Relativistic Exact Two-Component Coupled-Cluster Study of Molecular Sensitivity Factors for Nuclear Schiff Moments

Relativistic exact two-component coupled-cluster calculations of molecular sensitivity factors for nuclear Schiff moments (NSMs) are reported. We focus on molecules containing heavy nuclei, especially octupole-deformed nuclei. Analytic relativistic coupled-cluster gradient techniques are used and serve as useful tools for identifying candidate molecules that sensitively probe for physics beyond the Standard Model in the hadronic sector. Notably, these tools enable straightforward "black-box" calculations. Two competing chemical mechanisms that contribute to the NSM are analyzed, illuminating the physics of ligand effects on NSM sensitivity factors.

New Classes of Magnetic Noise Self-Compensation Effects in Atomic Comagnetometer

Precision measurements of anomalous spin-dependent interactions are often hindered by magnetic noise and other magnetic systematic effects. Atomic comagnetometers use the distinct spin precession of two species and have emerged as important tools for effectively mitigating the magnetic noise. Nevertheless, the operation of existing comagnetometers is limited to very low-frequency noise commonly below 1 Hz. Here, we report a new type of atomic comagnetometer based on a magnetic noise self-compensation mechanism originating from the destructive interference between alkali-metal and noble-gas spins. Our comagnetometer employing K-^{3}He system remarkably suppresses magnetic noise exceeding 2 orders of magnitude at higher frequencies up to 160 Hz. Moreover, we discover that the capability of our comagnetometer to suppress magnetic noise is spatially dependent on the orientation of the noise and can be conveniently controlled by adjusting the applied bias magnetic field. Our findings open up new possibilities for precision measurements, including enhancing the search sensitivity of spin-dark matter particles interactions into unexplored parameter space.

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].

Quantum control of trapped polyatomic molecules for eEDM searches

Ultracold polyatomic molecules are promising candidates for experiments in quantum science and precision searches for physics beyond the Standard Model. A key requirement is the ability to achieve full quantum control over the internal structure of the molecules. In this work, we established coherent control of individual quantum states in calcium monohydroxide (CaOH) and demonstrated a method for searching for the electron electric dipole moment (eEDM). Optically trapped, ultracold CaOH molecules were prepared in a single quantum state, polarized in an electric field, and coherently transferred into an eEDM-sensitive state where an electron spin precession measurement was performed. To extend the coherence time, we used eEDM-sensitive states with tunable, near-zero magnetic field sensitivity. Our results establish a path for eEDM searches with trapped polyatomic molecules.

New constraints on exotic spin-dependent interactions with an ensemble-NV-diamond magnetometer

Laboratory search of exotic interactions is crucial for exploring physics beyond the standard model. We report new experimental constraints on two exotic spin-dependent interactions at the micrometer scale based on ensembles of nitrogen-vacancy (NV) centers in diamond. A thin layer of NV electronic spin ensembles is synthesized as the solid-state spin quantum sensor, and a lead sphere is taken as the interacting nucleon source. Our result establishes new bounds for two types of exotic spin interactions at the micrometer scale. For an exotic parity-odd spin- and velocity-dependent interaction, improved bounds are set within the force range from 5 to 500 μm. The upper limit of the corresponding coupling constant [Formula: see text] at 330 μm is more than 1000-fold more stringent than the previous constraint. For the P, T-violating scalar-pseudoscalar nucleon-electron interaction, improved constraints are established within the force range from 6 to 45 μm. The limit of the corresponding coupling constant [Formula: see text] is improved by more than one order of magnitude at 30 μm. This work demonstrates that a solid-state NV ensemble can be a powerful platform for probing exotic spin-dependent interactions.

