We have developed an apparatus capable of performing intrabeam and near-copropagating beam scattering experiments at collision energies from room temperature to below 1 K where interesting quantum phenomena can be observed. A detailed description of the major components of the apparatus, single and dual molecular beam valves, high speed chopper, and the discharge source, is presented. With the intrabeam scattering setup, a novel dual-slit chopper permits collision energies down to millikelvins with a collision energy spread of 20%. With the near-copropagating beam configuration, state-to-state differential cross sections for rotationally inelastic collisions of highly vibrationally excited NO molecules with Ar have been measured at broadly tunable energies documenting the versatility of the instrument. Future applications in stereodynamics and cold state-to-state collisions of vibrationally excited polyatomic molecules are briefly discussed.
We demonstrate a method to probe cold and ultracold chemistry in a single molecular beam. The approach exploits beam slippage, the velocity difference of different species in the same beam, to establish the relative velocity. Average collision energies of 2.5 mK are achieved but with a spread of 100% or more. However, by implementing a dual-slit chopper that can separately fix the velocities of the two species at the interaction region, we achieve precise control over the relative velocity and narrow its spread. Relative velocities of 7-10 ± 1.1 m/s are achieved with an angular divergence less than 0.25°. In the present study, we observe l-changing collisions occurring between Xe Rydberg atoms and Xe ground state atoms at subKelvin temperatures. We show that in this case the collision energies are tunable between 200 to 450 mK with a root-mean-square deviation of ∼18%. Application of the method to other species and access to much lower energies is straightforward.
The last decade has seen substantial advances in the exploration of inelastic and reactive collisions at collision energies in the cold ( <
< 1 K) and ultracold ( < 1
<1 mK) regime.1-13 These advances ushered in an understanding of cold and ultracold collisions that is impacting research areas ranging from molecular spectroscopy to quantum simulation and computation to quantum control of chemical reaction dynamics. Cold collisions are dominated by resonances, as amply manifest in most of the systems studied.1, 14 Resonances are also present in the thermal ( >
> 100 K) and hyperthermal ( >
> 1000 K) collision energy regimes,15 but obscured by background (non-resonant) scattering and the presence of many partial waves pertaining to higher angular momenta that blur the partial waves' individual contributions. Moreover, the outcome of thermal and hyperthermal collisions is somewhat insensitive to the details of the interaction potential – the potential energy surface (PES) – especially to its attractive long-range region. Only in a handful of cases, such as the F+HD exchange reaction, resonances in the thermal regime have been experimentally detected and theoretically accounted for by quantum mechanical scattering calculations.16, 17 In contrast, in the cold regime, collisions are dominated by only a few partial waves whose effects on the integral and differential scattering cross-sections can be singled out and linked to particular resonances. The cold collision energy regime has been attained by making use of crossed molecular beams that were either Stark- or Zeeman-decelerated or whose intersection angle could be reduced all the way down to the merging-beams limit. A beam emerging from a Stark or Zeeman decelerator has a variable, well-defined laboratory velocity. When crossed with a secondary beam at small angles (5 ∘
∘ –10 ∘
∘ ), collision energies in the 0.3–15 K could be readily achieved, as demonstrated by the group of van de Meerakker.9, 11 The technique of merged beams makes use of the ability to bend one of the beams by a magnetic or electric field such that the crossing angle becomes zero, thereby affording collision energies in the range 0.1 K–10 K. Merging beams have been used in studies of Penning ionization by the groups of Narevicius5, 12 and Osterwalder18 and made it possible to unravel shape and Feshbach resonances arising in this process. The techniques mentioned so far require the reactants to be polar or paramagnetic. For reactants that are neither, collision energies as low as 5 K could be achieved by taking advantage of a favorable combination of low intersection angles and low reduced mass of the reactants. This approach has been demonstrated by Bergeat, Costes, Naulin, and coworkers in a series of reactive3, 19 and inelastic collision experiments8, 20 of H 2
2 . Yet, another approach to achieving low relative collision velocities relies on the coexpansion of the collision partners in a single molecular beam.21 If their masses are similar, both partners will end up with nearly the same velocities, within a few ms − 1
