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

Physical Review Letters

Zero-Energy Resonances of Hydrogen Diatom Isotopologs: Tuning Quasiresonant Transitions in Vibration Space

Benhui Yang, Robert C. Forrey, Phillip C. Stancil, Samantha Fonseca dos Santos, N. Balakrishnan

Published Dec 4, 2012• 4 citations
Publisher

Abstract

Highly efficient and specific energy transfer mechanisms that involve rotation-rotation, vibration-vibration, and vibration-rotation exchange in diatomic molecules are examined theoretically in ultracold H(2), D(2), and HD self-collisions as a function of initial vibrational level v. The three quasiresonant mechanisms are found to operate for all vibrational levels and yield complex scattering lengths which vary smoothly with v. Exceptions to this trend occur at select high values of v where the scattering lengths are modulated by orders of magnitude corresponding to the location of an s-wave zero-energy resonance in "vibration space." The quasiresonant mechanisms, which are not very sensitive to the details of the interaction potential, generally control the final distribution of molecular states for any given initial distribution. The zero-energy resonances are more sensitive to the potential and may be used to vibrationally "tune" the interaction strength, similar to methods which vary applied external fields.

DOI
10.1103/physrevlett.109.233201

Related papers

Quasiresonant Energy Transfer in Ultracold Atom-Diatom Collisions

Robert C. Forrey, N. Balakrishnan, A. Dalgarno +2 more

Quantum and classical quasiresonant vibration-rotation energy transfer is investigated for ultracold $\mathrm{He}\ensuremath{-}{\mathrm{H}}_{2}$ collisions. Classical trajectory computations show that extremely strong correlations between $\ensuremath{\Delta}j$ and $\ensuremath{\Delta}v$ persist at low energies, though the changes themselves are less than one quantum. Quantum computations show that quasiresonant transitions occur in the limit of zero collision energy but that threshold effects become important and that some quasiresonant channels close. The qualitative similarity between classical and quantum results suggests that they share a common mechanism.

Physical Review Letters•Mar 29, 1999•97 citations

Isotope effects in complex scattering lengths for He collisions with molecular hydrogen

J. L. Nolte, Benhui Yang, Phillip C. Stancil +4 more

We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic ``hydrogen'' masses less than 1 u or a ``helium'' mass of $1.95$ u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ with ${\mathrm{H}}_{2}$, HD, HT, and DT should be feasible in the near future.

Physical Review A•Jan 8, 2010•12 citations

Vibration–rotation transfer in molecular super rotors

Anthony J. McCaffery

The collisional behavior of (X)6Li2 molecules in very high rotational levels of v=0 is considered. Highly efficient vibration–rotation transfer is predicted in these “super rotors” particularly when the conditions for quasiresonant transfer are fulfilled. This requires simultaneous near-resonance in energy and in angular momentum. Values of Δj for which quasiresonant vibration–rotation transfer (QRT) occurs become smaller as initial rotor state increases and transfer is likely to become particularly fast for Δj=2, predicted to occur when ji=130. This behavior is contrasted with the inefficiency of pure rotational transfer within the v=0 level for fast-rotating molecules. QRT will take place for quite cold collisions and thus will provide competition for the spinning-up process used to create the super rotors.

The Journal of Chemical Physics•Dec 22, 2000•13 citations

Ultracold collisions for atom--diatom systems with a reaction barrier

I. Simbotin

Theoretical results for ultracold atom-molecule collisions involving exoergic reactions are presented. Systems with a reaction barrier are considered; specifically, we report the results of extensive computations for D + H 2 and Cl + H2. We analyzed the extreme situation of translationally cold collisions between an atom and an internally hot molecule; namely, for D + H2 we explored the role played by the internal vibrational excitation of the diatomic target for initial states H2(υ) with υ = 0,1,2,…, 8. The υ-dependence of the zero-temperature limit of the reaction rate coefficient shows two distinct regimes: a barrier dominated regime for υ < 4, and a barrierless regime for υ > 4. Also, for highly excited initial states, the distribution over the final states of the products shows an approximate conservation of the internal vibrational energy. For Cl + H2 we studied in detail the isotopic effect by varying continuously the mass of H, which allowed us to find resonance effects in the threshold behavior of cross sections. These resonances are caused by long-lived van der Waals complexes (Cl···H2) which have vanishingly small binding energy, or by virtual states of the Cl···H 2 complex. ^

•Jan 1, 2012•0 citations

Ultracold collisions between two light indistinguishable diatomic molecules: Elastic and rotational energy transfer in HD+HD

