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:physics/0601073 · Physical Review A

Properties of quasi-one-dimensional molecules with Feshbach-resonance interaction

Vladimir Yurovsky

Published May 1, 2006• 16 citations
arXivHTMLPDF

Abstract

Bound states and collisions of atoms with two-channel two-body interactions in harmonic waveguides are analyzed. The closed-channel contributions to two-atom bound states become dominant in the case of a weak resonance. At low energies and values of the nonresonant scattering length the problem can be approximated by a one-dimensional resonant model. The three-body problem becomes nonintegrable and the properties of triatomic molecules become different from those predicted by the integrable Lieb-Liniger-McGuire model.

DOI
10.1103/physreva.73.052709

Related papers

One-Dimensional Bose Chemistry: Effects of Nonintegrability

Vladimir Yurovsky, A. Ben‐Reuven, Maxim Olshanii

Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy-dependent strength. The related integrable Lieb-Liniger-McGuire (LLMG) model, with an energy-independent strength, forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev equations. The results demonstrate that as the internal symmetry of the LLMG model is lifted, reflection and chemical reactions become allowed and may be observed in experiments.

arXiv:physics/0512033•Physical Review Letters•Apr 28, 2006•21 citations

Effects of nonintegrability on stabilization of Feshbach molecules in atom waveguides

Vladimir Yurovsky

Deactivation of broad quasi-one-dimensional dibosonic molecules is analyzed. Within the integrable Lieb-Liniger-McGuire (LLMG) model an exact expression does not demonstrate suppression of the deactivation at low collision energies. The solution of Faddeev equations demonstrates that when a Feshbach resonance lifts the symmetry of the LLMG model the deactivation becomes suppressed. This effect shows a way for formation of a stable gas of dibosonic Feshbach molecules.

arXiv:physics/0703168•Physical Review A•Jan 22, 2008•2 citations

Bound and scattering states in harmonic waveguides in the vicinity of free space Feshbach resonances

Gaoren Wang, Panagiotis Giannakeas, Peter Schmelcher

Abstract The two-body bound and scattering properties in an one-dimensional harmonic waveguide close to free space magnetic Feshbach resonances are investigated based on the local frame transformation approach within a single partial wave approximation. An energy and magnetic field dependent free space phase shift is adopted in the current theoretical framework. For both s - and p -wave interaction, the least bound state in the waveguide dissociates into the continuum at the resonant magnetic field where the effective one-dimensional scattering length a 1D diverges. Consequently, the association of atoms into molecules in the waveguide occurs when the magnetic field is swept adiabatically across the pole of a 1D . In the vicinity of broad s -wave resonances, the resonant magnetic field is nearly independent on the transverse confining frequency ω ⊥ of the waveguide. Close to p -wave and narrow s -wave resonances, the resonant magnetic field changes as ω ⊥ varies.

arXiv:1603.02616•Journal of Physics B Atomic Molecular and Optical Physics•Jul 29, 2016•4 citations

Ultracold-atom collisions in atomic waveguides: A two-channel analysis

Tom Kristensen, Ludovic Pricoupenko

Low-dimensional behavior of two ultracold atoms trapped in two- and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used, allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement-induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with those of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound-state properties.

arXiv:1412.4921•Physical Review A•Apr 8, 2015•7 citations

Feshbach resonance scattering under cylindrical harmonic confinement

Vladimir Yurovsky

A problem of collisions of atoms with two-channel zero-range interaction in an atomic waveguide is solved by using of a renormalization procedure. A matching of the solution to a solution of the related one-dimensional problem leads to relation between the one-dimensional and three-dimensional scattering parameters. The scattering amplitude and bound states for the confined system demonstrate differences from the related free and one-dimensional systems.

arXiv:cond-mat/0308465•Physical Review A•Jan 19, 2005•33 citations

Control of ultraslow inelastic collisions by Feshbach resonances and quasi-one- dimensional confinement

Vladimir Yurovsky, Y. B. Band

Inelastic collisions of ultracold atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of excited states due to inelastic collisions is suppressed. The relation of our results to the Lieb-Liniger model for bosonic atoms is addressed.

arXiv:physics/0602181•Physical Review A•Jan 23, 2007•13 citations
Bound states and collisions of atoms with two-channel two-body interactions in harmonic waveguides are analyzed. The closed-channel contributions to two-atom bound states become dominant in the case of a weak resonance. At low energies and values of the nonresonant scattering length the problem can be approximated by a one-dimensional resonant model. The three-body problem becomes nonintegrable and the properties of triatomic molecules become different from those predicted by the integrable Lieb-Liniger-McGuire model.
Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy-dependent strength. The related integrable Lieb-Liniger-McGuire (LLMG) model, with an energy-independent strength, forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev equations. The results demonstrate that as the internal symmetry of the LLMG model is lifted, reflection and chemical reactions become allowed and may be observed in experiments.
Abstract The two-body bound and scattering properties in an one-dimensional harmonic waveguide close to free space magnetic Feshbach resonances are investigated based on the local frame transformation approach within a single partial wave approximation. An energy and magnetic field dependent free space phase shift is adopted in the current theoretical framework. For both s - and p -wave interaction, the least bound state in the waveguide dissociates into the continuum at the resonant magnetic field where the effective one-dimensional scattering length a 1D diverges. Consequently, the association of atoms into molecules in the waveguide occurs when the magnetic field is swept adiabatically across the pole of a 1D . In the vicinity of broad s -wave resonances, the resonant magnetic field is nearly independent on the transverse confining frequency ω ⊥ of the waveguide. Close to p -wave and narrow s -wave resonances, the resonant magnetic field changes as ω ⊥ varies.
Low-dimensional behavior of two ultracold atoms trapped in two- and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used, allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement-induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with those of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound-state properties.
Inelastic collisions of ultracold atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of excited states due to inelastic collisions is suppressed. The relation of our results to the Lieb-Liniger model for bosonic atoms is addressed.