−1 . Using this technique, Zare, Mukherjee, and coworkers carried out a series of experiments in which rotational quenching of HD by H 2
2 , D 2
2 , and He was investigated. Moreover, in these experiments, the HD molecule was prepared in v
v =1 and j
j =2 using Stark-field-induced adiabatic Raman passage that allowed, in addition, to align the rotational angular momentum of the HD reactant molecule with respect to the initial relative velocity of the HD + He reactants.22-24 Collisional energy transfer between rotation and translation, in which a molecule is excited or relaxed via scattering by an atom or another molecule, has been of particular significance for developing our understanding of inelastic collisions. Most notably, the scattering of NO molecules by rare gas (Rg) atoms has served as a benchmark system for both experimentalists and theorists for decades. In its ground electronic state, NO is a 2 Π
2Π molecule with a single unpaired electron in an antibonding π ∗
π∗ orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω |
∣Ω∣ ( = 1 2
=21 or 3 2
23 ) of the electronic angular momentum (orbital and spin) on the internuclear axis. The rotational levels with the same j
j in the two manifolds are separated by approximately 123 cm − 1
−1 for v
v =0 (117 cm − 1
−1 for v
v =10). In addition, each rotational level within each manifold is further split into two Λ
Λ -doublet states ( ε = ± 1
ϵ=±1 , e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2
p=(−1)j−ϵ/2 . As the Rg atom approaches the NO molecule, the degeneracy of the Λ
Λ doublets is lifted, giving rise to two PESs, A ′
A′ and A ′ ′
A′′ , in which the orbital of the unpaired electron lies, respectively, in the plane of the three atoms or perpendicular to it. In computational practice, it is more convenient to use linear combinations (sums and differences) of the A ′ ′
A′′ and A ′
A′ PESs. Using hexapole focusing or Stark deceleration combined with detection via velocity ion imaging, fully state-to-state-resolved integral and differential cross sections for rotationally elastic and inelastic collisions could be measured with high resolution.9, 11, 25, 26 More than that, the orientation and alignment of the scattered (outgoing) NO molecules could be measured as a function of the scattering angle27-30 and, quite recently, the effects of orientation of the reactant (incoming) NO molecules on the differential cross section in collisions with Rg, mostly Ar, could be established.31-35 On the theory side, quantum mechanical close coupling (QMCC) scattering calculations on accurate two-dimensional ab initio PESs using the benchmark coupled-cluster, CCSD(T), method with the NO internuclear distance fixed at its equilibrium value36 were performed and found to account for all the details revealed by the experiments. Although state of the art, most of these experiments except for those described in Refs. 9, 11 were carried out at thermal energies for NO molecules in their lowest level, | v = 0 , j = 1 2 , Ω = 1 2 , f ⟩
∣v=0,j=21,Ω=21,f⟩ . Scattering of highly vibrationally excited molecules in the cold energy regime remained an unexplored frontier until the recent work by the groups of Arthur Suits, Ad van der Avoird, Gerrit Groenenboom, and Hua Guo who added spin–orbit and rotational state selection and looked for spin- and rotational-state changing collisions to boot. Published in the current issue of Natural Sciences,37 this work is a culmination of a 3-year collaboration that included both implementation of new experimental techniques and boosting of theoretical methods. Working with the NO+Ar system, the authors made use of stimulated emission pumping via the electronically excited A 2 Σ +
A2Σ+ state to promote NO( 2 Π 1 2
2Π21 ) molecules to the vibrationally excited state with v = 10
v=10 and a selected spin–orbit state | Ω |
∣Ω∣ and rotational state j
j , | v = 10 , j , Ω , f ⟩
∣v=10,j,Ω,f⟩ .38, 39 Low (cold) collision energies were achieved in a novel experimental setup of two beams (dual-beam arrangement) crossing at 4 ∘
∘ and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′
′ REMPI with the ionization laser tuned just above the ionization threshold. Fully state-resolved angular distributions of the scattered NO molecules were measured by velocity ion slice imaging and detected by a charge-coupled device (CCD). In order to be able to detect the product (outgoing) molecules resulting from the cold NO + Ar collisions, some excess energy had to be made available to the products. This came in the form of the initial spin–orbit and/or rotational state energy. In the study highlighted herein,37 angular distributions leading to the spin–orbit changing transition | v = 10 , Ω = 3 2 , j = 3 2 f ⟩ → | v ′ = 10 , Ω ′ = 1 2 , j ′ = 9 2 , e ⟩