Excited Electronic States of Sr2: Ab Initio Predictions and Experimental Observation of the 21Σu+ State

Despite its apparently simple nature with four valence electrons, the strontium dimer constitutes a challenge for modern electronic structure theory. Here we focus on excited electronic states of Sr₂, which we investigate theoretically up to 25000 cm^-1 above the ground state, to guide and explain new spectroscopic measurements. In particular, we focus on potential energy curves for the 1¹Σ_u⁺, 2¹Σ_u⁺, 1¹Π_u, 2¹Π_u, and 1¹Δ_u states computed using several variants of ab initio coupled-cluster and configuration-interaction methods to benchmark them. In addition, a new experimental study of the excited 2¹Σ_u⁺ state using polarization labeling spectroscopy is presented, which extends knowledge of this state to high vibrational levels, where perturbation by higher electronic states is observed. The available experimental observations are compared with the theoretical predictions and help to assess the accuracy and limitations of employed theoretical models. The present results pave the way for future more accurate theoretical and experimental spectroscopic studies.

Nonresonant cavity for multipass laser intensity buildup

A nonresonant cavity to build up laser intensity is modeled, developed, and tested. It can be used for overlapping multiple lasers of different wavelengths, increasing their intensities by more than an order of magnitude while maintaining good uniformity. It is simple to set up, has flexible optical characteristics, and is robust against perturbations. The intensity buildup requires no resonances, and the wavelength dependence of the performance is limited only by the mirror coatings. The cavity can be used, for example, in applications requiring a spatially constrained intensity buildup, such as in atomic and molecular traps.

Search for exotic parity-violation interactions with quantum spin amplifiers

Quantum sensing provides sensitive tabletop tools to search for exotic spin-dependent interactions beyond the standard model, which have attracted great attention in theories and experiments. Here, we develop a technique based on Spin Amplifier for Particle PHysIcs REsearch (SAPPHIRE) to resonantly search for exotic interactions, specifically parity-odd spin-spin interactions. The present technique effectively amplifies exotic interaction fields by a factor of about 200 while being insensitive to spurious magnetic fields. Our studies, using such a quantum amplification technique, explore the parity-violation interactions mediated by a new vector boson in the challenging parameter space (force range between 3 mm and 1 km) and set the most stringent constraints on axial-vector electron-neutron couplings, substantially improving previous limits by five orders of magnitude. Moreover, our constraints on axial-vector couplings between nucleons reach into a hitherto unexplored parameter space. The present constraints complement the existing astrophysical and laboratory studies on potential standard model extensions.

Limits on Axions and Axionlike Particles within the Axion Window Using a Spin-Based Amplifier

Searches for the axion and axionlike particles may hold the key to unlocking some of the deepest puzzles about our Universe, such as dark matter and dark energy. Here, we use the recently demonstrated spin-based amplifier to constrain such hypothetical particles within the well-motivated "axion window" (10  μeV-1  meV) through searching for an exotic dipole-dipole interaction between polarized electron and neutron spins. The key ingredient is the use of hyperpolarized long-lived ^{129}Xe nuclear spins as an amplifier for the pseudomagnetic field generated by the exotic interaction. Using such a spin sensor, we obtain a direct upper bound on the product of coupling constants g_{p}^{e}g_{p}^{n}. The spin-based amplifier technique can be extended to searches for a wide variety of hypothetical particles beyond the standard model.

Spectroscopy of Alkali Atoms in Solid Matrices of Rare Gases: Experimental Results and Theoretical Analysis

We present an experimental and theoretical investigation of the spectroscopy of dilute alkali atoms in a solid matrix of inert gases at cryogenic temperatures, specifically Rubidium atoms in a solid Argon or Neon matrix, and related aspects of the interaction energies between the alkali atoms and the atoms of the solid matrix. The system considered is relevant for matrix isolation spectroscopy, and it is at the basis of a recently proposed detector of cosmological axions, exploiting magnetic-type transitions between Zeeman sublevels of alkali atoms in a magnetic field, tuned to the axion mass, assumed in the meV range. Axions are one of the supposed constituents of the dark matter (DM) of the Universe. This kind of spectroscopy could be also relevant for the experimental search of new physics beyond the Standard Model, in particular the search of violations of time-reversal or parity-charge-conjugation (CP) symmetry. In order to efficiently resolve the axion-induced transition in alkali-doped solid matrices, it is necessary to reduce as much as possible the spectral linewidth of the electronic transitions involved. The theoretical investigation presented in this paper aims to estimate the order of magnitude of the inhomogeneous contribution to the linewidth due to the alkali–matrix interactions (Coulomb/exchange and dispersion), and to compare the theoretical results with our experimental measurements of spectra of dilute Rubidium atoms in Argon and Neon solid matrix. The comparison of the expected or measured spectral linewidths will be important for selecting the most appropriate combination of alkali atoms and matrix inert elements to be used in the proposed axion detection scheme. It is finally suggested that dilute Lithium atoms diffused in a cold parahydrogen solid matrix could be, overall, a good system upon which the proposed detector could be based.

