, and we use this result to constrain the ALP-gluon coupling over the mass range 10^{-22}-10^{-15}  eV. This is the first laboratory constraint on the ALP-gluon coupling in the 10^{-17}-10^{-15}  eV range, and the first laboratory constraint to properly account for the stochastic nature of the ALP field.

Quantum-State Control and Manipulation of Paramagnetic Molecules with Magnetic Fields

Since external magnetic fields were first employed to deflect paramagnetic atoms in 1921, a range of magnetic field-based methods have been introduced to state-selectively manipulate paramagnetic species. These methods include magnetic guides, which selectively filter paramagnetic species from all other components of a beam, and magnetic traps, where paramagnetic species can be spatially confined for extended periods of time. However, many of these techniques were developed for atomic-rather than molecular-paramagnetic species. It has proven challenging to apply some of these experimental methods developed for atoms to paramagnetic molecules. Thanks to the emergence of new experimental approaches and new combinations of existing techniques, the past decade has seen significant progress toward the manipulation and control of paramagnetic molecules. This review identifies the key methods that have been implemented for the state-selective manipulation of paramagnetic molecules-discussing the motivation, state of the art, and future prospects of the field. Key applications include the ability to control chemical interactions, undertake precise spectroscopic measurements, and challenge our understanding of chemical reactivity at a fundamental level.

Flavor-diagonal CP violation: the electric dipole moment

The observed baryon asymmetry in the universe cannot be reconciled with the current form of the Standard Model (SM) of particle physics. The Standard Model breaks charge conjugation parity (CP) symmetry, but not in a sufficient amount to explain the observed matter-antimatter asymmetry. Historically one of the first systems to be studied in the search of symmetry breaking within the Standard Model is the electric dipole moment (EDM) of the neutron. The contribution to the neutron EDM coming from the SM is several order of magnitudes smaller than the current experimental bound, thus providing a unique, background-free window for potential discovery of physics Beyond the Standard Model (BSM). The strong CP-violating θ term can also contribute to the neutron EDM, as can all the CP-violating effective operators describing, at energies below the electro-weak scale, the contributions from BSM. To constrain all these contributions to the neutron EDM we need to precisely determine the hadronic matrix elements of the corresponding renormalized operators. After a brief introduction on baryon asymmetry and baryogenesis, I summarize the current stuatus for experiments in search of a neutron EDM. I then describe in more details the different CP-violating sources, and some results in Chiral Perturbation Theory precede a discussion on the current status of Lattice QCD calculations. I will in particular focus on the 2 main challenges for these type of calculations: the signal-to-noise ratio and the renormalization. I will discuss several improvement techniques trying to improve these two aspects of the calculation and I will conclude with an optimistic view into the future.

Analytic evaluation of energy first derivatives for spin-orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties

A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin-orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the applicability and usefulness of the present analytic scheme.

Study of HgOH to Assess Its Suitability for Electron Electric Dipole Moment Searches

In search of suitable molecular candidates for probing the electric dipole moment (EDM) of the electron (de), a property that arises due to parity and time-reversal violating (P,T-odd) interactions, we consider the triatomic mercury hydroxide (HgOH) molecule. The impetus for this proposal is based on previous works on two systems: the recently proposed ytterbium hydroxide (YbOH) experiment that demonstrates the advantages of polyatomics for such EDM searches, and the finding that mercury halides provide the highest enhancement due to de compared to other diatomic molecules. We identify the ground state of HgOH as being in a bent geometry, and show that its intrinsic EDM sensitivity is comparable to the corresponding value for YbOH. Along with the theoretical results, we discuss plausible experimental schemes for an EDM measurement in HgOH. Furthermore, we provide pilot calculations of the EDM sensitivity for de for HgCH3 and HgCF3, that are natural extensions of HgOH.

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.

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

We present an all-optical mass spectrometry technique to identify trapped ions. The new method uses laser-cooled ions to determine the mass of a cotrapped dark ion with a sub-dalton resolution within a few seconds. We apply the method to identify the first controlled synthesis of cold, trapped RaOH^{+} and RaOCH_{3}^{+}. These molecules are promising for their sensitivity to time and parity violations that could constrain sources of new physics beyond the standard model. The nondestructive nature of the mass spectrometry technique may help identify molecular ions or highly charged ions prior to optical spectroscopy. Unlike previous mass spectrometry techniques for small ion crystals that rely on scanning, the method uses a Fourier transform that is inherently broadband and comparatively fast. The technique's speed provides new opportunities for studying state-resolved chemical reactions in ion traps.

