Efficient rotational cooling of Coulomb-crystallized molecular ions by a helium buffer gas

Vibrational Quenching of Optically Pumped Carbon Dimer Anions

Careful control of quantum states is a gateway to research in many areas of science such as quantum information, quantum-controlled chemistry, and astrophysical processes. Precise optical control of molecular ions remains a challenge due to the scarcity of suitable level schemes, and direct laser cooling has not yet been achieved for either positive or negative molecular ions. Using a cryogenic wire trap, we show how the internal quantum states of C_{2}^{-} anions can be manipulated using optical pumping and inelastic quenching collisions with H_{2} gas. We obtained optical pumping efficiencies of about 96% into the first vibrational level of C_{2}^{-} and determined the absolute inelastic rate coefficient from v=1 to 0 to be k_{q}=(3.2±0.2_{stat}±1.3_{sys})×10^{-13}  cm^{3}/s at 20(3) K, over 3 orders of magnitude smaller than the capture limit. Reduced-dimensional quantum scattering calculations yield a small rate coefficient as well, but significantly larger than the experimental value. Using optical pumping and inelastic collisions, we also realized fluorescence imaging of negative molecular ions. Our work demonstrates high control of a cold ensemble of C_{2}^{-}, providing a solid foundation for future work on laser cooling of molecular ions.

Design and characterization of a cryogenic linear Paul ion trap for ion-neutral reaction studies

Ultra-high vacuum conditions are ideal for the study of trapped ions. They offer an almost perturbation-free environment, where ions confined in traps can be studied for extended periods of time-facilitating precision measurements and allowing infrequent events to be observed. However, if one wishes to study processes involving molecular ions, it is important to consider the effect of blackbody radiation (BBR). The vast majority of molecular ions interact with BBR. At 300 K, state selection in trapped molecular ions can be rapidly lost (in a matter of seconds). To address this issue, and to maintain state selectivity in trapped molecular ions, a cryogenic ion trap chamber has been constructed and characterized. At the center of the apparatus is a linear Paul ion trap, where Coulomb crystals can be formed for ion-neutral reaction studies. Optical access is provided, for lasers and for imaging of the crystals, alongside ion optics and a flight tube for recording time-of-flight mass spectra. The ion trap region, encased within two nested temperature stages, reaches temperatures below 9 K. To avoid vibrations from the cryocooler impeding laser cooling or imaging of the ions, vibration-damping elements are explicitly included. These components successfully inhibit the coupling of vibrations from the cold head to the ion trap-confirmed by accelerometer measurements and by the resolution of images recorded at the trap center (at 9 and 295 K). These results confirm that the cryogenic ion trap apparatus meets all requirements for studying ion-neutral reactions under cold, controlled conditions.

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

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

Photon-mediated charge exchange reactions between 39K atoms and 40Ca+ ions in a hybrid trap

We present experimental evidence of charge exchange between laser-cooled potassium ³⁹K atoms and calcium ⁴⁰Ca⁺ ions in a hybrid atom-ion trap and give quantitative theoretical explanations for the observations. The ³⁹K atoms and ⁴⁰Ca⁺ ions are held in a magneto-optical (MOT) and a linear Paul trap, respectively. Fluorescence detection and high resolution time of flight mass spectra for both species are used to determine the remaining number of ⁴⁰Ca⁺ ions, the increasing number of ³⁹K⁺ ions, and ³⁹K number density as functions of time. Simultaneous trap operation is guaranteed by alternating periods of MOT and ⁴⁰Ca⁺ cooling lights, thus avoiding direct ionization of ³⁹K by the ⁴⁰Ca⁺ cooling light. We show that the K-Ca⁺ charge-exchange rate coefficient increases linearly from zero with ³⁹K number density and the fraction of ⁴⁰Ca⁺ ions in the 4p ²P_1/2 electronically-excited state. Combined with our theoretical analysis, we conclude that these data can only be explained by a process that starts with a potassium atom in its electronic ground state and a calcium ion in its excited 4p ²P_1/2 state producing ground-state ³⁹K⁺ ions and metastable, neutral Ca (3d4p ³P₁) atoms, releasing only 150 cm^-1 equivalent relative kinetic energy. Charge-exchange between either ground- or excited-state ³⁹K and ground-state ⁴⁰Ca⁺ is negligibly small as no energetically-favorable product states are available. Our experimental and theoretical rate coefficients are in agreement given the uncertainty budgets.

Cold and controlled chemical reaction dynamics

State-to-state chemical reaction dynamics, with complete control over the reaction parameters, offers unparalleled insight into fundamental reactivity.