Renat A. Sultanov, Dennis C. Guster, Sadhan K. Adhikari

A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T\ensuremath{\sim}{10}^{\ensuremath{-}8}$ K. A global six-dimensional H${}_{2}$-H${}_{2}$ potential-energy surface is adopted from a previous work [Boothroyd et al., J. Chem. Phys. 116, 666 (2002)]. State-resolved integral cross sections ${\ensuremath{\sigma}}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}({\ensuremath{\varepsilon}}_{\text{kin}})$ of different quantum-mechanical rotational transitions $ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}$ in the HD molecules and corresponding state-resolved thermal rate coefficients ${k}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}(T)$ have been computed. Additionally, for comparison, H${}_{2}$+H${}_{2}$ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.

arXiv:1111.2598•Physical Review A•May 3, 2012•4 citations

Ultracold atom-molecule collisions and bound states in magnetic fields: Tuning zero-energy Feshbach resonances in He−NH (Σ−3)

Maykel Leonardo González-Martínez, Jeremy M. Hutson

We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.

arXiv:physics/0610214•Physical Review A•Feb 5, 2007•82 citations
Highly efficient and specific energy transfer mechanisms that involve rotation-rotation, vibration-vibration, and vibration-rotation exchange in diatomic molecules are examined theoretically in ultracold H(2), D(2), and HD self-collisions as a function of initial vibrational level v. The three quasiresonant mechanisms are found to operate for all vibrational levels and yield complex scattering lengths which vary smoothly with v. Exceptions to this trend occur at select high values of v where the scattering lengths are modulated by orders of magnitude corresponding to the location of an s-wave zero-energy resonance in "vibration space." The quasiresonant mechanisms, which are not very sensitive to the details of the interaction potential, generally control the final distribution of molecular states for any given initial distribution. The zero-energy resonances are more sensitive to the potential and may be used to vibrationally "tune" the interaction strength, similar to methods which vary applied external fields.
Quantum and classical quasiresonant vibration-rotation energy transfer is investigated for ultracold $\mathrm{He}\ensuremath{-}{\mathrm{H}}_{2}$ collisions. Classical trajectory computations show that extremely strong correlations between $\ensuremath{\Delta}j$ and $\ensuremath{\Delta}v$ persist at low energies, though the changes themselves are less than one quantum. Quantum computations show that quasiresonant transitions occur in the limit of zero collision energy but that threshold effects become important and that some quasiresonant channels close. The qualitative similarity between classical and quantum results suggests that they share a common mechanism.
We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic ``hydrogen'' masses less than 1 u or a ``helium'' mass of 1.951.951.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He with H2{\mathrm{H}}_{2}H2​, HD, HT, and DT should be feasible in the near future.
The collisional behavior of (X)6Li2 molecules in very high rotational levels of v=0 is considered. Highly efficient vibration–rotation transfer is predicted in these “super rotors” particularly when the conditions for quasiresonant transfer are fulfilled. This requires simultaneous near-resonance in energy and in angular momentum. Values of Δj for which quasiresonant vibration–rotation transfer (QRT) occurs become smaller as initial rotor state increases and transfer is likely to become particularly fast for Δj=2, predicted to occur when ji=130. This behavior is contrasted with the inefficiency of pure rotational transfer within the v=0 level for fast-rotating molecules. QRT will take place for quite cold collisions and thus will provide competition for the spinning-up process used to create the super rotors.
Theoretical results for ultracold atom-molecule collisions involving exoergic reactions are presented. Systems with a reaction barrier are considered; specifically, we report the results of extensive computations for D + H 2 and Cl + H2. We analyzed the extreme situation of translationally cold collisions between an atom and an internally hot molecule; namely, for D + H2 we explored the role played by the internal vibrational excitation of the diatomic target for initial states H2(υ) with υ = 0,1,2,…, 8. The υ-dependence of the zero-temperature limit of the reaction rate coefficient shows two distinct regimes: a barrier dominated regime for υ < 4, and a barrierless regime for υ > 4. Also, for highly excited initial states, the distribution over the final states of the products shows an approximate conservation of the internal vibrational energy. For Cl + H2 we studied in detail the isotopic effect by varying continuously the mass of H, which allowed us to find resonance effects in the threshold behavior of cross sections. These resonances are caused by long-lived van der Waals complexes (Cl···H2) which have vanishingly small binding energy, or by virtual states of the Cl···H 2 complex. ^
A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T\ensuremath{\sim}{10}^{\ensuremath{-}8}$ K. A global six-dimensional H2{}_{2}2​-H2{}_{2}2​ potential-energy surface is adopted from a previous work [Boothroyd et al., J. Chem. Phys. 116, 666 (2002)]. State-resolved integral cross sections ${\ensuremath{\sigma}}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}({\ensuremath{\varepsilon}}_{\text{kin}})$ of different quantum-mechanical rotational transitions $ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}$ in the HD molecules and corresponding state-resolved thermal rate coefficients ${k}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}(T)$ have been computed. Additionally, for comparison, H2{}_{2}2​+H2{}_{2}2​ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.
We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.