∣v=10,Ω=23,j=23f⟩→∣v′=10,Ω′=21,j′=29,e⟩ were measured at energies in the 2 K–5 K range. Although intrabeam scattering could have been used as an alternative as it had been in previous work,21 the authors demonstrated that a dual-beam setup provides a superior angular and energy resolution. The highlighted experiment challenged the existing theoretical treatments of the NO+ Rg systems: first, the approximation of fixing NO at its equilibrium distance was bound to fail for NO in v = 10
v=10 due to the concomitant elongation of the NO bond. Second, for such a highly excited vibrational state, both the long- and short-range interactions are affected, triggering nonadiabatic effects involving rotational and spin–orbit degrees of freedom. The above rendered the single-reference coupled-cluster method used in previous treatments of NO( 2 Π 1 2 , v = 0
2Π21,v=0 ) inadequate. Therefore, the authors of the highlighted paper37 constructed a new coupled-cluster PES as well as a multireference configuration-interaction (MRCI) PES and carried out full-fledged (3D) QMCC calculations on both PESs. These tour-de-force calculations reproduced quite well the experimental differential cross sections and defined a new state of the art in scattering calculations. However, some discrepancies remain as at low collision energies, and the accuracy of the long-range potential needed is a challenge for any ab initio method. Moreover, treating spin-changing collisions that are dominated by the essentially attractive difference potential, V A ′ ′ − V A ′
VA′′−VA′ , puts additional demands on the accuracy of the A ′ ′
A′′ and A ′
A′ PESs. The calculated integral cross section in the 3–4 cm − 1
−1 energy interval exhibits a bump that may indicate the presence of resonances that show up as backscattering in the measured differential cross section. A partial-wave analysis points to overlapping resonances associated with contributions from several of the highest partial waves involved. In any case, tracing the resonances may require additional improvements of the existing PESs. All in all, the highlighted combined experimental and theoretical study sets a new standard for our understanding of cold collisions. There is no conflict of interest. The peer review history for this article is available at https://publons.com/publon/10.1002/ntls.20210088. This Highlight has been internally reviewed and edited by Bretislav Friedrich and Gerard Meijer. No data available.
This thesis describes the design and construction of a novel molecule-surface scattering apparatus. The setup combines a Stark decelerator with a state-of- the-art surface scattering chamber, and allows background-gas free scattering of packets of velocity-controlled polar molecules in selected quantum states from well-defined surfaces with unprecedented energy resolution. Results for scattering of CO (a3Π) in different vibrational quantum states from a clean Au(111) surface are presented. CO is co-expanded with Xe or Ar to yield a supersonic molecular beam which produces fast, internally cold molecules. Excitation of CO to the long-lived electronically excited a3Π1 state makes it accessible to manipulation with electric fields due to the state’s large dipole moment. The complete removal of both carrier gas and remaining ground- state CO is achieved by focusing and deflecting the metastable CO with a switched electrostatic hexapole state selector. The 131-stage Stark decelerator is used to tune the velocity of a part of the metastable CO pulse, with an initial velocity of 360 m/s, in the range from (512 ± 4) m/s – (50 ± 4) m/s, corresponding to an incident translational energy between (307 ± 5) cm-1 and (3.0 ± 0.5) cm-1, respectively.This range can be extended up to (1300 ± 25) m/s, corresponding to an energy of(1980 ± 80) cm-1, by simple modifications to the setup. Prior to collision, the molecules can be laser- prepared in different vibrational and rotational quantum states. State- selective detection of the scattering products makes it possible to determine the quantum state, the scattering angle, and the kinetic energy of the scattered molecules. Therefore, detailed information about the scattering process can be obtained. The design of the machine allows for flexible laser access near the surface, such that a variety of different preparation and detection schemes can be employed. Ultra-high vacuum conditions in the scattering chamber are achieved by baking the entire apparatus, including the decelerator and the hexapole. Because of the carrier gas removal and a total of three differential pumping stages, no pressure rise is detected in the scattering chamber due to the incident molecular beam. Scattering experiments of CO (a3Π) on Au(111) have been performed. The scattering process leads to electron emission because the metastable excitation energy exceeds the work function of the surface. The electron emission yield, i.e. the number of electrons emitted per incident metastable particle, has been measured to be 0.13 ± 0.05. A