Coherent manipulation of the internal state of ultracold 87Rb133Cs molecules with multiple microwave fields

We explore coherent multi-photon processes in 87Rb133Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of 87Rb133Cs up to N = 6, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient Dv = h × 207.3(2) Hz.

Large Long-Distance Contributions to the Electric Dipole Moments of Charged Leptons in the Standard Model

We reevaluate the electric dipole moment (EDM) of charged leptons in the standard model using hadron effective models. We find unexpectedly large EDM generated by the hadron level long-distance effect, d_{e}=5.8×10^{-40}, d_{μ}=1.4×10^{-38}, and d_{τ}=-7.3×10^{-38}  e cm, with an error bar of 70%, exceeding the conventionally known four-loop level elementary contribution by several orders of magnitude.

Towards accurate prediction for laser-coolable molecules: relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies

Benchmark relativistic coupled-cluster calculations for yttrium monoxide (YO) with accurate treatment of relativistic and electron correlation effects are reported. The spin-orbit mixing of 2Π and 2Δ is found to be an order of magnitude smaller than previously reported in the literature. Together with the measurement of the lifetime of the A'2Δ3/2 state, it implies an enhanced capability of a narrow-line cooling scheme to bring YO to sub-recoil temperature. The computed electronic transition properties also support a four-photon scheme to close the leakage of the A2Π1/2 ↔ X2Σ1/2+ cycle through the A'2Δ3/2 state by repumping the A'2Δ3/2 state to the B2Σ1/2+ state, which subsequently decays back to X2Σ1/2+. Relativistic coupled-cluster methods, capable of providing accurate spectroscopic parameters that characterize the local potential curves and hence of providing accurate Franck-Condon factors, appear to be promising candidates for accurate calculation of properties for laser-coolable molecules.

Dipole-phonon quantum logic with alkaline-earth monoxide and monosulfide cations

Dipole-phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO⁺, and discuss progress towards experimental realization. We also further develop the theory of DPQL to include state preparation and measurement and entanglement of multiple molecular ions.

The effect of the electric trapping field on state-selective loading of molecules into rf ion traps

Trapped molecular ions in pure rovibronic states are desirable in experiments ranging from cold chemistry to searches for physics beyond the Standard Model. Resonance-enhanced multiphoton ionisation (REMPI) can be used to prepare molecular ions in specific internal states with high fidelities. However, in the presence of electric fields, ionisation spectra exhibit frequency shifts and the ionisation thresholds are broadened. For this reason, REMPI studies are normally conducted in low and highly homogeneous electric fields, whereas the operating principle of rf ion traps requires electric fields that vary in space and time. In order to investigate the impact of this on the state-selectivity of REMPI in ion traps, we have simulated the expected broadening of the ionisation threshold under various operating conditions of a typical linear Paul trap. In many cases, the width of the ionisation threshold exceeds the separation between rotational energy levels, preventing state-selective ionisation. Careful choice of the trapping and laser parameters during loading can reduce this broadening, enabling state-selective ionisation in some instances. Where this strategy is not sufficient, the broadening can be reduced further by rapidly switching the trapping voltages off and on again during loading. This has been demonstrated experimentally for a Coulomb crystal of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{40}\hbox {Ca}^+$$\end{document}40Ca+ ions without descrystallising it.

Electron Electric Dipole Moment Searches Using Clock Transitions in Ultracold Molecules

Permanent electric dipole moments (EDMs) of fundamental particles such as the electron are signatures of parity and time-reversal violation occurring in physics beyond the standard model. EDM measurements probe new physics at energy scales well beyond the reach of present-day colliders. Recent advances in assembling molecules from ultracold atoms have opened up new opportunities for improving the reach of EDM experiments. However, the magnetic field sensitivity of such ultracold molecules means that new measurement techniques are needed before these opportunities can be fully exploited. We present a technique that takes advantage of magnetically insensitive hyperfine clock transitions in polar molecules, offering a way to improve both the precision and accuracy of EDM searches with ultracold assembled molecules.

Nondestructive dispersive imaging of rotationally excited ultracold molecules

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using 23Na87Rb and 87Rb133Cs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules.

