# Vibrational Quenching of Weakly Bound Cold Molecular Ions Immersed in Their Parent Gas

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. System

#### 2.2. Inelastic Scattering

#### 2.3. Effective Potentials

#### 2.4. Distorted Wave Born Approximation

## 3. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Tomza, M.; Jachymski, K.; Gerritsma, R.; Negretti, A.; Calarco, T.; Idziaszek, Z.; Julienne, P.S. Cold hybrid ion-atom systems. Rev. Mod. Phys.
**2019**, 91, 035001. [Google Scholar] [CrossRef] [Green Version] - Krükow, A.; Mohammadi, A.; Härter, A.; Denschlag, J.H.; Pérez-Ríos, J.; Greene, C.H. Energy scaling of cold atom-atom-ion three-body recombination. Phys. Rev. Lett.
**2016**, 116, 193201. [Google Scholar] [CrossRef] [Green Version] - Wolf, J.; Deiß, M.; Krükow, A.; Tiemann, E.; Ruzic, B.P.; Wang, Y.; D’Incao, J.P.; Julienne, P.S.; Denschlag, J.H. State-to-state chemistry for three-body recombination in an ultracold rubidium gas. Science
**2017**, 358, 921–924. [Google Scholar] [CrossRef] [Green Version] - Feldker, T.; Fürst, H.; Hirzler, H.; Ewald, N.V.; Mazzanti, M.; Wiater, D.; Tomza, M.; Gerritsma, R. Buffer gas cooling of a trapped ion to the quantum regime. Nat. Phys.
**2020**. [Google Scholar] [CrossRef] - Schmidt, J.; Weckesser, P.; Thielemann, F.; Schaetz, T.; Karpa, L. Optical Traps for sympathetic Cooling of Ions with ultracold neutral Atoms. Phys. Rev. Lett.
**2020**, 124, 053402. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kleinbach, K.S.; Engel, F.; Dieterle, T.; Löw, R.; Pfau, T.; Meinert, F. Ionic impurity in a Bose-Einstein condensate at submicrokelvin temperatures. Phys. Rev. Lett.
**2018**, 120, 193401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Engel, F.; Dieterle, T.; Schmid, T.; Tomschitz, C.; Veit, C.; Zuber, N.; Löw, R.; Pfau, T.; Meinert, F. Observation of rydberg blockade induced by a single ion. Phys. Rev. Lett.
**2018**, 121, 193401. [Google Scholar] [CrossRef] [Green Version] - Quemener, G.; Julienne, P.S. Ultracold molecules under control! Chem. Rev.
**2012**, 112, 4949–5011. [Google Scholar] [CrossRef] [PubMed] - Bohn, J.L.; Rey, A.M.; Ye, J. Cold molecules: Progress in quantum engineering of chemistry and quantum matter. Science
**2017**, 357, 1002–1010. [Google Scholar] [CrossRef] [Green Version] - Bonnet, L.; Rayez, J.C. Some key factors of energy distributions in the products of complex-forming elementary reactions. Phys. Chem. Chem. Phys.
**1999**, 1, 2383–2400. [Google Scholar] [CrossRef] - Forrey, R.C.; Balakrishnan, N.; Dalgarno, A.; Haggerty, M.R.; Heller, E.J. Quasiresonant energy transfer in ultracold atom-diatom collisions. Phys. Rev. Lett.
**1999**, 82, 2657. [Google Scholar] [CrossRef] [Green Version] - Rackham, E.J.; Huarte-Larranaga, F.; Manolopoulos, D.E. Coupled-channel statistical theory of the N (
^{2}D)+ H_{2}and O (^{1}D)+ H_{2}insertion reactions. Chem. Phys. Lett.**2001**, 343, 356–364. [Google Scholar] - González-Martínez, M.L.; Dulieu, O.; Larrégaray, P.; Bonnet, L. Statistical product distributions for ultracold reactions in external fields. Phys. Rev. A
**2014**, 90, 052716. [Google Scholar] [CrossRef] [Green Version] - Soley, M.B.; Heller, E.J. Classical approach to collision complexes in ultracold chemical reactions. Phys. Rev. A
**2018**, 98, 052702. [Google Scholar] [CrossRef] [Green Version] - Pérez-Ríos, J.; Greene, C.H. Universal temperature dependence of the ion-neutral-neutral three-body recombination rate. Phys. Rev. A
**2018**, 98, 062707. [Google Scholar] [CrossRef] [Green Version] - Pérez-Ríos, J. Vibrational quenching and reactive processes of weakly bound molecular ions colliding with atoms at cold temperatures. Phys. Rev. A
**2019**, 99, 022707. [Google Scholar] [CrossRef] [Green Version] - Bodo, E.; Gianturco, F.A.; Yurtsever, E. Vibrational quenching at ultralow energies: Calculations of the Li
_{2}(^{1}${\sum}_{g}^{+}$;v≫0) + He superelastic scattering cross sections. Phys. Rev. A**2006**, 73, 052715. [Google Scholar] [CrossRef] [Green Version] - Quéméner, G.; Launay, J.-M.; Honvault, P. Ultracold collisions between Li atoms and Li