A combined experimental and computational study on the transition of the calcium isopropoxide radical as a candidate for direct laser cooling

Vibronically resolved laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down (CRD) spectra of the electronic transition of the calcium isopropoxide [CaOCH(CH₃)₂] radical have been obtained under jet-cooled conditions. An essentially constant energy separation of 68 cm^-1 has been observed for the vibrational ground levels and all fundamental vibrational levels accessed in the LIF measurement. To simulate the experimental spectra and assign the recorded vibronic bands, Franck-Condon (FC) factors and vibrational branching ratios (VBRs) are predicted from vibrational modes and their frequencies calculated using the complete-active-space self-consistent field (CASSCF) and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) methods. Combined with the calculated electronic transition energy, the computational results, especially those from the EOM-CCSD calculations, reproduced the experimental spectra with considerable accuracy. The experimental and computational results suggest that the FC matrix for the studied electronic transition is largely diagonal, but transitions from the vibrationless levels of the à state to the X̃-state levels of the CCC bending (ν₁₄ and ν₁₅), CaO stretch (ν₁₃), and CaOC asymmetric stretch (ν₉ and ν₁₁) modes also have considerable intensities. Transitions to low-frequency in-plane [ν₁₇(a')] and out-of-plane [ν₃₀(a'')] CaOC bending modes were observed in the experimental LIF/DF spectra, the latter being FC-forbidden but induced by the pseudo-Jahn-Teller (pJT) effect. Both bending modes are coupled to the CaOC asymmetric stretch mode via the Duschinsky rotation, as demonstrated in the DF spectra obtained by pumping non-origin vibronic transitions. The pJT interaction also induces transitions to the ground-state vibrational level of the ν₁₀(a') mode, which has the CaOC bending character. Our combined experimental and computational results provide critical information for future direct laser cooling of the target molecule and other alkaline earth monoalkoxide radicals.

Precision Determination of Isotope Shifts in Ytterbium and Implications for New Physics

We report measurements of isotope shifts for the five spinless Yb isotopes on the 6s^{2} ^{1}S_{0}→5d6s ^{1}D_{2} transition using Doppler-free two-photon spectroscopy. We combine these data with existing measurements on two transitions in Yb^{+} [Counts et al. Phys. Rev. Lett. 125, 123002 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.123002], where deviation from King-plot linearity showed hints of a new bosonic force carrier at the 3σ level. The combined data strongly reduce the significance of the new-physics signal. We show that the observed nonlinearity in the joint Yb/Yb^{+} King-plot analysis can be accounted for by the deformation of the Yb nuclei.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Perspectives on parity violation in chiral molecules: theory, spectroscopic experiment and biomolecular homochirality

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number parity and a fundamental ‘non-observable’ property of space (as defined by an absolute ‘left-handed’ or ‘right-handed’ coordinate system). The discovery of the violation of this symmetry – the non-conservation of parity or ‘parity violation’ – in 1956/1957 had an important influence on the further development of physics. In chemistry the mirror symmetry of space is connected to the existence of enantiomers as isomers of chiral (‘handed’) molecules. These isomers would relate to each other as idealized left or right hand or as image and mirror image and would be energetically exactly equivalent with perfect space inversion symmetry. Parity violation results in an extremely small ‘parity violating’ energy difference between the ground states of the enantiomers which can be theoretically calculated to be about 100 aeV to 1 feV (equivalent to 10⁻¹¹ to 10⁻¹⁰ J mol⁻¹), depending on the molecule, but which has not yet been detected experimentally. Its detection remains one of the great challenges of current physical–chemical stereochemistry, with implications also for fundamental problems in physics. In biochemistry and molecular biology one finds a related fundamental question unanswered for more than 100 years: the evolution of ‘homochirality’, which is the practically exclusive preference of one chiral, enantiomeric form as building blocks in the biopolymers of all known forms of life (the l-amino acids in proteins and d-sugars in DNA, not the reverse d-amino acids or l-sugars). In astrobiology the spectroscopic detection of homochirality could be used as strong evidence for the existence of extraterrestrial life, if any. After a brief conceptual and historical introduction we review the development, current status, and progress along these three lines of research: theory, spectroscopic experiment and the outlook towards an understanding of the evolution of biomolecular homochirality.