Cooling of a Zero-Nuclear-Spin Molecular Ion to a Selected Rotational State

We demonstrate rotational cooling of the silicon monoxide cation via optical pumping by a spectrally filtered broadband laser. Compared with diatomic hydrides, SiO^{+} is more challenging to cool because of its smaller rotational interval. However, the rotational level spacing and the large dipole moment of SiO^{+} allows for direct manipulation by microwaves, and the absence of hyperfine structure in its dominant isotopologue greatly reduces demands for pure quantum state preparation. These features make ^{28}Si^{16}O^{+} a good candidate for future applications such as quantum information processing. Cooling to the ground rotational state is achieved on a 100 ms timescale and attains a population of 94(3)%, with an equivalent temperature T=0.53(6)  K. We also describe a novel spectral-filtering approach to cool into arbitrary rotational states and use it to demonstrate a narrow rotational population distribution (N±1) around a selected state.

Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

This article demonstrates new observation of the high-resolution ro-vibrational bichromatic photoassociation spectra (BPAS) of Cs₂ in the 0u+ long-range state below the asymptotes 6S_1/2 + 6P_1/2. By combining with a modulation spectroscopic technique, precise references of the frequency differences have been engineered through the BPAS, with which the rotational constants of low-lying vibrational levels of the Cs₂0u+ long-range state have been accurately determined by fitting the frequency differences to the non-rigid-rotor model. The rotational constants for the newly observed seven ro-vibrational levels are summarized and disagreement for the level ῦ = 498 is clarified. The rotational constants of different vibrational levels demonstrate strong perturbations of the related energy structures. A simple analysis is performed and shows good agreement with experimental results.

A new Collinear Apparatus for Laser Spectroscopy and Applied Science (COALA)

We present a new collinear laser spectroscopy setup that has been designed to overcome systematic uncertainty limits arising from high-voltage and frequency measurements, beam superposition, and collisions with residual gas that are present in other installations utilizing this technique. The applied methods and experimental realizations are described, including an active stabilization of the ion-source potential, new types of ion sources that have not been used for collinear laser spectroscopy so far, dedicated installations for pump-and-probe measurements, and a versatile laser system referenced to a frequency comb. The advanced setup enables us to routinely determine transition frequencies, which was so far demonstrated only for a few cases and with lower accuracy at other facilities. It has also been designed to perform accurate high-voltage measurements for metrological applications. Demonstration and performance measurements were carried out with Ca⁺ and In⁺ ions.

Spectroscopy of short-lived radioactive molecules

Molecular spectroscopy offers opportunities for the exploration of the fundamental laws of nature and the search for new particle physics beyond the standard model1-4. Radioactive molecules-in which one or more of the atoms possesses a radioactive nucleus-can contain heavy and deformed nuclei, offering high sensitivity for investigating parity- and time-reversal-violation effects5,6. Radium monofluoride, RaF, is of particular interest because it is predicted to have an electronic structure appropriate for laser cooling6, thus paving the way for its use in high-precision spectroscopic studies. Furthermore, the effects of symmetry-violating nuclear moments are strongly enhanced5,7-9 in molecules containing octupole-deformed radium isotopes10,11. However, the study of RaF has been impeded by the lack of stable isotopes of radium. Here we present an experimental approach to studying short-lived radioactive molecules, which allows us to measure molecules with lifetimes of just tens of milliseconds. Energetically low-lying electronic states were measured for different isotopically pure RaF molecules using collinear resonance ionisation at the ISOLDE ion-beam facility at CERN. Our results provide evidence of the existence of a suitable laser-cooling scheme for these molecules and represent a key step towards high-precision studies in these systems. Our findings will enable further studies of short-lived radioactive molecules for fundamental physics research.

Search for electric dipole moments

Searches for permanent electric dipole moments of fundamental particles and systems with spin are the experiments most sensitive to new CP violating physics and a top priority of a growing international community. We briefly review the current status of the field emphasizing on the charged leptons and lightest baryons.

1D Magneto-Optical Trap of Polyatomic Molecules

We demonstrate a 1D magneto-optical trap of the polar free radical calcium monohydroxide (CaOH). A quasiclosed cycling transition is established to scatter ∼10^{3} photons per molecule, predominantly limited by interaction time. This enables radiative laser cooling of CaOH while compressing the molecular beam, leading to a significant increase in on axis beam brightness and reduction in temperature from 8.4 to 1.4 mK.

