Precision measurements in molecules have advanced rapidly in recent years through developments in techniques to cool, trap, and control. The complexity of molecules makes them a challenge to study, but also offers opportunities for enhanced sensitivity to many interesting effects. Polyatomic molecules offer additional complexity compared to diatomic molecules, yet are still "simple" enough to be laser-cooled and controlled. While laser cooling molecules is still a research frontier itself, there are many proposed and ongoing experiments seeking to combine the advanced control enabled by ultracold temperatures with the intrinsic sensitivity of molecules. In this perspective, we discuss some applications where laser-cooled polyatomic molecules may offer advantages for precision measurements of fundamental physics, both within and beyond the Standard Model.
Over the past decade, tremendous progress has been made to extend the tools of laser cooling and trapping to molecules. Those same tools have recently been applied to polyatomic molecules (molecules containing three or more atoms). In this review, we discuss the scientific drive to bring larger molecules to ultralow temperatures, the features of molecular structure that provide the most promising molecules for this pursuit, and some technical aspects of how lasers can be used to control the motion and quantum states of polyatomic molecules. We also present opportunities for and challenges to t…
Precision searches for time-reversal symmetry violating interactions in polar molecules are extremely sensitive probes of high energy physics beyond the Standard Model. To extend the reach of these probes into the PeV regime, long coherence times and large count rates are necessary. Recent advances in laser cooling of polar molecules offer one important tool -- optical trapping. However, the types of molecules that have been laser-cooled so far do not have the highly desirable combination of features for new physics searches, such as the ability to fully polarize and the existence of internal …
We present a rigorous theoretical study of low-temperature collisions of polyatomic molecular radicals with ^1S_0 atoms in the presence of an external magnetic field. Accurate quantum scattering calculations based on ab initio and scaled interaction potentials show that collision-induced spin relaxation of the prototypical organic molecule CH_2(X^3B_1) (methylene) and nine other triatomic radicals in cold 3He gas occurs at a slow rate, demonstrating that cryogenic buffer-gas cooling and magnetic trapping of these molecules is feasible with current technology. Our calculations further suggest t…
We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the $10^{-5}$ level, including for nominally symmetry forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.
Optical control of polyatomic molecules promises new opportunities in precision metrology, fundamental chemistry, quantum information, and many-body science. Contemporary experimental and theoretical efforts have mostly focused on cycling photons via excitation of a single electron localized to an alkaline earth (group 2)-like metal center. In this manuscript, we consider pathways towards optical cycling in polyatomic molecules with multi-electron degrees of freedom, which arise from two or more cycling electrons localized to $p$-block post-transition metal and metalloid (group 13, 14, and 15)…
Recently a number of diatomic and polyatomics molecules has been identified as a prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows to decrease the kinetic energy of molecules down to microkelvin temperatures with high efficiency and then capture them to molecular traps, including magneto-optical trap. Trapped molecules can be used for creation of molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements and a multitude of other applications. Polyatomic molecules with heavy nuclei present considerable interest for th…
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 …
In polyatomic molecules with Π electronic ground state the ro-vibrational spectrum can be strongly modified by the Renner-Teller effect. The linear form of C3H molecule has particularly strong Renner-Teller interaction and a very low lying vibronic Σ+ level, which corresponds to the excited bending vibrational mode. This leads to the increased sensitivities of the microwave and submillimeter transition frequencies to the possible variation of the fine structure constant alpha and electron to proton mass ratio mu.