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number purity and its violation and has a fundamental relation to stereochemistry and molecular chirality.

High Phase-Space Density of Laser-Cooled Molecules in an Optical Lattice

We report laser cooling and trapping of yttrium monoxide molecules in an optical lattice. We show that gray molasses cooling remains exceptionally efficient for yttrium monoxide molecules inside the lattice with a molecule temperature as low as 6.1(6)  μK. This approach has produced a trapped sample of 1200 molecules, with a peak spatial density of ∼1.2×10^{10}  cm^{-3}, and a peak phase-space density of ∼3.1×10^{-6}. By ramping down the lattice depth, we cool the molecules further to 1.0(2)  μK, 20 times colder than previously reported for laser-cooled molecules in a trap.

Zeeman-Sisyphus Deceleration of Molecular Beams

We present a robust, continuous molecular decelerator that employs high magnetic fields and few optical pumping steps. CaOH molecules are slowed, accumulating at low velocities in a range sufficient for loading both magnetic and magneto-optical traps. During the slowing, the molecules scatter only seven photons, removing around 8 K of energy. Because large energies can be removed with only a few spontaneous radiative decays, this method can in principle be applied to nearly any paramagnetic atomic or molecular species, opening a general path to trapping of complex molecules.

Search for exotic spin-dependent interactions with a spin-based amplifier

Development of new techniques to search for particles beyond the standard model is crucial for understanding the ultraviolet completion of particle physics. Several hypothetical particles are predicted to mediate exotic spin-dependent interactions between standard-model particles that may be accessible to laboratory experiments. However, laboratory searches are mostly conducted for static spin-dependent interactions, with a few experiments addressing spin- and velocity-dependent interactions. Here, we demonstrate a search for these interactions with a spin-based amplifier. Our technique uses hyperpolarized nuclear spins as an amplifier for pseudo-magnetic fields produced by exotic interactions by a factor of more than 100. Using this technique, we establish constraints on the spin- and velocity-dependent interactions between polarized neutrons and unpolarized nucleons for the force range of 0.03 to 100 meters, improving previous constraints by at least two orders of magnitude in partial force range. This technique can be further extended to investigate other exotic spin-dependent interactions.

High-Resolution "Magic"-Field Spectroscopy on Trapped Polyatomic Molecules

Rapid progress in cooling and trapping of molecules has enabled first experiments on high-resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a"magic" offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We thereby reduce Stark broadening on the J=5←4 (K=3) transition of formaldehyde at 364 GHz to well below 1 kHz, observe Doppler-limited linewidths down to 3.8 kHz, and determine the magic-field line position with an uncertainty below 100 Hz. Our approach opens a multitude of possibilities for investigating diverse polyatomic molecule species.

Experimental Constraint on an Exotic Parity-Odd Spin- and Velocity-Dependent Interaction with a Single Electron Spin Quantum Sensor

Improved laboratory limits on the exotic spin- and velocity-dependent interaction at the micrometer scale are established with a single electron spin quantum sensor. The single electron spin of a near-surface nitrogen-vacancy center in diamond is used as the quantum sensor, and a fused-silica half-sphere lens is taken as the source of the moving nucleons. The exotic interaction between the polarized electron and the moving nucleon source is explored by measuring the possible magnetic field sensed by the electron spin quantum sensor. Our experiment sets improved constraints on the exotic spin- and velocity-dependent interaction within the force range from 1.4 to 330  μm. The upper limit of the coupling g_{A}^{e}g_{V}^{N} at 200  μm is |g_{A}^{e}g_{V}^{N}|≤5.3×10^{-19}, significantly improving the current laboratory limit by more than 4 orders of magnitude.

