Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1905.06691 · Physical Review A

Quasiclassical method for calculating the density of states of ultracold collision complexes

Arthur Christianen, Tijs Karman, Gerrit C. Groenenboom

Published Sep 17, 2019• 70 citations
arXivHTMLPDF

Abstract

We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, $N$-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the ${\mathrm{K}}_{2}\text{\ensuremath{-}}\mathrm{Rb}$ and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124 $\ensuremath{\mu}{\mathrm{K}}^{\ensuremath{-}1}$, with an associated Rice-Ramsperger-Kassel-Marcus sticking time of 6.0 $\ensuremath{\mu}\mathrm{s}$. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.

DOI
10.1103/physreva.100.032708

Related papers

Photoinduced Two-Body Loss of Ultracold Molecules

Arthur Christianen, Martin W. Zwierlein, Gerrit C. Groenenboom +1 more

The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of NaK+NaK collision complexes by the trapping laser leads to the experimentally observed two-body loss. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.

arXiv:1905.06846•Physical Review Letters•Sep 17, 2019•120 citations

AlF-AlF sticking time and prospects for ultracold dimers

Mahmoud A. E. Ibrahim, Mateo Londoño, Jesús Pérez‐Ríos

We report on the sticking time of the AlF dimer in the ultracold regime. We employ a full-dimensional potential energy surface for AlF-AlF, constructed using a machine learning approach [X. Liu et al., J. Chem. Phys. 159, 144103 (2023)], to compute the density of states using a semiclassical counting method. Next, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, we determine an RRKM sticking time of 216.0 $\ifmmode\pm\else\textpm\fi{}$ 4.8 ns, which is shorter than that of other previously reported nonreactive dimers. Then, based on the available potential energy surfaces and RRKM sticking time data for a few dimers, we observe that the RRKM sticking time correlates with the ratio of the dimer dissociation energy to the dissociation energy of its parent molecule. Thus, we propose this ratio as a parameter to estimate RRKM sticking times. Furthermore, using ab initio methods, we optimize and calculate the energies of the equilibrium geometries of AlCl-AlCl, CaH-CaH, and MgF-MgF, thereby determining the ratio of the dimer dissociation energy to the parent molecule dissociation energy. Based on this ratio, we propose a hierarchy to order the sticking lifetimes of those dimers in the ultracold regime.

arXiv:2508.00676•Physical Review A•Nov 12, 2025•0 citations

Sticking Lifetime of Ultracold CaF Molecules in Triplet Interactions

Dibyendu Sardar, John L. Bohn

A six-dimensional potential energy surface is constructed for the spin-polarized triplet state of CaF–CaF by ab initio calculations at the CCSD(T) level of theory, followed by Gaussian process interpolation. The potential is utilized to calculate the density of states for this bialkaline-earth-halogen system where we find the value 0.038 μK –1, implying a mean resonance spacing of 26 μK in the collision complex. This value implies an associated Rice–Ramsperger–Kassel–Marcus lifetime of 1.8 μs, thus predicting long-lived complexes in collisions at ultracold temperatures.

arXiv:2303.07611•The Journal of Physical Chemistry A•May 25, 2023•5 citations

Six-dimensional potential energy surface for NaK–NaK collisions: Gaussian process representation with correct asymptotic form

Arthur Christianen, Tijs Karman, Rodrigo A. Vargas–Hernández +2 more

Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three- and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range. We propose an efficient sampling technique, which allows us to construct an accurate global PES accounting for different chemical arrangements with <2500 ab initio calculations. We apply this method to (NaK)2 and obtain the first global PES for a system of four alkali metal atoms. The resulting surface exhibits a complex landscape including a pair and a quartet of symmetrically equivalent local minima and a seam of conical intersections. The dissociation energy found from our ab initio calculations is 4534 cm−1. This result is reproduced by the GP models with an error of less than 3%. The GP models of the PES allow us to analyze the features of the global PES, representative of general alkali metal four-atom interactions. Understanding these interactions is of key importance in the field of ultracold chemistry.