_{2}diatoms in high vibrational states. Phys. Rev. A**2007**, 75, 050701. [Google Scholar] [CrossRef] [Green Version] - Lara, M.; Jambrina, P.G.; Launay, J.-M.; Aoiz, F.J. Beyond universality: Parametrizing ultracold complex-mediated reactions using statistical assumptions. Phys. Rev. A
**2015**, 91, 030701. [Google Scholar] [CrossRef] [Green Version] - Stoecklin, T.; Halvick, P.; Gannouni, M.A.; Hochlaf, M.; Kotochigova, S.; Hudson, E.R. Explanation of efficient quenching of molecular ion vibrational motion by ultracold atoms. Nat. Commun.
**2016**, 7, 11234. [Google Scholar] [CrossRef] [Green Version] - Croft, J.; Makrides, C.; Li, M.; Petrov, A.; Kendrick, B.; Balakrishnan, N.; Kotochigova, S. Universality and chaoticity in ultracold K + KRb chemical reactions. Nat. Commun.
**2017**, 8, 1. [Google Scholar] [CrossRef] [PubMed] - Dalgarno, A.; Bates, D.R. The mobilities of ions in their parent gases. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1958**, 250, 426. [Google Scholar] - da Silva, H., Jr.; Raoult, M.; Aymar, M.; Dulieu, O. Formation of molecular ions by radiative association of cold trapped atoms and ions. New J. Phys.
**2015**, 17, 045015. [Google Scholar] [CrossRef] - Härter, A.; Krükow, A.; Brunner, A.; Schnitzler, W.; Schmid, S.; Denschlag, J.H. Single ion as a three-body reaction center in an ultracold atomic gas. Phys. Rev. Lett.
**2012**, 109, 123201. [Google Scholar] [CrossRef] [Green Version] - Côté, R.; Dalgarno, A. Ultracold atom-ion collisions. Phys. Rev. A
**2000**, 62, 012709. [Google Scholar] [CrossRef] [Green Version] - Taylor, J.R. Scattering Theory: The Quantum Theory of Nonrelativistic Collisions; Courier Corporation: Chelmsford, MA, USA, 2006. [Google Scholar]
- Curtiss, C.F.; Adler, F. The scattering of atoms from diatomic molecules. J. Chem. Phys.
**1952**, 20, 249–256. [Google Scholar] [CrossRef] - Arthurs, A.; Dalgarno, A. The theory of scattering by a rigid rotator. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1960**, 256, 540–551. [Google Scholar] - Pérez-Ríos, J.; Robicheaux, F. Rotational relaxation of molecular ions in a buffer gas. Phys. Rev. A
**2016**, 94, 032709. [Google Scholar] [CrossRef] [Green Version] - McGuire, P.; Kouri, D.J. Quantum mechanical close coupling approach to molecular collisions. j
_{z}-conserving coupled states approximation. J. Chem. Phys.**1974**, 60, 2488–2499. [Google Scholar] [CrossRef] - Pack, R.T. Space-fixed vs body-fixed axes in atom-diatomic molecule scattering. Sudden approximations. J. Chem. Phys.
**1974**, 60, 633. [Google Scholar] [CrossRef] - Jyothi, S.; Ray, T.; Dutta, S.; Allouche, A.R.; Vexiau, R.; Dulieu, O.; Rangwala, S.A. Photodissociation of Trapped ${\mathrm{Rb}}_{2}^{+}$: Implications for Simultaneous Trapping of Atoms and Molecular Ions. Phys. Rev. Lett.
**2016**, 117, 213002. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Idziaszek, Z.; Simoni, A.; Calarco, T.; Julienne, P.S. Multichannel quantum-defect theory for ultracold atom–ion collisions. New J. Phys.
**2011**, 13, 083005. [Google Scholar] [CrossRef] - Chin, C.; Grimm, R.; Julienne, P.S.; Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys.
**2010**, 82, 1225. [Google Scholar] [CrossRef] - Jachymski, K.; Krych, M.; Julienne, P.S.; Idziaszek, Z. Quantum-defect model of a reactive collision at finite temperature. Phys. Rev. A
**2014**, 90, 042705. [Google Scholar] [CrossRef] [Green Version] - Child, M.S. Molecular Collision Theory; Courier Corporation: Chelmsford, MA, USA, 1996. [Google Scholar]
- Miller, W.H. Distorted-Wave Theory for Collisions of an Atom and a Diatomic Molecule. J. Chem. Phys.
**1968**, 49, 2373. [Google Scholar] [CrossRef] - Volpi, A.; Bohn, J.L. Molecular vibration in cold-collision theory. Phys. Rev. A
**2002**, 65, 064702. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**(