Fine and hyperfine interactions in 171YbOH and 173YbOH

The odd isotopologues of ytterbium monohydroxide, ^171,173YbOH, have been identified as promising molecules to measure parity (P) and time reversal (T) violating physics. Here, we characterize the òΠ_1/2(0,0,0)-X̃²Σ⁺(0,0,0) band near 577 nm for these odd isotopologues. Both laser-induced fluorescence excitation spectra of a supersonic molecular beam sample and absorption spectra of a cryogenic buffer-gas cooled sample were recorded. In addition, a novel spectroscopic technique based on laser-enhanced chemical reactions is demonstrated and used in absorption measurements. This technique is especially powerful for disentangling congested spectra. 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) hyperfine parameters with recently predicted values [Denis et al., J. Chem. Phys. 152, 084303 (2020); K. Gaul and R. Berger, Phys. Rev. A 101, 012508 (2020); and Liu et al., J. Chem. Phys. 154,064110 (2021)] is made. The measured hyperfine parameters provide experimental confirmation of the computational methods used to compute the P,T-violating coupling constants W_d and W_M, which correlate P,T-violating physics to P,T-violating energy shifts in the molecule. The dependence of the fine and hyperfine parameters of the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states for all isotopologues of YbOH are discussed, and a comparison to isoelectronic YbF is made.

Search for Axionlike Dark Matter Using Solid-State Nuclear Magnetic Resonance

We report the results of an experimental search for ultralight axionlike dark matter in the mass range 162-166 neV. The detection scheme of our Cosmic Axion Spin Precession Experiment is based on a precision measurement of ^{207}Pb solid-state nuclear magnetic resonance in a polarized ferroelectric crystal. Axionlike dark matter can exert an oscillating torque on ^{207}Pb nuclear spins via the electric dipole moment coupling g_{d} or via the gradient coupling g_{aNN}. We calibrate the detector and characterize the excitation spectrum and relaxation parameters of the nuclear spin ensemble with pulsed magnetic resonance measurements in a 4.4 T magnetic field. We sweep the magnetic field near this value and search for axionlike dark matter with Compton frequency within a 1 MHz band centered at 39.65 MHz. Our measurements place the upper bounds |g_{d}|<9.5×10^{-4}  GeV^{-2} and |g_{aNN}|<2.8×10^{-1}  GeV^{-1} (95% confidence level) in this frequency range. The constraint on g_{d} corresponds to an upper bound of 1.0×10^{-21}  e cm on the amplitude of oscillations of the neutron electric dipole moment and 4.3×10^{-6} on the amplitude of oscillations of CP-violating θ parameter of quantum chromodynamics. Our results demonstrate the feasibility of using solid-state nuclear magnetic resonance to search for axionlike dark matter in the neV mass range.

Dynamical Generation of Spin Squeezing in Ultracold Dipolar Molecules

We study a bulk fermionic dipolar molecular gas in the quantum degenerate regime confined in a two-dimensional geometry. Using two rotational states of the molecules, we encode a spin 1/2 degree of freedom. To describe the many-body spin dynamics of the molecules, we derive a long-range interacting XXZ model valid in the regime where motional degrees of freedom are frozen. Because of the spatially extended nature of the harmonic oscillator modes, the interactions in the spin model are very long ranged, and the system behaves close to the collective limit, resulting in robust dynamics and generation of entanglement in the form of spin squeezing even at finite temperature and in the presence of dephasing and chemical reactions. We discuss how the internal state structure can be exploited to realize time reversal and enhanced metrological sensing protocols.