laser ionization-depletion method is used which makes it possible to directly compare the intensity of the metastable CO ionization signal to the intensity decrease of the electron emission signal. It was also shown that vibrationally excited metastable CO leads to a higher electron emission yield. By preparing different vibrational distributions of CO in the a3Π electronic state via Franck-Condon pumping, the electron emission yield was determined for groups of vibrational levels. The first three vibrationally excited levels have an increased electron emission yield which on average is a factor of 1.5 larger than that of the vibrational ground state. Averaged over the vibrational levels with quantum number v = 4, 5, 6 , this factor is approximately 2.6 . In the range between 93 m/s and 512 m/s, the electron emission was observed to be independent of the velocity of the incident molecules. When the surface temperature is raised from 250 K to 900 K, the intensity of the electron emission signal increases by 27 %. These results are not in agreement with the models currently used to describe the de-excitation of electronically excited molecules at metal surfaces. This demonstrates the need for more theoretical work to incorporate the role of vibration into the description of the de-excitation mechanism.
Ultracold molecular collision dynamics Ultracold collision dynamics are of great importance in understanding the quantum nature of chemical interactions, but achieving the ultracold regime for molecules is challenging. Traditional techniques based on alternative routes to assemble the ultracold atomic constituents are only able to produce a type of ultracold molecules that cannot probe state-selective dynamics. Using Stark deceleration and velocity map–imaging techniques, de Jongh et al. achieved the ultracold regime directly for a nitric oxide–helium system and measured the state-to-state cross sections for inelastic scattering with high precision (see the Perspective by Yang and Yang). The observed scattering resonances confirmed high sensitivity to the underlying interaction potential because only the most accurate electronic structure theory could reproduce their structure. Science , this issue p. 626 ; see also p. 582
Research in the field of cold polar molecules is progressing rapidly. An array of interesting\ntopics is being developed including precision measurement and fundamental tests, quantum phase transitions, and ultracold chemistry. In particular, dipolar molecules in well-defined quantum states enable exquisite control of their interactions via applied electric fields. The long-range, anisotropic interaction between dipolar molecules leads to new collision dynamics that could be used for novel collective effects, quantum state engineering, and information processing. The focus of this Thesis is the production of cold samples of neutral OH molecules via Stark deceleration and magnetic trapping for novel collision experiments. This novelty results from our combination of cold external beams and trapped target molecules which facilitates observation of dipolar effects as well as low temperature collision resonances. The large permanent electric dipole moment of OH allows us to precisely tune the lab-frame velocity of the molecular packets from ∼ 500 m/s to rest. We have magnetically trapped OH packets at the terminus of our Stark decelerator at a temperature of 70 mK and density of 106 cm−3. With improved understanding of Stark deceleration, we optimize the decelerator efficiency and its coupling to the magnetic trap. Our latest trap design uses permanent ring magnets to create a three-dimensional magnetic quadrupole field. Use of magnetically trapped OH molecules for collision experiments with external beams allow us the unique opportunity of observing both elastic and inelastic collisions. In addition, the trap confinement yields sensitivity to differential elastic cross sections at low collision energies. This open magnetic trap has allowed measurement of collision cross sections between trapped OH and external supersonic beams of He and D2, the latter of which is of astrophysical interest due to the role of H2-OH collisions in pumping interstellar OH megamasers. The combination of trapped OH molecules and temperature tuned beams of He and D2 has facilitated measurement of the lowest-energy D2-OH collision cross sections yet reported. More recently, we report the first observation of electric-field dependent cross sections between two different species of cold polar molecules - OH and ND3 - thereby demonstrating control over molecular scattering in the cold regime. By combining for the first time the production techniques of Stark deceleration and buffer gas cooling, we increase the molecular interaction time by∼ 105 over traditional crossed-beam experiments to gain enhanced sensitivity at the characteristic densities of cold molecule production.