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:1710.09057 · Physical Review Letters

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

Jiayu Huang, Shu Liu, Dong Hui Zhang, Roman V. Krems

Published Apr 4, 2018• 44 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.120.143401

Related papers

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Four-Atom Reactions

Jiayu Huang, Jun Chen, Shu Liu +1 more

We report here the first time-dependent wave packet dynamics study for an ultracold four-atom reaction. Our calculations provide accurate integral cross sections and rate constants all the way down to the Bethe–Wigner threshold regime for the benchmark OH + H 2 ( v = 2, j = 0) → H 2 O + H reaction, indicating that the time-dependent wave packet method is a powerful tool for studying ultracold four-atom reactions.

The Journal of Physical Chemistry Letters•Sep 24, 2020•20 citations

Wave Packet Approach to Adiabatic and Nonadiabatic Dynamics of Cold Inelastic Scatterings

Bayaer Buren, Maodu Chen

Due to the extremely large de Broglie wavelength of cold molecules, cold inelastic scattering is always characterized by the time-independent close-coupling (TICC) method. However, the TICC method is difficult to apply to collisions of large molecular systems. Here, we present a new strategy for characterizing cold inelastic scattering using wave packet (WP) method. In order to deal with the long de Broglie wavelength of cold molecules, the total wave function is divided into interaction, asymptotic and long-range regions (IALR). The three regions use different numbers of ro-vibrational basis functions, especially the long-range region, which uses only one function corresponding to the initial ro-vibrational state. Thus, a very large grid range can be used to characterize long de Broglie wavelengths in scattering coordinates. Due to its better numerical scaling law, the IALR-WP method has great potential in studying the inelastic scatterings of larger collision systems at cold and ultracold regimes.

Molecules•May 3, 2022•8 citations

Ultracold molecular collision dynamics

Yury Suleymanov

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

Science•May 7, 2020•0 citations

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. 582

arXiv:2003.10742•Science•May 7, 2020•103 citations

Ultracold collisions of molecules

Goulven Quéméner

This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent quantum formalism. It starts from the Schrödinger equation and introduces the experimental observables such as the differential or integral cross sections, and rate coefficients. Using a partial-wave expansion of the scattering wavefunction, the radial motion of the collision is described through a linear system of coupled equations, which is solved numerically. Using a matching procedure of the scattering wavefunction with its asymptotic form, the observables such as cross sections and rate coefficients are obtained from the extraction of the reactance, scattering and transition matrices. The example of the collision of two dipolar molecules in the presence of an electric field is presented, showing how dipolar interactions and collisions can be controlled.

arXiv:1703.09174•Mar 27, 2017•4 citations

Time-Dependent Wave-Packet Approach to Reactions for Quantum Computation

Evan Rule, Ionel Stetcu

We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time evolution, making this approach ideal for simulations on quantum hardware. The central quantity is a time-dependent overlap between incoming and outgoing wave packets whose Fourier transform corresponds to the scattering matrix at fixed energy, from which one can calculate elastic and inelastic cross sections for reactions involving two interacting clusters. Working in Cartesian coordinates enables an efficient encoding of the problem on quantum hardware via the first quantization mapping, with favorable qubit scaling for describing asymptotic scattering states. Within this framework, we describe a quantum algorithm for probing the scattering amplitude through different angles, including the forward direction, which provides access to the total cross section via the optical theorem. We demonstrate our methods through a series of numerical examples, for both elastic and inelastic processes, comparing against exact calculations. The techniques we describe can more readily be extended to a large number of constituent particles than other existing approaches, once fault-tolerant quantum hardware becomes available.

nucl-thCross-listedarXiv:2603.26881•Physical Review Letters•Mar 31, 2026•0 citations
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.
Due to the extremely large de Broglie wavelength of cold molecules, cold inelastic scattering is always characterized by the time-independent close-coupling (TICC) method. However, the TICC method is difficult to apply to collisions of large molecular systems. Here, we present a new strategy for characterizing cold inelastic scattering using wave packet (WP) method. In order to deal with the long de Broglie wavelength of cold molecules, the total wave function is divided into interaction, asymptotic and long-range regions (IALR). The three regions use different numbers of ro-vibrational basis functions, especially the long-range region, which uses only one function corresponding to the initial ro-vibrational state. Thus, a very large grid range can be used to characterize long de Broglie wavelengths in scattering coordinates. Due to its better numerical scaling law, the IALR-WP method has great potential in studying the inelastic scatterings of larger collision systems at cold and ultracold regimes.
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
Ultracold molecular collision dynamics Ultracold collision dynamics are of great importance in understanding the quantum nature of chemical interactions, but achieving the ultracold regime for molecules is challenging. Traditional techniques based on alternative routes to assemble the ultracold atomic constituents are only able to produce a type of ultracold molecules that cannot probe state-selective dynamics. Using Stark deceleration and velocity map–imaging techniques, de Jongh et al. achieved the ultracold regime directly for a nitric oxide–helium system and measured the state-to-state cross sections for inelastic scattering with high precision (see the Perspective by Yang and Yang). The observed scattering resonances confirmed high sensitivity to the underlying interaction potential because only the most accurate electronic structure theory could reproduce their structure. Science , this issue p. 626 ; see also p. 582
This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent quantum formalism. It starts from the Schrödinger equation and introduces the experimental observables such as the differential or integral cross sections, and rate coefficients. Using a partial-wave expansion of the scattering wavefunction, the radial motion of the collision is described through a linear system of coupled equations, which is solved numerically. Using a matching procedure of the scattering wavefunction with its asymptotic form, the observables such as cross sections and rate coefficients are obtained from the extraction of the reactance, scattering and transition matrices. The example of the collision of two dipolar molecules in the presence of an electric field is presented, showing how dipolar interactions and collisions can be controlled.
We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time evolution, making this approach ideal for simulations on quantum hardware. The central quantity is a time-dependent overlap between incoming and outgoing wave packets whose Fourier transform corresponds to the scattering matrix at fixed energy, from which one can calculate elastic and inelastic cross sections for reactions involving two interacting clusters. Working in Cartesian coordinates enables an efficient encoding of the problem on quantum hardware via the first quantization mapping, with favorable qubit scaling for describing asymptotic scattering states. Within this framework, we describe a quantum algorithm for probing the scattering amplitude through different angles, including the forward direction, which provides access to the total cross section via the optical theorem. We demonstrate our methods through a series of numerical examples, for both elastic and inelastic processes, comparing against exact calculations. The techniques we describe can more readily be extended to a large number of constituent particles than other existing approaches, once fault-tolerant quantum hardware becomes available.