P , T -Violating and Magnetic Hyperfine Interactions in Atomic Thallium

We present state-of-the-art string-based relativistic general-excitation-rank configuration interaction and coupled cluster calculations of the electron electric dipole moment, the nucleon–electron scalar-pseudoscalar, and the magnetic hyperfine interaction constants ( α d e , α C S , A | | , respectively) for the thallium atomic ground state 2 P 1 / 2 . Our present best values are α d e = − 558 ± 28 , α C S = 6.77 ± 0.34 [ 10 − 18 e cm], and A | | = 21172 ± 1059 [MHz]. The central value of the latter constant agrees with the experimental result to within 0.7% and serves as a measurable probe of the P , T -violating interaction constants. Our findings lead to a significant reduction of the theoretical uncertainties for P , T -odd interaction constants for atomic thallium but not to stronger constraints on the electron electric dipole moment, d e , or the nucleon–electron scalar-pseudoscalar coupling constant, C S .

Frequency-comb spectroscopy on pure quantum states of a single molecular ion

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state nondestructively, leaving the molecule ready for further manipulation. We can resolve rotational transitions to 11 significant digits and derive the rotational constant of 40CaH+ to be B R = 142 501 777.9(1.7) kilohertz. Our approach is suited for a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.

Hyperfine structure of the NaCs b3Π2 state near the dissociation limit 3S1/2 + 6P3/2 observed with ultracold atomic photoassociation

We report new observations of the hyperfine structure in three ro-vibrational levels of the b³Π₂ state of NaCs near the dissociation limit 3S_1/2 + 6P_3/2. The experiment was done via photoassociation of ultracold atoms in a dual-species dark-spot magneto-optical trap, and the spectra were measured as atomic trap losses. The simulation of the hyperfine structure showed that the greater part of the observed structure belongs to almost isolated levels of the b³Π₂ state, but there are other parts of mixed character where the contribution from the ¹Σ symmetry dominates.

Second-Scale Coherence Measured at the Quantum Projection Noise Limit with Hundreds of Molecular Ions

Cold molecules provide an excellent platform for quantum information, cold chemistry, and precision measurement. Certain molecules have enhanced sensitivity to beyond standard model physics, such as the electron's electric dipole moment (eEDM). Molecular ions are easily trappable and are therefore particularly attractive for precision measurements where sensitivity scales with interrogation time. Here, we demonstrate a spin precession measurement with second-scale coherence at the quantum projection noise (QPN) limit with hundreds of trapped molecular ions, chosen for their sensitivity to the eEDM rather than their amenability to state control and readout. Orientation-resolved resonant photodissociation allows us to simultaneously measure two quantum states with opposite eEDM sensitivity, reaching the QPN limit and fully exploiting the high count rate and long coherence.

Sub-Doppler Cooling and Compressed Trapping of YO Molecules at μK Temperatures

Complex molecular structure demands customized solutions to laser cooling by extending its general set of principles and practices. Compared with other laser-cooled molecules, yttrium monoxide (YO) exhibits a large electron-nucleus interaction, resulting in a dominant hyperfine interaction over the electron spin-rotation coupling. The YO ground state is thus comprised of two manifolds of closely spaced states, with one of them possessing a negligible Landé g factor. This unique energy level structure favors dual-frequency dc magneto-optical trapping (MOT) and gray molasses cooling (GMC). We report exceptionally robust cooling of YO at 4 μK over a wide range of laser intensity, detunings (one- and two-photon), and magnetic field. The magnetic insensitivity enables the spatial compression of the molecular cloud by alternating GMC and MOT under the continuous operation of the quadrupole magnetic field. A combination of these techniques produces a laser-cooled molecular sample with the highest phase space density in free space.

Probing ultracold chemistry using ion spectrometry

Reactions between KRb molecules at sub-microkelvin temperatures were probed using ion spectrometry.

Actinide and lanthanide molecules to search for strong CP-violation

Actinide and lanthanide molecules are prospective candidates to search for the violation of fundamental symmetries and test grand unification theories.

A simple method for in situ measurement of vacuum window birefringence

We present a simple method to measure the degrees of circular polarization (DoCP) of laser light inside a vacuum chamber and the birefringence of a vacuum window by detecting the fluorescence emitted by Doppler cooled ions in an ion trap. Imperfect laser polarization will cause ions to be pumped to the dark state which will decrease the fluorescence rates of the ions. With a simulation based on the rate equations of the relevant energy levels of ²⁵Mg⁺ ions, we find that the fluorescence rate is sensitive to the DoCP of the laser. Based on the simulation result, we present a new method to optimize the DoCP of the laser inside the vacuum chamber by adjusting fast axis azimuthal angles of a half-wave plate and a quarter-wave plate outside the vacuum chamber. The laser light is optimized to be circularly polarized with an uncertainty of the DoCP of 7.8 × 10^-5. With the obtained polarization information on both sides of the vacuum window and treating the vacuum window as an unknown wave plate, the phase delay and the fast axis azimuthal angle of the vacuum window can be determined in the form of Mueller matrix. The phase delay is determined to be 197.60(39)°, and the fast axis azimuthal angle is determined to be 104.00(5)°.

