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 approach can be used for direct laser cooling of SrOH and more complex, isoelectronic species.
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…
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)…
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 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.
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…
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…
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 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…
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…
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…
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 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…
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.
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 ultrac…
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 …
We propose and demonstrate a novel technique that combines Raman scattering and optical cycling in molecules with diagonal Franck-Condon factors. This resonance Raman optical cycling manipulates molecules to behave like efficient fluorophores with discrete absorption and emission profiles that are readily separated for sensitive fluorescence detection in high background light environments. Using a molecular beam of our test species, SrF, we realize up to an average of $\approx20$ spontaneously emitted photons per molecule, limited by the interaction time, while using a bandpass filter to suppr…
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 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…
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…
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 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…
Recent theoretical investigations have indicated that rapid optical cycling should be feasible in complex polyatomic molecules with diverse constituents, geometries and symmetries. However, as a composite molecular mass grows, so does the required number of photon scattering events necessary to decelerate and confine molecular beams using laser light. Utilizing coherent momentum exchange between light fields and molecules can suppress spontaneous emission and significantly reduce experimental complexity for slowing and trapping. Working with BaH as a test species, we have identified a robust, …
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…
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 …
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 …
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.
We examine the prospects for utilizing the optical bichromatic force (BCF) to greatly enhance laser deceleration and cooling for near-cycling transitions in small molecules. We discuss the expected behavior of the BCF in near-cycling transitions with internal degeneracies, then consider the specific example of decelerating a beam of calcium monofluoride molecules. We have selected CaF as a prototype molecule both because it has an easily-accessible near-cycling transition, and because it is well-suited to studies of ultracold molecular physics and chemistry. We also report experimental verific…
Photon Cycling and Laser Cooling of an Asymmetric Top Molecule
Harvard University（哈佛大学）；Harvard-MIT Center for Ultracold Atoms（哈佛-麻省理工学院超冷原子中心）；Korea University（高丽大学）；Massachusetts Institute of Technology（麻省理工学院）；University of California, Berkeley（加州大学伯克利分校）；Michigan State University（密歇根州立大学）；University of Southern California（南加州大学）
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…
Electron-ion-ion coincidence experiments for photofragmentation of polyatomic molecules using pulsed electric fields: treatment of random coincidences
在通过软X射线的分子光致碎裂过程中，可以产生许多离子碎片，每个离子碎片具有不同的丰度和与发射的电子动能的相关性。为了研究这些碎裂过程，电子-离子和电子-离子-离子符合实验是非常强大的，其中使用静电分析仪分析电子的动能，同时使用脉冲电场分析离子的质量。然而，对于这样的测量，随机巧合的贡献是巨大的，并以非平凡的方式影响数据。不能应用简单直观的减法。在本文中，我们描述了这些电子-离子和电子-离子-离子符合实验，以及随机符合贡献的扣除方法。我们提供了一套全面的数据处理方程，包括计算误差条的方程。我们通过将其应用于游离CF $_3$ SF $_5$分子的片段化来证明该方法。
Optical cycling on thorium monoxide (ThO) for an improved test of fundamental symmetries
Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位束设施）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）
High-sensitivity molecular spectroscopy of SrOH using magneto-optical trapping
Harvard-MIT Center for Ultracold Atoms（哈佛-麻省理工学院超冷原子中心）；Department of Physics, Harvard University（哈佛大学物理系）；University of California, Berkeley（加州大学伯克利分校）；IonQ, Inc.（IonQ公司）
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 …
We present a practical roadmap to achieve optical cycling and laser cooling of asymmetric top molecules (ATMs). Our theoretical analysis describes how reduced molecular symmetry, as compared to diatomic and symmetric non-linear molecules, plays a role in photon scattering. We present methods to circumvent limitations on rapid photon cycling in these systems. We calculate vibrational branching ratios for a diverse set of asymmetric top molecules and find that many species within a broad class of molecules can be effectively cooled with a manageable number of lasers. We also describe methods to …
We demonstrate a scheme for optical cycling in the polar, diatomic molecule strontium monofluoride (SrF) using the $X ^2Σ^+\toA^2Π_{1/2}$ electronic transition. SrF's highly diagonal Franck-Condon factors suppress vibrational branching. We eliminate rotational branching by employing a quasi-cycling $N=1\to N^\prime=0$ type transition in conjunction with magnetic field remixing of dark Zeeman sublevels. We observe cycling fluorescence and deflection through radiative force of an SrF molecular beam using this scheme. With straightforward improvements our scheme promises to allow more than $10^5$…
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…
In atomic and molecular phase measurements using laser-induced fluorescence detection, optical cycling can enhance the effective photon detection efficiency and hence improve sensitivity. We show that detecting many photons per atom or molecule, while necessary, is not a sufficient condition to approach the quantum projection limit for detection of the phase in a two-level system. In particular, detecting the maximum number of photons from an imperfectly closed optical cycle reduces the signal-to-noise ratio (SNR) by a factor of $\sqrt{2}$, compared to the ideal case in which leakage from the …