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

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

A cryogenic radio-frequency ion trap for quantum logic spectroscopy of highly charged ions

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions (HCI) is presented. It includes a segmented linear Paul trap, an in-vacuum imaging lens, and a helical resonator. We demonstrate ground state cooling of all three modes of motion of a single ⁹Be⁺ ion and determine their heating rates as well as excess axial micromotion. The trap shows one of the lowest levels of electric field noise published to date. We investigate the magnetic-field noise suppression in cryogenic shields made from segmented copper, the resulting magnetic field stability at the ion position and the resulting coherence time. Using this trap in conjunction with an electron beam ion trap and a deceleration beamline, we have been able to trap single highly charged Ar¹³⁺ (Ar XIV) ions concurrently with single Be⁺ ions, a key prerequisite for the first quantum logic spectroscopy of a HCI. This major stepping stone allows us to push highly-charged-ion spectroscopic precision from the gigahertz to the hertz level and below.

Collisional Quantum Dynamics for MgH- (1Σ+) With He as a Buffer Gas: Ionic State-Changing Reactions in Cold Traps

We present in this paper a detailed theoretical and computational analysis of the quantum inelastic dynamics involving the lower rotational levels of the MgH⁻ (X¹Σ⁺) molecular anion in collision with He atoms which provide the buffer gas in a cold trap. The interaction potential between the molecular partner and the He (¹S) gaseous atoms is obtained from accurate quantum chemical calculations at the post-Hartree-Fock level as described in this paper. The spatial features and the interaction strength of the present potential energy surface (PES) are analyzed in detail and in comparison with similar, earlier results involving the MgH⁺ (¹Σ) cation interacting with He atoms. The quantum, multichannel dynamics is then carried out using the newly obtained PES and the final inelastic rats constants, over the range of temperatures which are expected to be present in a cold ion trap experiment, are obtained to generate the multichannel kinetics of population changes observed for the molecular ion during the collisional cooling process. The rotational populations finally achieved at specific temperatures are linked to state-selective laser photo-detachment experiments to be carried out in our laboratory.All intermediate steps of the quantum modeling are also compared with the behavior of the corresponding MgH⁺ cation in the trap and the marked differences which exist between the collisional dynamics of the two systems are dicussed and explained. The feasibility of the present anion to be involved in state-selective photo-detachment experiments is fully analyzed and suggestions are made for the best performing conditions to be selected during trap experiments.

Multi-photon ionisation spectroscopy for rotational state preparation of [Formula: see text]

In this paper we investigate the 2 + 1' resonance enhanced multi-photon ionisation (REMPI) of molecular nitrogen via the a1Πg(v = 6) intermediate state and analyse its feasibility to generate molecular nitrogen ions in a well defined ro-vibrational state. This is an important tool for high precision experiments based on trapped molecular ions, and is crucial for studying the time variation of the fundamental constant mp/me using [Formula: see text]. The transition is not reported in the literature and detailed spectral analysis has been conducted to extract the molecular constants of the intermediate state. By carefully choosing the intermediate ro-vibrational state, the ionisation laser wavelength and controlling the excitation laser pulse energy, unwanted formation of rotationally excited molecular ions can be suppressed and ro-vibrational ground state ions can be generated with high purity.

Collisional relaxation kinetics for ortho and para NH2- under photodetachment in cold ion traps

The collisional cooling of the internal rotational states of the nonlinear anion NH2- (1A1), occurring at the low temperature of a cold ion trap under helium buffer gas cooling, is examined via quantum dynamics calculations and ion decay rate measurements. The calculations employ a novel ab initio potential energy surface that describes the interaction anisotropy and range of action between the molecular anions and the neutral He atoms. The state changing integral cross sections are employed to obtain the state-to-state rate coefficients, separately for the ortho- and the para-NH2- ions. These rates are in turn used to compute the state population evolution in the trap for both species, once photodetachment by a laser is initiated in the trap. The present work shows results for the combined losses of both species after the photodetachment laser is switched on and analyzes the differences of loss kinetics between the two hyperfine isomers.