Resonant collisional shielding of reactive molecules using electric fields

Full control of molecular interactions, including reactive losses, would open new frontiers in quantum science. We demonstrate extreme tunability of ultracold chemical reaction rates by inducing resonant dipolar interactions by means of an external electric field. We prepared fermionic potassium-rubidium molecules in their first excited rotational state and observed a modulation of the chemical reaction rate by three orders of magnitude as we tuned the electric field strength by a few percent across resonance. In a quasi-two-dimensional geometry, we accurately determined the contributions from the three dominant angular momentum projections of the collisions. Using the resonant features, we shielded the molecules from loss and suppressed the reaction rate by an order of magnitude below the background value, thereby realizing a long-lived sample of polar molecules in large electric fields.

Floquet maser

The invention of the maser stimulated revolutionary technologies such as lasers and atomic clocks. Yet, realizations of masers are still limited; in particular, the physics of masers remains unexplored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic phenomena such as time crystals. Here, we investigate the Floquet system of periodically driven ¹²⁹Xe gas under damping feedback and unexpectedly observe a multimode maser that oscillates at frequencies of transitions between Floquet states. Our findings extend maser techniques to Floquet systems and open avenues to probe Floquet phenomena unaffected by decoherence, enabling a previously unexplored class of maser sensors. As a first application, our maser offers the capability of measuring low-frequency (1 to 100 mHz) magnetic fields with subpicotesla-level sensitivity, which is substantially better than state-of-the-art magnetometers and can be applied to, for example, ultralight dark matter searches.

Dipolar evaporation of reactive molecules to below the Fermi temperature

The control of molecules is key to the investigation of quantum phases, in which rich degrees of freedom can be used to encode information and strong interactions can be precisely tuned1. Inelastic losses in molecular collisions2-5, however, have greatly hampered the engineering of low-entropy molecular systems6. So far, the only quantum degenerate gas of molecules has been created via association of two highly degenerate atomic gases7,8. Here we use an external electric field along with optical lattice confinement to create a two-dimensional Fermi gas of spin-polarized potassium-rubidium (KRb) polar molecules, in which elastic, tunable dipolar interactions dominate over all inelastic processes. Direct thermalization among the molecules in the trap leads to efficient dipolar evaporative cooling, yielding a rapid increase in phase-space density. At the onset of quantum degeneracy, we observe the effects of Fermi statistics on the thermodynamics of the molecular gas. These results demonstrate a general strategy for achieving quantum degeneracy in dipolar molecular gases in which strong, long-range and anisotropic dipolar interactions can drive the emergence of exotic many-body phases, such as interlayer pairing and p-wave superfluidity.

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.

Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2. Phys Chem Chem Phys 2020;22:23083-23098. [PMID: 33048077 DOI: 10.1039/d0cp03906c]

Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency, illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG, translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and is thus well suited for testing a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N2+ through the magnetically enhanced mixing of nuclear-spin states.

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.

Improved Isotope-Shift-Based Bounds on Bosons beyond the Standard Model through Measurements of the ^{2}D_{3/2}-^{2}D_{5/2} Interval in Ca^{+}

We perform high-resolution spectroscopy of the 3d ^{2}D_{3/2}-3d ^{2}D_{5/2} interval in all stable even isotopes of ^{A}Ca^{+} (A=40, 42, 44, 46, and 48) with an accuracy of ∼20  Hz using direct frequency-comb Raman spectroscopy. Combining these data with isotope shift measurements of the 4s ^{2}S_{1/2}↔3d ^{2}D_{5/2} transition, we carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the standard model. Furthermore, we estimate the sensitivity to such bosons from equivalent spectroscopy in Ba^{+} and Yb^{+}. Finally, the data yield isotope shifts of the 4s ^{2}S_{1/2}↔3d ^{2}D_{3/2} transition at 10 parts per billion through combination with recent data of Knollmann, Patel, and Doret [Phys. Rev. A 100, 022514 (2019)PLRAAN2469-992610.1103/PhysRevA.100.022514].

