Science

Ultracold molecular collision dynamics

Yury Suleymanov

Published May 7, 2020• 0 citations

Abstract

Ultracold Chemistry 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][1]; see also p. [582][2] [1]: /lookup/doi/10.1126/science.aba3990 [2]: /lookup/doi/10.1126/science.abb8020

DOI: 10.1126/science.368.6491.616-l

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Science

Ultracold molecular collision dynamics

Yury Suleymanov

Published May 7, 2020• 0 citations

Publisher

Abstract

Ultracold Chemistry
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

DOI: 10.1126/science.368.6491.616-l

Related papers

Imaging the onset of the resonance regime in low-energy NO-He collisions

Tim de Jongh, Matthieu Besemer, Quan Shuai +4 more

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. 582Ultracold 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

arXiv:2003.10742ScienceMay 7, 2020103 citations

When experiment challenges theory: Scattering of vibrationally excited molecules in the cold collision energy regime

F. Javier Aoiz

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 ∘ $^{\circ }$ –10 ∘ $^{\circ }$ ), 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 $^2\Pi$ molecule with a single unpaired electron in an antibonding π ∗ $\pi ^*$ orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω | $|\Omega |$ ( = 1 2 $=\frac{1}{2}$ or 3 2 $\frac{3}{2}$ ) 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 $\Lambda$ -doublet states ( ε = ± 1 $\epsilon = \pm 1$ , e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2 $p = (-1)^{j-\epsilon /2}$ . As the Rg atom approaches the NO molecule, the degeneracy of the Λ $\Lambda$ doublets is lifted, giving rise to two PESs, A ′ $A^{\prime }$ and A ′ ′ $A^{\prime \prime }$ , 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 ′ ′ $A^{\prime \prime }$ and A ′ $A^{\prime }$ 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 ⟩ $|v=0, j=\frac{1}{2}, \Omega =\frac{1}{2}, f\rangle$ . 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 + $A^2\Sigma ^+$ state to promote NO( 2 Π 1 2 $^2\Pi _{\frac{1}{2}}$ ) molecules to the vibrationally excited state with v = 10 $v=10$ and a selected spin–orbit state | Ω | $|\Omega |$ and rotational state j $j$ , | v = 10 , j , Ω , f ⟩ $|v=10, j,\Omega , f\rangle$ .38, 39 Low (cold) collision energies were achieved in a novel experimental setup of two beams (dual-beam arrangement) crossing at 4 ∘ $^{\circ }$ and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′ $^{\prime }$ 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 ⟩ $|v=10, \Omega =\frac{3}{2}, j=\frac{3}{2} f\rangle \rightarrow |v^{\prime }=10, \Omega ^{\prime }=\frac{1}{2}, j^{\prime }=\frac{9}{2}, e \rangle$ 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 $^2\Pi _{\frac{1}{2}},v=0$ ) 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 ′ $V_{A^{\prime \prime }}-V_{A^{\prime }}$ , puts additional demands on the accuracy of the A ′ ′ $A^{\prime \prime }$ and A ′ $A^{\prime }$ 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.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 ∘ $^{\circ }$ –10 ∘ $^{\circ }$ ), 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 $^2\Pi$ molecule with a single unpaired electron in an antibonding π ∗ $\pi ^*$ orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω | $|\Omega |$ ( = 1 2 $=\frac{1}{2}$ or 3 2 $\frac{3}{2}$ ) 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 $\Lambda$ -doublet states ( ε = ± 1 $\epsilon = \pm 1$ , e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2 $p = (-1)^{j-\epsilon /2}$ . As the Rg atom approaches the NO molecule, the degeneracy of the Λ $\Lambda$ doublets is lifted, giving rise to two PESs, A ′ $A^{\prime }$ and A ′ ′ $A^{\prime \prime }$ , 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 ′ ′ $A^{\prime \prime }$ and A ′ $A^{\prime }$ 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 ⟩ $|v=0, j=\frac{1}{2}, \Omega =\frac{1}{2}, f\rangle$ . 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 + $A^2\Sigma ^+$ state to promote NO( 2 Π 1 2 $^2\Pi _{\frac{1}{2}}$ ) molecules to the vibrationally excited state with v = 10 $v=10$ and a selected spin–orbit state | Ω | $|\Omega |$ and rotational state j $j$ , | v = 10 , j , Ω , f ⟩ $|v=10, j,\Omega , f\rangle$ .38, 39 Low (cold) collision energies were achieved in a novel experimental setup of two beams (dual-beam arrangement) crossing at 4 ∘ $^{\circ }$ and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′ $^{\prime }$ 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 ⟩ $|v=10, \Omega =\frac{3}{2}, j=\frac{3}{2} f\rangle \rightarrow |v^{\prime }=10, \Omega ^{\prime }=\frac{1}{2}, j^{\prime }=\frac{9}{2}, e \rangle$ 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 $^2\Pi _{\frac{1}{2}},v=0$ ) 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 ′ $V_{A^{\prime \prime }}-V_{A^{\prime }}$ , puts additional demands on the accuracy of the A ′ ′ $A^{\prime \prime }$ and A ′ $A^{\prime }$ 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.

