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:1807.05783 · Physical Review A

Defining the p -wave scattering volume in the presence of dipolar interactions

A. Crubellier, Rosario González‐Férez, Christiane P. Koch, Eliane Luc-Koenig

Published Mar 25, 2019• 3 citations
arXivHTMLPDF

Abstract

The definition of the scattering volume for $p$-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as $1/{R}^{3}$. Here, we propose a way to define the scattering volume characterizing the short-range interactions in odd-parity waves, by analyzing the $p$-wave component of the two-body threshold wave function. Our approach uses an asymptotic model and introduces explicitly the anisotropic dipole-dipole interaction, which governs the ultracold collision dynamics at long range. The short-range interactions, which are essential to describe threshold resonances, are taken into account by a single parameter related to the nodal structure of the wave functions at short distances.

DOI
10.1103/physreva.99.032709

Related papers

Controlling ultracold p -wave collisions with nonresonant light: Predictions of an asymptotic model

A. Crubellier, Rosario González‐Férez, Christiane P. Koch +1 more

Interactions in a spin-polarized ultracold Fermi gas are governed by $p$-wave collisions and can be characterized by the $p$-wave scattering volume. Control of these collisions by Feshbach resonances is hampered by huge inelastic losses. Here, we suggest nonresonant light control of $p$-wave collisions, exploiting the anisotropic coupling of nonresonant light to the polarizability of the atoms. The $p$-wave scattering volume can be controlled by strong nonresonant light, in close analogy to the $s$-wave scattering length. For collision partners that are tightly trapped, the nonresonant light induces an energy shift directly related to the scattering volume (as defined by A. Crubellier, R. Gonz\'alez-F\'erez, C. P. Koch, and E. Luc-Koenig, preceding paper, Phys. Rev. A 99, 032709 (2019). This effect could be used to climb the ladder of the trap. We also show that controlling the scattering volume implies control, at least roughly, over the orientation at short interatomic distances of the interparticle axis relative to the polarization direction of the light. Our proposal is based on an asymptotic model that explicitly accounts for the anisotropic dipole-dipole interaction which governs the ultracold collision dynamics at long range.

arXiv:1807.05787•Physical Review A•Mar 25, 2019•5 citations

Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

Eugene A. Koval, Oksana A. Koval

We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.

EPJ Web of Conferences•Jan 1, 2018•2 citations

Dispersion interactions and reactive collisions of ultracold polar molecules

Svetlana Kotochigova

Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40 K 87 Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.

arXiv:1003.2672•New Journal of Physics•Jul 29, 2010•74 citations

The scattering of a few particles with short-range interactions at low energies

Shangguo Zhu

The low-energy scattering of three bosons or distinguishable particles with short-range interactions is characterized by a fundamental parameter, the three-body scattering hypervolume, which is responsible for the nonuniversal effects in dilute Bose-Einstein condensates. We derive an analytical formula of the three-body scattering hypervolumes for weak interactions. When the interaction supports two-body bound states, the three-body scattering hypervolume gains a negative imaginary part, which is directly related to the rate constant for three-body recombinations. We develop a numerical method to calculate the three-body scattering hypervolumes for some model potentials with variable strengths. For real atoms with van der Waals potential, the three-body scattering hypervolumes are much harder to compute, because the three-body wave function is highly oscillatory at smaller inter-atomic distances. However, they may be extractable from precision data such as the collective-mode frequencies of trapped Bose-Einstein condensates. In many numerical simulations, the system being simulated is put into a large but finite volume, such as a large periodic box of size $L$. To extract the low-energy scattering properties of two particles in infinite space from such simulations, L\\"uscher's formula must be used. In the second part of this thesis, we generalize L\\"uscher's formula to $d$ spatial dimensions. We obtain its $s$-wave and $p$-wave approximations and the systematic expansions of the energies of the low-lying states. At a $s$-wave resonance in $d\\ge4$ dimensions, we identify two low-lying states close to the threshold with nearly opposite energies, $E\\sim \\pm 1/L^{d/2}$ when $d\\ge 5$, or $E \\sim \\pm 1/L^2 \\sqrt{\\ln L}$ when $d= 4$. These calculations provide important insights to the physics of three particles at a three-body resonance in finite volumes in two or three dimensions. Three-body resonances are important phenomena not yet completely explored in the experiments on cold atoms.

•Nov 8, 2018•0 citations

Controlling the s -wave scattering length with nonresonant light: Predictions of an asymptotic model

A. Crubellier, Rosario González‐Férez, Christiane P. Koch +1 more

A pair of atoms interacts with nonresonant light via its anisotropic polarizability. This effect can be used to tune the scattering properties of the atoms. Although the light-atom interaction varies with interatomic separation as $1/{R}^{3}$, the effective $s$-wave potential decreases more rapidly as $1/{R}^{4}$ such that the field-dressed scattering length can be determined without any formal difficulty. The scattering dynamics are essentially governed by the long-range part of the interatomic interaction and can thus be accurately described by an asymptotic model [A. Crubellier et al., New J. Phys. 17, 045020 (2015)]. Here we use the asymptotic model to determine the field-dressed scattering length from the $s$-wave radial component of a particular threshold wave function. Applying our theory to the scattering of two strontium isotopes, we calculate the variation of the scattering length with the intensity of the nonresonant light. Moreover, we predict the intensities at which the scattering length becomes infinite for any pair of atoms.