We report magneto-optical trapping (MOT) of a polyatomic molecule, calcium monohydroxide (CaOH). The MOT contains $2.0(5)\times 10^4$ CaOH molecules at a peak density of $3.0(8)\times10^{6}$ cm$^{-3}$. CaOH molecules are further sub-Doppler laser cooled in an optical molasses, to a temperature of 110(4) $μ$K. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including the creation of optical tweezer arrays of CaOH molecules. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomi…
Detecting the internal state of polar molecules is a substantial challenge when standard techniques such as resonance-enhanced multi photon ionization (REMPI) or laser-induced fluorescense (LIF) do not work. As this is the case for most polyatomic molecule species, we here investigate an alternative based on state selective removal of molecules from an electrically trapped ensemble. Specifically, we deplete molecules by driving rotational and/or vibrational transitions to untrapped states. Fully resolving the rotational state with this method can be a considerable challenge as the frequency di…
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and cons…
We present a generic approach for treating the effect of nuclear motion in the high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH$_4$ and…
The internal electric field of a Rydberg atom electron can bind a polar molecule to form a giant ultralong-range stable polyatomic molecule. Such molecules not only share their properties with Rydberg atoms, they possess huge permanent electric dipole moments and in addition allow for coherent control of the polar molecule orientation. In this work, we include additional Rydberg manifolds which couple to the nearly degenerate set of Rydberg states employed in [S. T. Rittenhouse and H. R. Sadeghpour, Phys. Rev. Lett. 104, 243002 (2010)]. The coupling of a set of $(n+3)s$ Rydberg states with the…
Laser-induced electron diffraction is an evolving tabletop method, which aims to image ultrafast structural changes in gas-phase polyatomic molecules with sub-Ångström spatial and femtosecond temporal resolution. Here, we provide the general foundation for the retrieval of multiple bond lengths from a polyatomic molecule by simultaneously measuring the C-C and C-H bond lengths in aligned acetylene. Our approach takes the method beyond the hitherto achieved imaging of simple diatomic molecules and is based upon the combination of a 160 kHz mid-IR few-cycle laser source with full three-dimension…
A rational approach to identify polyatomic molecules that appear to be promising candidates for direct Doppler cooling with lasers is outlined. First-principle calculations for equilibrium structures and Franck--Condon factors of selected representatives with different point-group symmetries (including chiral non-symmetric group C$_1$) have been performed and high potential for laser-cooling of these molecules is indicated.
Controlling the internal degrees of freedom is a key challenge for applications of cold and ultracold molecules. Here, we demonstrate rotational-state cooling of trapped methyl fluoride molecules (CH3F) by optically pumping the population of 16 M-sublevels in the rotational states J=3,4,5, and 6 into a single level. By combining rotational-state cooling with motional cooling, we increase the relative number of molecules in the state J=4, K=3, M=4 from a few percent to over 70%, thereby generating a translationally cold (~30mK) and nearly pure state ensemble of about 10^6 molecules. Our scheme …
The rich internal structure and long-range dipole-dipole interactions establish polar molecules as unique instruments for quantum-controlled applications and fundamental investigations. Their potential fully unfolds at ultracold temperatures, where a plethora of effects is predicted in many-body physics, quantum information science, ultracold chemistry, and physics beyond the standard model. These objectives have inspired the development of a wide range of methods to produce cold molecular ensembles. However, cooling polyatomic molecules to ultracold temperatures has until now seemed intractab…
We investigate properties of ultralong-range polyatomic molecules formed with a Rb Rydberg atom and several ground-state atoms whose distance from the Rydberg atom is of the order of n^2a_0, where n is the principle quantum number of the Rydberg electron. In particular, we put emphasis on the splitting of the energy levels, and elucidate the nature of the splitting via the construction of symmetry-adapted orbitals.
We demonstrate a 1D magneto-optical trap of the polar free radical calcium monohydroxide (CaOH). A quasi-closed cycling transition is established to scatter $\sim 10^3$ 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 mK to 1.4 mK.