Identification of molecular quantum states using phase-sensitive forces

Quantum-logic techniques used to manipulate quantum systems are now increasingly being applied to molecules. Previous experiments on single trapped diatomic species have enabled state detection with excellent fidelities and highly precise spectroscopic measurements. However, for complex molecules with a dense energy-level structure improved methods are necessary. Here, we demonstrate an enhanced quantum protocol for molecular state detection using state-dependent forces. Our approach is based on interfering a reference and a signal force applied to a single atomic and molecular ion. By changing the relative phase of the forces, we identify states embedded in a dense molecular energy-level structure and monitor state-to-state inelastic scattering processes. This method can also be used to exclude a large number of states in a single measurement when the initial state preparation is imperfect and information on the molecular properties is incomplete. While the present experiments focus on N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{+}$$\end{document}2+, the method is general and is expected to be of particular benefit for polyatomic systems.

The identification of molecular quantum states becomes challenging with increasing complexity of the molecular level structure. Here, the authors non-destructively identified excited molecular states of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{N}}}_{2}^{+}$$\end{document}N2+ by interfering forces applied to both the molecular ion and to a co-trapped atomic ion.

Generating Multipartite Spin States with Fermionic Atoms in a Driven Optical Lattice

We propose a protocol for generating generalized Greenberger-Horne-Zeilinger (GHZ) states using ultracold fermions in 3D optical lattices or optical tweezer arrays. The protocol uses the interplay between laser driving, on site interactions and external trapping confinement to enforce energetic spin- and position-dependent constraints on the atomic motion. These constraints allow us to transform a local superposition into a GHZ state through a stepwise protocol that flips one site at a time. The protocol requires no site-resolved drives or spin-dependent potentials, exhibits robustness to slow global laser phase drift, and naturally makes use of the harmonic trap that would normally cause difficulties for entanglement-generating protocols in optical lattices. We also discuss an improved protocol that can compensate for holes in the loadout at the cost of increased generation time. The state can immediately be used for quantum-enhanced metrology in 3D optical lattice clocks, opening a window to push the sensitivity of state-of-the-art sensors beyond the standard quantum limit.

Quantum-nondemolition state detection and spectroscopy of single trapped molecules

Trapped atoms and ions, which are among the best-controlled quantum systems, find widespread applications in quantum science. For molecules, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially for homonuclear species that decouple from blackbody radiation. Here, a quantum-nondemolition protocol on single trapped [Formula: see text] molecules is demonstrated. The spin-rovibronic state of the molecule is detected with >99% fidelity, and a spectroscopic transition is measured without destroying the quantum state. This method lays the foundations for new approaches to molecular spectroscopy, state-to-state chemistry, and the implementation of molecular qubits.

Toolbox approach for quasi-relativistic calculation of molecular properties for precision tests of fundamental physics

A generally applicable approach for the calculation of relativistic properties described by one-electron operators within a two-component wave function approach is presented. The formalism is explicitly evaluated for the example of quasirelativistic wave functions obtained within the zeroth order regular approximation (ZORA). The wide applicability of the scheme is demonstrated for the calculation of parity (P) and time-reversal (T  ) symmetry violating properties, which are important for searches of physics beyond the standard model of particle physics. The quality of the ZORA results is shown exemplarily for the molecules RaF and TlF by comparison with data from four-component calculations as far as available. Finally, the applicability of RaF in experiments that search for P,T-violation not only in the electronic but also in the quark sector is demonstrated.

Approaching the transit time limit for high-precision spectroscopy on metastable CO around 6 μm

As molecular spectroscopy makes its comeback to the limelight of fundamental sciences, scientists need ever better coherent light sources and diagnostic methods. Of particular importance for molecular spectroscopy is the mid infrared spectral region, where strong and narrow ro-vibrational excitations have their fundamental transition frequencies. Unfortunately, much technology in some portions of this spectral region is still rather pioneering. Here we present a high-resolution spectroscopy experiment, based on a molecular beam setup, which pushes the measured linewidth close to the transit time limit, on the order of 100 kHz. Moreover, we discuss the issue of frequency-noise characterization and the linewidth measurement of the ultrastable infrared laser used in the experiment.

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.