Natural SciencesNov 11, 20210 citations

Cold State-Selected Molecular Collisions and Reactions

Benjamin Stuhl, Matthew T. Hummon, Jun Ye

Over the past decade, and particularly the past five years, a quiet revolution has been building at the border between atomic physics and experimental quantum chemistry. The rapid development of techniques for producing cold and even ultracold molecules without a perturbing rare-gas cluster shell is now enabling the study of chemical reactions and scattering at the quantum scattering limit with only a few partial waves contributing to the incident channel. Moreover, the ability to perform these experiments with nonthermal distributions comprising one or a few specific states enables the observation and even full control of state-to-state collision rates in this computation-friendly regime: This is perhaps the most elementary study possible of scattering and reaction dynamics.Over the past decade, and particularly the past five years, a quiet revolution has been building at the border between atomic physics and experimental quantum chemistry. The rapid development of techniques for producing cold and even ultracold molecules without a perturbing rare-gas cluster shell is now enabling the study of chemical reactions and scattering at the quantum scattering limit with only a few partial waves contributing to the incident channel. Moreover, the ability to perform these experiments with nonthermal distributions comprising one or a few specific states enables the observation and even full control of state-to-state collision rates in this computation-friendly regime: This is perhaps the most elementary study possible of scattering and reaction dynamics.

Annual Review of Physical ChemistryJan 14, 201491 citations

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Scattering of Molecules

Jiayu Huang, Shu Liu, Dong Hui Zhang +1 more

Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

arXiv:1710.09057Physical Review LettersApr 4, 201844 citations

Universal relations between Feshbach resonances and molecules

M. R. Goosen

The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.

Jan 1, 20111 citation

Non-Feshbach ultracold molecules

Yury Suleymanov

Ultracold Chemistry The formation of ultracold molecules has already had a profound impact on many research areas of physics. However, conventional methods of producing such molecules are attainable only for a limited number of systems or they suffer for strong dephasing. He et al. sought to pair atoms, through coupling of their spins, to the two-body relative motion mediated by the inherent polarization gradients in a strongly focused trapping laser. They report a successful assembly of an ultracold 87Rb-85Rb molecule in an optical tweezer and observed coherent, long-lived atom-molecule Rabi oscillations. They further demonstrate the full control of the internal and external degrees of freedom in the atom-molecule system. Science , this issue p. [331][1] [1]: /lookup/doi/10.1126/science.aba7468Ultracold Chemistry The formation of ultracold molecules has already had a profound impact on many research areas of physics. However, conventional methods of producing such molecules are attainable only for a limited number of systems or they suffer for strong dephasing. He et al. sought to pair atoms, through coupling of their spins, to the two-body relative motion mediated by the inherent polarization gradients in a strongly focused trapping laser. They report a successful assembly of an ultracold 87Rb-85Rb molecule in an optical tweezer and observed coherent, long-lived atom-molecule Rabi oscillations. They further demonstrate the full control of the internal and external degrees of freedom in the atom-molecule system. Science , this issue p. [331][1] [1]: /lookup/doi/10.1126/science.aba7468

ScienceOct 15, 20200 citations

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 ∘

^{\circ }

–10 ∘

^{\circ }

), 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

^2\Pi

molecule with a single unpaired electron in an antibonding π ∗

\pi ^*

orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω |

|\Omega |

( = 1 2

=\frac{1}{2}

or 3 2

\frac{3}{2}

) 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

\Lambda

-doublet states ( ε = ± 1

\epsilon = \pm 1

, e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2

p = (-1)^{j-\epsilon /2}

. As the Rg atom approaches the NO molecule, the degeneracy of the Λ

\Lambda

doublets is lifted, giving rise to two PESs, A ′

A^{\prime }

and A ′ ′

A^{\prime \prime }

, 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^{\prime \prime }

and A ′

A^{\prime }

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=\frac{1}{2}, \Omega =\frac{1}{2}, f\rangle

. 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 +

A^2\Sigma ^+

state to promote NO( 2 Π 1 2

^2\Pi _{\frac{1}{2}}

) molecules to the vibrationally excited state with v = 10

v=10

and a selected spin–orbit state | Ω |

|\Omega |

and rotational state j

j

, | v = 10 , j , Ω , f ⟩

|v=10, j,\Omega , f\rangle

.38, 39 Low (cold) collision energies were achieved in a novel experimental setup of two beams (dual-beam arrangement) crossing at 4 ∘

^{\circ }

and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′

^{\prime }

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, \Omega =\frac{3}{2}, j=\frac{3}{2} f\rangle \rightarrow |v^{\prime }=10, \Omega ^{\prime }=\frac{1}{2}, j^{\prime }=\frac{9}{2}, e \rangle

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

^2\Pi _{\frac{1}{2}},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 ′

V_{A^{\prime \prime }}-V_{A^{\prime }}

, puts additional demands on the accuracy of the A ′ ′

A^{\prime \prime }

and A ′

A^{\prime }

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.