Modeling state-selective photodetachment in cold ion traps: Rotational state "crowding" in small anions

Using accurate ab initio calculations of the interaction forces, we employ a quantum mechanical description of the collisional state-changing processes that occur in a cold ion trap with He as a buffer gas. We generate the corresponding inelastic rates for rotational transitions involving three simple molecular anions OH^-(¹Σ), MgH^-(¹Σ), and C₂H^-(¹Σ) colliding with the helium atoms of the trap. We show that the rotational constants of these molecular anions are such that within the low-temperature regimes of a cold ion trap (up to about 50 K), a different proportion of molecular states are significantly populated when loading helium as a buffer gas in the trap. By varying the trap operating conditions, population equilibrium at the relevant range of temperatures is reached within different time scales. In the modeling of the photodetachment experiments, we analyze the effects of varying the chosen values for photodetachment rates as well as the laser photon fluxes. Additionally, the changing of the collision dynamics under different buffer gas densities is examined and the best operating conditions, for the different anions, for yielding higher populations of specific rotational states within the ion traps are extracted. The present modeling thus illustrates possible preparation of the trap conditions for carrying out more efficiently state-selected experiments with the trapped anions.

Measurement of the variation of electron-to-proton mass ratio using ultracold molecules produced from laser-cooled atoms

Experimental techniques to manipulate cold molecules have seen great development in recent years. The precision measurements of cold molecules are expected to give insights into fundamental physics. Here we use a rovibrationally pure sample of ultracold KRb molecules to improve the measurement on the stability of electron-to-proton mass ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\mu = \frac{{m_{\mathrm{e}}}}{{M_{\mathrm{p}}}}} \right)$$\end{document}μ=meMp. The measurement is based upon a large sensitivity coefficient of the molecular spectroscopy, which utilizes a transition between a nearly degenerate pair of vibrational levels each associated with a different electronic potential. Observed limit on temporal variation of μ is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{\mu }\frac{{d\mu }}{{dt}} = (0.30 \pm 1.0) \times 10^{ - 14} \, {\mathrm{year}}^{ - 1}$$\end{document}1μdμdt=(0.30±1.0)×10-14year-1, which is better by a factor of five compared with the most stringent laboratory molecular limits to date. Further improvements should be straightforward, because our measurement was only limited by statistical errors.

Ultracold molecules are suitable platforms for precision measurements due to their internal degrees of freedom. Here the authors derive a limit on the variation of the electron-to-proton mass ratio by using the spectroscopy of ultracold KRb molecules.

Stereodynamical Control of a Quantum Scattering Resonance in Cold Molecular Collisions

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H_{2}, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.

The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules

In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects.

Laser Cooling of Radium Ions

The unstable radium nucleus is appealing for probing new physics due to its high mass, octupole deformation, and energy level structure. Ion traps, with long hold times and low particle numbers, are excellent for work with radioactive species, such as radium and radium-based molecular ions, where low activity, and hence low total numbers, is desirable. We address the challenges associated with the lack of stable isotopes in a tabletop experiment with a low-activity (∼10  μCi) source where we laser-cool trapped radium ions. With a laser-cooled radium ion we measured the 7p^{2}P_{1/2}^{o} state's branching fractions to the ground state, 7s^{2}S_{1/2}, and a metastable excited state, 6d^{2}D_{3/2}, to be p=0.9104(7) and 0.0896(7), respectively. With a nearby tellurium reference line we measured the 7s^{2}S_{1/2}→7p^{2}P_{1/2}^{o} transition frequency, 640.096 63(6) THz.

Optical Rotation Approach to Search for the Electric Dipole Moment of the Electron

The P , T -odd Faraday effect (i.e., rotation of the polarization plane of light propagating through a medium in presence of the external electric field due to P , T symmetry violating interactions) is considered for several atomic species: Ra, Pb, Tl, Hg, Cs, and Xe. Corresponding theoretical simulation of P , T -odd Faraday experiment, with already achieved intracavity absorption spectroscopy characteristics and parameters, is performed. The results show that the magnetic dipole transitions in the Tl and Pb atoms as well as the electric dipole transitions in the Ra, Hg and Cs atoms are favorable for the observation of the P , T -odd Faraday optical rotation. The estimation of the rotation angle of the light polarization plane demonstrates that recently existing boundaries for the electron electric dipole moment can be improved by one-two orders of magnitude.