Deep Laser Cooling and Efficient Magnetic Compression of Molecules

We introduce a scheme for deep laser cooling of molecules based on robust dark states at zero velocity. By simulating this scheme, we show it to be a widely applicable method that can reach the recoil limit or below. We demonstrate and characterize the method experimentally, reaching a temperature of 5.4(7)  μK. We solve a general problem of measuring low temperatures for large clouds by rotating the phase-space distribution and then directly imaging the complete velocity distribution. Using the same phase-space rotation method, we rapidly compress the cloud. Applying the cooling method a second time, we compress both the position and velocity distributions.

Search for Axionlike Dark Matter with a Liquid-State Nuclear Spin Comagnetometer

We report the results of a search for axionlike dark matter using nuclear magnetic resonance (NMR) techniques. This search is part of the multifaceted Cosmic Axion Spin Precession Experiment program. In order to distinguish axionlike dark matter from magnetic fields, we employ a comagnetometry scheme measuring ultralow-field NMR signals involving two different nuclei (^{13}C and ^{1}H) in a liquid-state sample of acetonitrile-2-^{13}C (^{13}CH_{3}CN). No axionlike dark matter signal was detected above the background. This result constrains the parameter space describing the coupling of the gradient of the axionlike dark matter field to nucleons to be g_{aNN}<6×10^{-5}  GeV^{-1} (95% confidence level) for particle masses ranging from 10^{-22}  eV to 1.3×10^{-17}  eV, improving over previous laboratory limits for masses below 10^{-21}  eV. The result also constrains the coupling of nuclear spins to the gradient of the square of the axionlike dark matter field, improving over astrophysical limits by orders of magnitude over the entire range of particle masses probed.

Homochirality: A Perspective from Fundamental Physics

In this brief review, possible mechanisms which could lead to complete biological homochirality are discussed from the viewpoint of fundamental physics. In particular, the role played by electroweak parity violation, including neutrino-induced homochirality, and contributions from the gravitational interaction, will be emphasized.

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.

Relativistic Normal Coupled-Cluster Theory for Accurate Determination of Electric Dipole Moments of Atoms: First Application to the ^{199}Hg Atom

Recent relativistic coupled-cluster (RCC) calculations of electric dipole moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating (P,T-odd) interactions, which are essential ingredients for probing new physics beyond the standard model of particle interactions, differ substantially from the previous theoretical results. It is therefore necessary to perform an independent test of the validity of these results. In view of this, the normal coupled-cluster method has been extended to the relativistic regime [relativistic normal coupled-cluster (RNCC) method] to calculate the EDMs of atoms by simultaneously incorporating the electrostatic and P,T-odd interactions in order to overcome the shortcomings of the ordinary RCC method. This new relativistic method has been applied to ^{199}Hg, which currently has a lower EDM limit than that of any other system. The results of our RNCC and self-consistent RCC calculations of the EDM of this atom are found to be close. The discrepancies between these two results on the one hand and those of previous calculations on the other are elucidated. Furthermore, the electric dipole polarizability of this atom, which has computational similarities with the EDM, is evaluated and it is in very good agreement with its measured value.

Magnetic Trapping and Coherent Control of Laser-Cooled Molecules

We demonstrate coherent microwave control of the rotational, hyperfine, and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about 5×10^{3} molecules for almost 2 s at a temperature of 70(8)  μK and a density of 1.2×10^{5}  cm^{-3}. We measure the state-specific loss rate due to collisions with background helium.

Coherent Bichromatic Force Deflection of Molecules

We demonstrate the effect of the coherent optical bichromatic force on a molecule, the polar free radical strontium monohydroxide (SrOH). A dual-frequency retroreflected laser beam addressing the X[over ˜]^{2}Σ^{+}↔A[over ˜]^{2}Π_{1/2} electronic transition coherently imparts momentum onto a cryogenic beam of SrOH. This directional photon exchange creates a bichromatic force that transversely deflects the molecules. By adjusting the relative phase between the forward and counterpropagating laser beams we reverse the direction of the applied force. A momentum transfer of 70ℏk is achieved with minimal loss of molecules to dark states. Modeling of the bichromatic force is performed via direct numerical solution of the time-dependent density matrix and is compared with experimental observations. Our results open the door to further coherent manipulation of molecular motion, including the efficient optical deceleration of diatomic and polyatomic molecules with complex level structures.