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:cond-mat/0506272 · New Journal of Physics

Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps

Vittorio Peano, Michael Thorwart, Christophe Mora, Reinhold Egger

Published Sep 12, 2005• 61 citations
arXivHTMLPDF

Abstract

We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional (1D) trapping potentials, allowing for two different atom species. As a consequence, the centre-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.

DOI
10.1088/1367-2630/7/1/192

Related papers

Three-body problem for ultracold atoms in quasi-one-dimensional traps

Christophe Mora, Reinhold Egger, Alexander O. Gogolin

We study the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale ${a}_{\ensuremath{\perp}}$. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$ and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths ${a}_{\mathit{ad}}$ and ${b}_{\mathit{ad}}$. In the tightly bound ``dimer limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{\infty}$, we find ${b}_{\mathit{ad}}=0$ and ${a}_{\mathit{ad}}$ is linked to the 3D atom-dimer scattering length. In the weakly bound ``BCS limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: ${a}_{\mathit{ad}}$ and ${b}_{\mathit{ad}}$ depend both on ${a}_{\ensuremath{\perp}}∕a$ and on a parameter ${R}^{*}$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.

arXiv:cond-mat/0412225•Physical Review A•May 9, 2005•46 citations

Scattering and Bound States of Two Heteronuclear Ultracold Atoms in a Quasi-Two-Dimensional Confinement

B. Wang, F. Yang, P. Zhang

We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal ($z$-) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (CoM) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length $a_{\rm 2D}$, the 2D effective range parameter $R_{\rm 2D}$, and the bound-state energies, as functions of the $s$-wave scattering length and effective range of the two atoms in free three-dimensional (3D) space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal CoM and relative motion. Around these resonances, $a_{\rm 2D}$ varies rapidly with the 3D scattering parameters, while $R_{\rm 2D}$ is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by i.e., the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.

cond-mat.quant-gasCross-listedarXiv:2606.02987•Jun 3, 2026•0 citations

Photon-Assisted Confinement-Induced Resonances for Ultracold Atoms

Vicente Leyton‐Ortega, Maryam Roghani, Vittorio Peano +1 more

We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi's pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. The modulation opens additional photon-assisted resonant scattering channels. Applying the Bethe-Peierls boundary condition, we obtain the general scattering solution of the time-dependent Floquet-Schrödinger equation which is universal at low energies. The effective one-dimensional scattering length can be controlled by the external driving.

arXiv:1403.0348•Physical Review Letters•Jun 10, 2014•5 citations

Separation induced resonances in quasi-1D ultracold atomic gases

Wenbo Fu, Zhenhua Yu, Xiaoling Cui

We study quasi-1D effective scattering and bound states for two atoms confined individually by {\it separated} transverse traps. With equal trapping frequency for two atoms, we find that tuning the separation can induce {\it double} 1D scattering resonances when the ratio between the confinement length and s-wave scattering length is within $(0.791,1.46]$. The sign and amplitude of resonance width show nontrivial dependences on the resonance position. The universal properties of a many-body system at double resonances are manifested by studying the interaction effect of a localized impurity immersed in a Fermi sea of light atoms.

•Jun 28, 2011•0 citations

Separation-induced resonances in quasi-one-dimensional ultracold atomic gases

Wenbo Fu, Zhenhua Yu, Xiaoling Cui

We study the effective one-dimensional (1D) scattering of two distinguishable atoms confined individually by separatedtransverse harmonic traps. With equal trapping frequency for two $s$-wave interacting atoms, we find that by tuning the trap separations, the system can undergo double 1D scattering resonance, named as the separation-induced resonance (SIR), when the ratio between the confinement length and $s$-wave scattering length is within $(0.791,1.46]$. Near SIR, the scattering property shows unique dependence on the resonance position. The universality of a many-body system on scattering branch near SIR is demonstrated by studying the interaction effect of a localized impurity coupled with a Fermi sea of light atoms in a quasi-1D trap.

arXiv:1106.5604•Physical Review A•Jan 12, 2012•5 citations

Atom-Dimer Scattering for Confined Ultracold Fermion Gases

Christophe Mora, Reinhold Egger, Alexander O. Gogolin +1 more

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.

arXiv:cond-mat/0406627•Physical Review Letters•Oct 22, 2004•51 citations
We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional (1D) trapping potentials, allowing for two different atom species. As a consequence, the centre-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.
We study the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale ${a}_{\ensuremath{\perp}}$. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length aaa and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths aad{a}_{\mathit{ad}}aad​ and bad{b}_{\mathit{ad}}bad​. In the tightly bound ``dimer limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{\infty}$, we find bad=0{b}_{\mathit{ad}}=0bad​=0 and aad{a}_{\mathit{ad}}aad​ is linked to the 3D atom-dimer scattering length. In the weakly bound ``BCS limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: aad{a}_{\mathit{ad}}aad​ and bad{b}_{\mathit{ad}}bad​ depend both on ${a}_{\ensuremath{\perp}}∕a$ and on a parameter R∗{R}^{*}R∗ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.
We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal (zzz-) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (CoM) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length a2Da_{\rm 2D}a2D​, the 2D effective range parameter R2DR_{\rm 2D}R2D​, and the bound-state energies, as functions of the sss-wave scattering length and effective range of the two atoms in free three-dimensional (3D) space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal CoM and relative motion. Around these resonances, a2Da_{\rm 2D}a2D​ varies rapidly with the 3D scattering parameters, while R2DR_{\rm 2D}R2D​ is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by i.e., the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.
We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi's pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. The modulation opens additional photon-assisted resonant scattering channels. Applying the Bethe-Peierls boundary condition, we obtain the general scattering solution of the time-dependent Floquet-Schrödinger equation which is universal at low energies. The effective one-dimensional scattering length can be controlled by the external driving.
We study quasi-1D effective scattering and bound states for two atoms confined individually by {\it separated} transverse traps. With equal trapping frequency for two atoms, we find that tuning the separation can induce {\it double} 1D scattering resonances when the ratio between the confinement length and s-wave scattering length is within (0.791,1.46](0.791,1.46](0.791,1.46]. The sign and amplitude of resonance width show nontrivial dependences on the resonance position. The universal properties of a many-body system at double resonances are manifested by studying the interaction effect of a localized impurity immersed in a Fermi sea of light atoms.
We study the effective one-dimensional (1D) scattering of two distinguishable atoms confined individually by separatedtransverse harmonic traps. With equal trapping frequency for two sss-wave interacting atoms, we find that by tuning the trap separations, the system can undergo double 1D scattering resonance, named as the separation-induced resonance (SIR), when the ratio between the confinement length and sss-wave scattering length is within (0.791,1.46](0.791,1.46](0.791,1.46]. Near SIR, the scattering property shows unique dependence on the resonance position. The universality of a many-body system on scattering branch near SIR is demonstrated by studying the interaction effect of a localized impurity coupled with a Fermi sea of light atoms in a quasi-1D trap.
We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.