arXiv:1611.07229•Physical Review A•Feb 8, 2017•9 citations

Resonances in Non-universal Dipolar Collisions

Tijs Karman

Scattering resonances due to the dipole-dipole interaction between ultracold molecules, induced by static or microwave fields, are studied theoretically. We develop a method for coupled-channel calculations that can efficiently impose many short-range boundary conditions, defined by a short-range phase shift and loss probability as in quantum defect theory. We study how resonances appear as the short-range loss probability is lowered below the universal unit probability. This may become realizable for nonreactive ultracold molecules in blue-detuned box potentials.

arXiv:2212.03065•The Journal of Physical Chemistry A•Feb 24, 2023•4 citations
The definition of the scattering volume for ppp-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as 1/R31/{R}^{3}1/R3. Here, we propose a way to define the scattering volume characterizing the short-range interactions in odd-parity waves, by analyzing the ppp-wave component of the two-body threshold wave function. Our approach uses an asymptotic model and introduces explicitly the anisotropic dipole-dipole interaction, which governs the ultracold collision dynamics at long range. The short-range interactions, which are essential to describe threshold resonances, are taken into account by a single parameter related to the nodal structure of the wave functions at short distances.
Interactions in a spin-polarized ultracold Fermi gas are governed by ppp-wave collisions and can be characterized by the ppp-wave scattering volume. Control of these collisions by Feshbach resonances is hampered by huge inelastic losses. Here, we suggest nonresonant light control of ppp-wave collisions, exploiting the anisotropic coupling of nonresonant light to the polarizability of the atoms. The ppp-wave scattering volume can be controlled by strong nonresonant light, in close analogy to the sss-wave scattering length. For collision partners that are tightly trapped, the nonresonant light induces an energy shift directly related to the scattering volume (as defined by A. Crubellier, R. Gonz\'alez-F\'erez, C. P. Koch, and E. Luc-Koenig, preceding paper, Phys. Rev. A 99, 032709 (2019). This effect could be used to climb the ladder of the trap. We also show that controlling the scattering volume implies control, at least roughly, over the orientation at short interatomic distances of the interparticle axis relative to the polarization direction of the light. Our proposal is based on an asymptotic model that explicitly accounts for the anisotropic dipole-dipole interaction which governs the ultracold collision dynamics at long range.
We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40 K 87 Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.
The low-energy scattering of three bosons or distinguishable particles with short-range interactions is characterized by a fundamental parameter, the three-body scattering hypervolume, which is responsible for the nonuniversal effects in dilute Bose-Einstein condensates. We derive an analytical formula of the three-body scattering hypervolumes for weak interactions. When the interaction supports two-body bound states, the three-body scattering hypervolume gains a negative imaginary part, which is directly related to the rate constant for three-body recombinations. We develop a numerical method to calculate the three-body scattering hypervolumes for some model potentials with variable strengths. For real atoms with van der Waals potential, the three-body scattering hypervolumes are much harder to compute, because the three-body wave function is highly oscillatory at smaller inter-atomic distances. However, they may be extractable from precision data such as the collective-mode frequencies of trapped Bose-Einstein condensates. In many numerical simulations, the system being simulated is put into a large but finite volume, such as a large periodic box of size LLL. To extract the low-energy scattering properties of two particles in infinite space from such simulations, L\\"uscher's formula must be used. In the second part of this thesis, we generalize L\\"uscher's formula to ddd spatial dimensions. We obtain its sss-wave and ppp-wave approximations and the systematic expansions of the energies of the low-lying states. At a sss-wave resonance in dge4d\\ge4dge4 dimensions, we identify two low-lying states close to the threshold with nearly opposite energies, Esimpm1/Ld/2E\\sim \\pm 1/L^{d/2}Esimpm1/Ld/2 when dge5d\\ge 5dge5, or Esimpm1/L2sqrtlnLE \\sim \\pm 1/L^2 \\sqrt{\\ln L}Esimpm1/L2sqrtlnL when d=4d= 4d=4. These calculations provide important insights to the physics of three particles at a three-body resonance in finite volumes in two or three dimensions. Three-body resonances are important phenomena not yet completely explored in the experiments on cold atoms.
A pair of atoms interacts with nonresonant light via its anisotropic polarizability. This effect can be used to tune the scattering properties of the atoms. Although the light-atom interaction varies with interatomic separation as 1/R31/{R}^{3}1/R3, the effective sss-wave potential decreases more rapidly as 1/R41/{R}^{4}1/R4 such that the field-dressed scattering length can be determined without any formal difficulty. The scattering dynamics are essentially governed by the long-range part of the interatomic interaction and can thus be accurately described by an asymptotic model [A. Crubellier et al., New J. Phys. 17, 045020 (2015)]. Here we use the asymptotic model to determine the field-dressed scattering length from the sss-wave radial component of a particular threshold wave function. Applying our theory to the scattering of two strontium isotopes, we calculate the variation of the scattering length with the intensity of the nonresonant light. Moreover, we predict the intensities at which the scattering length becomes infinite for any pair of atoms.
Scattering resonances due to the dipole-dipole interaction between ultracold molecules, induced by static or microwave fields, are studied theoretically. We develop a method for coupled-channel calculations that can efficiently impose many short-range boundary conditions, defined by a short-range phase shift and loss probability as in quantum defect theory. We study how resonances appear as the short-range loss probability is lowered below the universal unit probability. This may become realizable for nonreactive ultracold molecules in blue-detuned box potentials.