The Journal of Chemical Physics•Feb 13, 2019•51 citations

Complex collisions of ultracold molecules: A toy model

Jia Yao, Cooper A. Johnson, Nirav P. Mehta +1 more

We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.

arXiv:1906.06960•Physical Review A•Nov 10, 2021•1 citation

Universal ultracold collision rates for polar molecules of two alkali-metal atoms

Paul S. Julienne, Thomas M. Hanna, Zbigniew Idziaszek

Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vibrational state v = 0 and for vibrational quenching of non-reactive dimers with v ≥ 1. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with an electric field of less than 20 kV cm(-1).

arXiv:1106.0494•Physical Chemistry Chemical Physics•Jan 1, 2011•88 citations
We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, NNN-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the K2\ensuremath-Rb{\mathrm{K}}_{2}\text{\ensuremath{-}}\mathrm{Rb}K2​\ensuremath-Rb and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124 \ensuremathμK\ensuremath−1\ensuremath{\mu}{\mathrm{K}}^{\ensuremath{-}1}\ensuremathμK\ensuremath−1, with an associated Rice-Ramsperger-Kassel-Marcus sticking time of 6.0 \ensuremathμs\ensuremath{\mu}\mathrm{s}\ensuremathμs. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.
The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of NaK+NaK collision complexes by the trapping laser leads to the experimentally observed two-body loss. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.
We report on the sticking time of the AlF dimer in the ultracold regime. We employ a full-dimensional potential energy surface for AlF-AlF, constructed using a machine learning approach [X. Liu et al., J. Chem. Phys. 159, 144103 (2023)], to compute the density of states using a semiclassical counting method. Next, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, we determine an RRKM sticking time of 216.0 $\ifmmode\pm\else\textpm\fi{}$ 4.8 ns, which is shorter than that of other previously reported nonreactive dimers. Then, based on the available potential energy surfaces and RRKM sticking time data for a few dimers, we observe that the RRKM sticking time correlates with the ratio of the dimer dissociation energy to the dissociation energy of its parent molecule. Thus, we propose this ratio as a parameter to estimate RRKM sticking times. Furthermore, using ab initio methods, we optimize and calculate the energies of the equilibrium geometries of AlCl-AlCl, CaH-CaH, and MgF-MgF, thereby determining the ratio of the dimer dissociation energy to the parent molecule dissociation energy. Based on this ratio, we propose a hierarchy to order the sticking lifetimes of those dimers in the ultracold regime.
A six-dimensional potential energy surface is constructed for the spin-polarized triplet state of CaF–CaF by ab initio calculations at the CCSD(T) level of theory, followed by Gaussian process interpolation. The potential is utilized to calculate the density of states for this bialkaline-earth-halogen system where we find the value 0.038 μK –1, implying a mean resonance spacing of 26 μK in the collision complex. This value implies an associated Rice–Ramsperger–Kassel–Marcus lifetime of 1.8 μs, thus predicting long-lived complexes in collisions at ultracold temperatures.
Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three- and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range. We propose an efficient sampling technique, which allows us to construct an accurate global PES accounting for different chemical arrangements with <2500 ab initio calculations. We apply this method to (NaK)2 and obtain the first global PES for a system of four alkali metal atoms. The resulting surface exhibits a complex landscape including a pair and a quartet of symmetrically equivalent local minima and a seam of conical intersections. The dissociation energy found from our ab initio calculations is 4534 cm−1. This result is reproduced by the GP models with an error of less than 3%. The GP models of the PES allow us to analyze the features of the global PES, representative of general alkali metal four-atom interactions. Understanding these interactions is of key importance in the field of ultracold chemistry.
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.
Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vibrational state v = 0 and for vibrational quenching of non-reactive dimers with v ≥ 1. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with an electric field of less than 20 kV cm(-1).