Trilobites are exotic giant dimers with enormous dipole moments. They consist of a Rydberg atom and a distant ground-state atom bound together by short-range electron-neutral attraction. We show that highly polar, polyatomic trilobite states unexpectedly persist and thrive in a dense ultracold gas of randomly positioned atoms. This is caused by perturbation-induced quantum scarring and the localization of electron density on randomly occurring atom clusters. At certain densities these states also mix with a s-state, overcoming selection rules that hinder the photoassociation of ordinary trilob…
We explore the feasibility of optically forming long-range tetratomic and larger polyatomic molecules in their ground electronic state from ultracold pairs of polar molecules aligned by external fields. Depending on the relative orientation of the interacting diatomic molecules, we find that a tetratomic can be formed either as a weakly bound complex in a very extended halo state or as a pure long-range molecule composed of collinear or nearly-collinear diatomic molecules. The latter is a novel type of tetratomic molecule comprised of two diatomic molecules bound at long intermolecular range a…
High-order harmonic generation by a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $rω$ and $sω$ ($r$ and $s$ are integers), is investigated for a polyatomic molecule. This field possesses dynamical symmetry, which can be adjusted to the symmetry of the molecular Hamiltonian and used to investigate the molecular symmetry. For polyatomic molecules having the $C_{r+s}$ symmetry only the harmonics $n=q(r+s)\pm r$, $q=1,2,\ldots$, are emitted having the ellipticity $\varepsilon_n=\pm 1$. We illustrate this using the example of the planar …
An optical cycling center (OCC) is a recently coined term to indicate two electronic states within a complex quantum object that can repeatedly experience optical laser excitation and spontaneous decay, while being well isolated from its environment. Here we present a quantitative understanding of electronic, vibrational, and rotational excitations of the polyatomic SrOH molecule, which possesses a localized OCC near its Sr atom. In particular, we describe the vibrationally-dependent trends in the Franck-Condon factors of the bending and stretching modes of the molecular electronic states coup…
We predict the existence of a class of ultracold giant molecules formed from trapped ultracold Rydberg atoms and polar molecules. The interaction which leads to the formation of such molecules is the anisotropic charge-dipole interaction ($a/R^2$). We show that prominent candidate molecules such as KRb and deuterated hydroxyl (OD) should bind to Rydberg rubidium atoms, with energies $E_b\simeq 5-25$ GHz at distances $R\simeq 0.1-1 \ μ$m. These molecules form in double wells, mimicking chiral molecules, with each well containing a particular dipole orientation. We prepare a set of correlated dr…
We demonstrate multiple photon cycling and radiative force deflection on the triatomic free radical strontium monohydroxide (SrOH). Optical cycling is achieved on SrOH in a cryogenic buffer-gas beam by employing the rotationally closed $P\left(N''=1\right)$ branch of the vibronic transition $\tilde{X}^{2}Σ^{+}\left(000\right)\leftrightarrow\tilde{A}^{2}Π_{1/2}\left(000\right)$. A single repumping laser excites the Sr-O stretching vibrational mode, and photon cycling of the molecule deflects the SrOH beam by an angle of $0.2^{\circ}$ via scattering of $\sim100$ photons per molecule. This approa…
High-order harmonic generation in polyatomic molecules generally involves multiple channels, each associated with a different orbital. Their unambiguous assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach, using unaligned SF$_6$ molecules as an example, where we combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Channel-resolved above-threshold ionization measurements reveal that strong-field ionization opens four channels. Two of them, identified by monitoring the ellipticity depen…
Doppler and Sisyphus cooling of $^{174}$YbOH are achieved and studied. This polyatomic molecule has high sensitivity to physics beyond the Standard Model and represents a new class of species for future high-precision probes of new T-violating physics. The transverse temperature of the YbOH beam is reduced by nearly two orders of magnitude to $< 600 \, μ$K and the phase-space density is increased by a factor of $>6$ via Sisyphus cooling. We develop a full numerical model of the laser cooling of YbOH and find excellent agreement with the data. We project that laser cooling and magneto-optical t…
We perform magnetically-assisted Sisyphus laser cooling of the triatomic free radical strontium monohydroxide (SrOH). This is achieved with principal optical cycling in the rotationally closed $P\left(N"=1\right)$ branch of either the $\tilde{X}^{2}Σ^{+}\left(000\right)\leftrightarrow\tilde{A}^{2}Π_{1/2}\left(000\right)$ or the $\tilde{X}^{2}Σ^{+}\left(000\right)\leftrightarrow\tilde{B}^{2}Σ^{+}\left(000\right)$ vibronic transitions. Molecules lost into the excited vibrational states during the cooling process are repumped back through the $\tilde{B}\left(000\right)$ state for both the $\left(…