Spectroscopy of Molecular Ions in Coulomb Crystals

In this Perspective, we examine the use of laser-cooled atomic ions and sympathetically cooled molecular ions in Coulomb crystals for molecular spectroscopy. Coulomb crystals are well-isolated environments that provide localization and long storage times for sensitive measurements of weak signals and cold temperatures for precise spectroscopy. Coulomb crystals of molecular and atomic ions enable the detection of single-photon molecular ion transitions at a range of wavelengths by a change in atomic ion fluorescence at visible wavelengths. We give an overview of the state of the art from action spectroscopy to quantum logic spectroscopy for a wide range of molecular transitions from rotational sublevels separated by 10^-7 cm^-1 to rovibronic transitions at 25 000 cm^-1. We emphasize how this system allows for unparalleled control of the molecular ion state for precision spectroscopy with applications in astrochemistry and fundamental physics. We conclude with an outlook of the use of this control in cold molecular ion reactions.

Rotational Spectroscopy of a Triatomic Molecular Anion

Rotational transitions of the nonlinear triatomic molecular anion NH_{2}^{-} have been observed by terahertz spectroscopy in a cryogenic radio frequency ion trap. Absorption of terahertz photons has been probed by rotational state-dependent photodetachment of the trapped negative ions near the detachment threshold. Using this two-photon scheme, the two lowest rotational transitions for the asymmetric top rotor NH_{2}^{-} have been found. For the para nuclear spin configuration, the 1_{0}←0_{0} transition frequency was determined to be 933 954(2) MHz, and for the ortho configuration the 1_{+1}←1_{-1} transition frequency was determined to be 447 375(3) MHz. This result appears to preclude the recent tentative assignment of an interstellar absorption feature to NH_{2}^{-}.

Direct Frequency-Comb-Driven Raman Transitions in the Terahertz Range

We demonstrate the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. More specifically, we address the 3d ^{2}D_{3/2} and 3d ^{2}D_{5/2} fine structure levels of a single trapped ^{40}Ca^{+} ion and spectroscopically resolve the transition frequency to be ν_{D}=1,819,599,021,534±8  Hz. The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy, and is currently limited by the stability of our atomic clock reference. Furthermore, the population dynamics of frequency-comb-driven Raman transitions can be fully predicted from the spectral properties of the frequency comb, and Rabi oscillations with a contrast of 99.3(6)% and millisecond coherence time have been achieved. Importantly, the technique can be easily generalized to transitions in the sub-kHz to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.

Rovibronic Spectroscopy of Sympathetically Cooled 40CaH. J Phys Chem A 2018. [PMID: 29521505 DOI: 10.1021/acs.jpca.7b12823]

We measure the rovibronic transitions X ¹Σ⁺, v″ = 0, J″ → A ¹Σ⁺, v' = 0-3, J' of CaH⁺ and obtain rotational constants for the A ¹Σ⁺ state. The spectrum is obtained using two-photon photodissociation of CaH⁺ cotrapped with Doppler cooled Ca⁺. The excitation is driven by a mode-locked, frequency-doubled Ti:Sapph laser, which is then pulse shaped to narrow the spectral bandwidth. The measured values of the rotational constants are in agreement with ab initio theory.

Cooling Dynamics of a Single Trapped Ion via Elastic Collisions with Small-Mass Atoms

We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the cooling efficiency per collision. The knowledge we obtained in this work is an important ingredient for advancing the technique of sympathetic cooling of ions with neutral atoms.

Rotationally Cold OH^{-} Ions in the Cryogenic Electrostatic Ion-Beam Storage Ring DESIREE

We apply near-threshold laser photodetachment to characterize the rotational quantum level distribution of OH^{-} ions stored in the cryogenic ion-beam storage ring DESIREE at Stockholm University. We find that the stored ions relax to a rotational temperature of 13.4±0.2  K with 94.9±0.3% of the ions in the rotational ground state. This is consistent with the storage ring temperature of 13.5±0.5  K as measured with eight silicon diodes but in contrast to all earlier studies in cryogenic traps and rings where the rotational temperatures were always much higher than those of the storage devices at their lowest temperatures. Furthermore, we actively modify the rotational distribution through selective photodetachment to produce an OH^{-} beam where 99.1±0.1% of approximately one million stored ions are in the J=0 rotational ground state. We measure the intrinsic lifetime of the J=1 rotational level to be 145±28  s.

Collisional Cooling of Light Ions by Cotrapped Heavy Atoms

We experimentally demonstrate cooling of trapped ions by collisions with cotrapped, higher-mass neutral atoms. It is shown that the lighter ^{39}K^{+} ions, created by ionizing ^{39}K atoms in a magneto-optical trap (MOT), when trapped in an ion trap and subsequently allowed to cool by collisions with ultracold, heavier ^{85}Rb atoms in a MOT, exhibit a longer trap lifetime than without the localized ^{85}Rb MOT atoms. A similar cooling of trapped ^{85}Rb^{+} ions by ultracold ^{133}Cs atoms in a MOT is also demonstrated in a different experimental configuration to validate this mechanism of ion cooling by localized and centered ultracold neutral atoms. Our results suggest that the cooling of ions by localized cold atoms holds for any mass ratio, thereby enabling studies on a wider class of atom-ion systems irrespective of their masses.