**a**) Diagonal effective potentials for the most weakly bound state (blue) and the 5th one counting from the dissociation threshold (orange). (

**b**) Couplings between the 5th vibrational state and the ones right below it as a function of the atom–molecule distance. (

**c**) Same couplings calculated for the most weakly bound state. The binding energies ${E}_{v}\approx 2\xb7{10}^{4}{E}^{\star}$ for $v=5$ and $0.16{E}^{\star}$ for $v=1$.

**Figure 3.**(

**a**) Effective coupling coefficients ${C}_{4}^{\mathrm{eff}}$ between the 5th vibrational state and the ones right below it in units of the diagonal coupling constant. (

**b**) Same, but for the most weakly bound state.

**Figure 4.**K matrix elements calculated within the distorted wave Born approximation (DWBA) for vanishing collision energy as a function of the energy difference between the channels for the entrance channel scattering length $a={R}^{\star}$ and initial kinetic energy $E={10}^{-4}{E}^{\star}$.

**Figure 5.**(

**a**) Distribution of product states for vanishing collision energy after the inelastic collision for the 5th vibrational state ($v=5$). (

**b**) Same, but for the most weakly bound state ($v=1$).

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jachymski, K.; Meinert, F.
Vibrational Quenching of Weakly Bound Cold Molecular Ions Immersed in Their Parent Gas. *Appl. Sci.* **2020**, *10*, 2371.
https://doi.org/10.3390/app10072371

**AMA Style**

Jachymski K, Meinert F.
Vibrational Quenching of Weakly Bound Cold Molecular Ions Immersed in Their Parent Gas. *Applied Sciences*. 2020; 10(7):2371.
https://doi.org/10.3390/app10072371

**Chicago/Turabian Style**

Jachymski, Krzysztof, and Florian Meinert.
2020. "Vibrational Quenching of Weakly Bound Cold Molecular Ions Immersed in Their Parent Gas" *Applied Sciences* 10, no. 7: 2371.
https://doi.org/10.3390/app10072371