A time-dependent bond-hardening process is discovered in a polyatomic molecule (tetramethyl silane, TMS) using few-cycle pulses of intense 800 nm light. In conventional mass spectrometry, symmetrical molecules like TMS do not exhibit a prominent molecular ion (TMS$^+$) as unimolecular dissociation into [Si(CH$_3$)$_3]^+$ proceeds very fast. Under strong field and few-cycle conditions, this dissociation channel is defeated by time-dependent bond-hardening: a field-induced potential well is created in the TMS$^+$ potential energy curve that effectively traps a wavepacket. The time-dependence of …
We study optical cycling in the polar free radical calcium monohydroxide (CaOH) and establish an experimental path towards scattering $\sim$$10^4$ photons. We report rovibronic branching ratio measurements with precision at the $\sim10^{-4}$ level and observe weak symmetry-forbidden decays to bending modes with non-zero vibrational angular momentum. Calculations are in excellent agreement with these measurements and predict additional decay pathways. Additionally, we perform high-resolution spectroscopy of the $\widetilde{\text{X}}\,^2Σ^+(12^00)$ and $\widetilde{\text{X}}\,^2Σ^+(12^20)$ hybrid…
The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory…
A model-potential approach to calculating positron-molecule binding energies and annihilation rates is developed. Unlike existing ab initio calculations, which have mostly been applied to strongly polar molecules, the present methodology can be applied to both strongly polar and weakly polar or nonpolar systems. The electrostatic potential of the molecule is calculated at the Hartree-Fock level, and a model potential that describes short-range correlations and long-range polarization of the electron cloud by the positron is then added. The Schrodinger equation for a positron moving in this eff…
In molecular photofragmentation processes by soft X-rays, a number of ionic fragments can be produced, each having a different abundance and correlation with the emitted electron kinetic energy. For investigating these fragmentation processes, electron-ion and electron-ion-ion coincidence experiments, in which the kinetic energy of electrons are analyzed using an electrostatic analyzer while the mass of the ions is analyzed using a pulsed electric field, are very powerful. For such measurements, however, the contribution of random coincidences is substantial and affects the data in a non-trivi…
Measurements of nuclear spin-dependent parity-violating (NSD-PV) effects provide an excellent opportunity to test nuclear models and to search for physics beyond the Standard Model. Molecules possess closely-spaced states with opposite parity which may be easily tuned to degeneracy to greatly enhance the observed parity-violating effects. A high-sensitivity measurement of NSD-PV effects using light triatomic molecules is in preparation [E. B. Norrgard, et al., Commun. Phys. 2, 77 (2019)]. Importantly, by comparing these measurements in light nuclei with prior and ongoing measurements in heavie…
Infrared absorption spectroscopy of a single polyatomic molecular ion
Institut für Experimentalphysik, Universität Innsbruck（因斯布鲁克大学实验物理研究所）；Department of Optics, Palacký University（帕尔察基大学光学系）；Faculty of Physics, University of Warsaw（华沙大学物理学院）
Positrons bind to molecules leading to vibrational excitation and spectacularly enhanced annihilation. Whilst positron binding energies have been measured via resonant annihilation spectra for $\sim$90 molecules in the past two decades, an accurate \emph{ab initio} theoretical description has remained elusive. Of the molecules studied experimentally, calculations exist for only 6, and for these, standard quantum chemistry approaches have proved severely deficient, agreeing with experiment to at best 25% accuracy for polar molecules, and failing to predict binding in nonpolar molecules. The mec…
General formulas describing the multiple scattering of electron by polyatomic molecules have been derived within the framework of the model of non-overlapping atomic potentials. These formulas are applied to different carbon molecules, both for fixed-in-space and randomly oriented molecules.
Sufficiently high densities in Bose-Einstein condensates provide favorable conditions for the production of ultralong-range polyatomic molecules consisting of one Rydberg atom and a number of neutral ground state atoms. The chemical binding properties and electronic wave functions of these exotic molecules are investigated analytically via hybridized diatomic states. The effects of the molecular geometry on the system's properties are studied through comparisons of the adiabatic potential curves and electronic structures for both symmetric and randomly configured molecular geometries. General …
Enhanced positron annihilation on polyatomic molecules is a long-standing and complex problem. We report the results of calculations of resonant positron annihilation on methyl halides. A free parameter of our theory is the positron binding energy. A comparison with energy-resolved annihilation rates measured for CH$_3$F, CH$_3$Cl, CH$_3$Br [Barnes et al. Phys. Rev. A {\bf 74}, 012706 (2006)] shows good agreement and yields estimates of the binding energies.