Cold interactions and chemical reactions of linear polyatomic anions with alkali-metal and alkaline-earth-metal atoms

Cold interactions and channels of chemical reactions between linear polyatomic anions and atoms are investigated, opening the way for sympathetic cooling and controlled chemistry in these systems.

Electronic ground state of Ni2. J Chem Phys 2016;145:194302. [PMID: 27875883 DOI: 10.1063/1.4967821]

The Φ9/24 ground state of the Ni₂⁺ diatomic molecular cation is determined experimentally from temperature and magnetic-field-dependent x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap, where an electronic and rotational temperature of 7.4±0.2 K was reached by buffer gas cooling of the molecular ion. The contribution of the spin dipole operator to the x-ray magnetic circular dichroism spin sum rule amounts to 7T_z=0.17±0.06μ_B per atom, approximately 11% of the spin magnetic moment. We find that, in general, homonuclear diatomic molecular cations of 3d transition metals seem to adopt maximum spin magnetic moments in their electronic ground states.

Blue-sky bifurcation of ion energies and the limits of neutral-gas sympathetic cooling of trapped ions

Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.

Explanation of efficient quenching of molecular ion vibrational motion by ultracold atoms

Buffer gas cooling of molecules to cold and ultracold temperatures is a promising technique for realizing a host of scientific and technological opportunities. Unfortunately, experiments using cryogenic buffer gases have found that although the molecular motion and rotation are quickly cooled, the molecular vibration relaxes at impractically long timescales. Here, we theoretically explain the recently observed exception to this rule: efficient vibrational cooling of BaCl(+) by a laser-cooled Ca buffer gas. We perform intense close-coupling calculations that agree with the experimental result, and use both quantum defect theory and a statistical capture model to provide an intuitive understanding of the system. This result establishes that, in contrast to the commonly held opinion, there exists a large class of systems that exhibit efficient vibrational cooling and therefore supports a new route to realize the long-sought opportunities offered by molecular structure.

Rotational Cooling of Trapped Polyatomic Molecules

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 (CH_{3}F) 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 (≈30  mK) and nearly pure state ensemble of about 10^{6} molecules. Our scheme is extendable to larger sets of initial states, other final states, and a variety of molecule species, thus paving the way for internal-state control of ever-larger molecules.

Observation of vibrational overtones by single-molecule resonant photodissociation

Molecular ions can be held in a chain of laser-cooled atomic ions by sympathetic cooling. This system is ideal for performing high-precision molecular spectroscopy with applications in astrochemistry and fundamental physics. Here we show that this same system can be coupled with a broadband laser to discover new molecular transitions. We use three-ion chains of Ca⁺ and CaH⁺ to observe vibrational transitions via resonance-enhanced multiphoton dissociation detected by Ca⁺ fluorescence. On the basis of theoretical calculations, we assign the observed peaks to the transition from the ground vibrational state, ν=0 to ν=9 and 10. Our method allows us to track single-molecular events, and it can be extended to work with any molecule by using normal mode frequency shifts to detect the dissociation. This survey spectroscopy serves as a bridge to the precision spectroscopy required for molecular ion control.

Studying the spectra of molecules typically requires large samples, which can be difficult to achieve for hard-to-generate ions. Here, the authors obtain spectra from single CaH⁺ molecules in a three-ion Columbic crystal, observing new molecular transitions.

Low-temperature kinetics and dynamics with Coulomb crystals

Coulomb crystals-as a source of translationally cold, highly localized ions-are being increasingly utilized in the investigation of ion-molecule reaction dynamics in the cold regime. To develop a fundamental understanding of ion-molecule reactions, and to challenge existing models that describe the rates, product branching ratios, and temperature dependence of such processes, investigators need to exercise full control over the experimental reaction parameters. This requires not only state selection of the reactants, but also control over the collision process (e.g., the collisional energy and angular momentum) and state-selective product detection. The combination of Coulomb crystals in ion traps with cold neutral-molecule sources is enabling the measurement of state-selective reaction rates in a diverse range of systems. With the development of appropriate product detection techniques, we are moving toward the ultimate goal of examining low-energy, state-to-state ion-molecule reaction dynamics.