Band structure and topological phase transition of photonic time crystals

We investigate the band structure and topological phase transition of photonic time crystals (PTC)-systems in which the physical parameter varies periodically in time. We find that the topological phase transition of the PTC system can be revealed by the wave vector gap (k-gap) size, which was induced by the temporal refraction and reflection. Interestingly, a temporal zero-averaged refractive index k-gap is obtained when the PTC system includes a dispersive medium. This special k-gap is invariant with modulation time scaling at a given modulation frequency.

A degenerate Fermi gas of polar molecules

Experimental realization of a quantum degenerate gas of molecules would provide access to a wide range of phenomena in molecular and quantum sciences. However, the very complexity that makes ultracold molecules so enticing has made reaching degeneracy an outstanding experimental challenge over the past decade. We now report the production of a degenerate Fermi gas of ultracold polar molecules of potassium-rubidium. Through coherent adiabatic association in a deeply degenerate mixture of a rubidium Bose-Einstein condensate and a potassium Fermi gas, we produce molecules at temperatures below 0.3 times the Fermi temperature. We explore the properties of this reactive gas and demonstrate how degeneracy suppresses chemical reactions, making a long-lived degenerate gas of polar molecules a reality.

Two-Photon Vibrational Transitions in 16O2+ as Probes of Variation of the Proton-to-Electron Mass Ratio

Vibrational overtones in deeply-bound molecules are sensitive probes for variation of the proton-to-electron mass ratio μ . In nonpolar molecules, these overtones may be driven as two-photon transitions. Here, we present procedures for experiments with 16 O 2 + , including state-preparation through photoionization, a two-photon probe, and detection. We calculate transition dipole moments between all X 2 Π g vibrational levels and those of the A 2 Π u excited electronic state. Using these dipole moments, we calculate two-photon transition rates and AC-Stark-shift systematics for the overtones. We estimate other systematic effects and statistical precision. Two-photon vibrational transitions in 16 O 2 + provide multiple routes to improved searches for μ variation.

Composite laser-pulses spectroscopy for high-accuracy optical clocks: a review of recent progress and perspectives

Probing an atomic resonance without disturbing it is an ubiquitous issue in physics. This problem is critical in high-accuracy spectroscopy or for the next generation of atomic optical clocks. Ultra-high resolution frequency metrology requires sophisticated interrogation schemes and robust protocols handling pulse length errors and residual frequency detuning offsets. This review reports recent progress and perspective in such schemes, using sequences of composite laser-pulses tailored in pulse duration, frequency and phase, inspired by NMR techniques and quantum information processing. After a short presentation of Rabi technique and NMR-like composite pulses allowing efficient compensation of electromagnetic field perturbations to achieve robust population transfers, composite laser-pulses are investigated within Ramsey's method of separated oscillating fields in order to generate non-linear compensation of probe-induced frequency shifts. Laser-pulses protocols such as hyper-Ramsey, modified hyper-Ramsey, generalized hyper-Ramsey and hybrid schemes as auto-balanced Ramsey spectroscopy are reviewed. These techniques provide excellent protection against both probe induced light-shift perturbations and laser intensity variations. More sophisticated schemes generating synthetic frequency-shifts are presented. They allow to reduce or completely eliminate imperfect correction of probe-induced frequency-shifts even in presence of decoherence due to the laser line-width. Finally, two universal protocols are presented which provide complete elimination of probe-induced frequency shifts in the general case where both decoherence and relaxation dissipation effects are present by using exact analytic expressions for phase-shifts and the clock frequency detuning. These techniques might be applied to atomic, molecular and nuclear frequency metrology, Ramsey-type mass spectrometry as well as precision spectroscopy.

Magnetic Trapping of an Ultracold Gas of Polar Molecules

We demonstrate the efficient transfer of molecules from a magneto-optical trap into a conservative magnetic quadrupole trap. Our scheme begins with a blue-detuned optical molasses to cool SrF molecules to ≈50  μK. Next, we optically pump the molecules into a strongly trapped sublevel. This two-step process reliably transfers ≈40% of the molecules initially trapped in the magneto-optical trap into a single quantum state in the magnetic trap. Once loaded, the molecule cloud is compressed by increasing the magnetic field gradient. We observe a magnetic trap lifetime of over 1 s. This opens a promising new path to study ultracold molecular collisions, and potentially to produce quantum-degenerate molecular gases via sympathetic cooling with co-trapped atoms.