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arXiv:1304.8094 · Physical Review A

Quasi-one-dimensional scattering with general transverse two-dimensional confinement

Chen Zhang, Chris H. Greene

Published Jul 30, 2013• 14 citations
arXivHTMLPDF

Abstract

Confinement-induced resonances (CIR) in quasi-one-dimensional (quasi-1D) systems have been theoretically predicted and observed in various ultracold atomic gases. Here a regularized local frame transformation method is developed to treat CIR in a quasi-1D system that has an arbitrary transverse trap shape in general. The method is applied to predict the CIR position in a system having a square transverse geometry with hard walls.

DOI
10.1103/physreva.88.012715

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Confinement-induced resonances (CIR) in quasi-one-dimensional (quasi-1D) systems have been theoretically predicted and observed in various ultracold atomic gases. Here a regularized local frame transformation method is developed to treat CIR in a quasi-1D system that has an arbitrary transverse trap shape in general. The method is applied to predict the CIR position in a system having a square transverse geometry with hard walls.
We develop a theoretical framework for the quasi-low-dimensional confinement-induced resonances (CIRs) of particles with three-dimensional two-body interactions describable by the Huang-Yang pseudopotential. Using this approach, we analytically obtain the universal properties of dipolar CIRs in quasi-one-dimensional (quasi-1D) waveguides. We also show that the tilting angle between the dipole moment and the waveguide can be used as a control knob for scatterings in quasi-1D geometry. More importantly, the tilting-angle-induced dipolar CIRs in quasi-1D Cr, Er, and Dy atomic gases are experimentally detectable.
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 studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom $\ensuremath{\alpha}$) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom $\ensuremath{\beta}$) is localized by a 3D harmonic trap. We show that in such a system if atom $\ensuremath{\alpha}$ is much heavier than $\ensuremath{\beta}$, confinement-induced resonance (CIR) can appear when the 3D sss-wave scattering length as{a}_{s}as​ of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either as>0{a}_{s}>0as​>0 or as<0{a}_{s}<0as​<0. This is quite different from the usual CIRs which occur only when as{a}_{s}as​ is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough to serve as a tool for the control of effective interatomic interaction. We further show the mechanism of these CIRs via the Born-Oppenheimer approximation. Our results can be used for the realization of strongly interacting systems with ultracold atoms with weak 3D background interaction (i.e., small as{a}_{s}as​), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic fields.
We theoretically investigate the confinement-induced resonance for quasi-one-dimensional quantum systems under transversely anisotropic confinement, using a two-body sss-wave-scattering model in the zero-energy collision limit. We predict a single resonance for any transverse anisotropy, whose position shows a slight downshift with increasing anisotropy. We compare our prediction with the recent experimental result by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], in which two resonances are observed in the presence of transverse anisotropy. The discrepancy between theory and experiment remains to be resolved.
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 atom-atom scattering in quasi-one-dimensional geometries with transverse anisotropy. By assuming an sss-wave pseudopotential of contact interaction, we show that the system would exhibit a single confinement-induced resonance, where the scattering process degenerates to a total reflection as a one-dimensional gas of impenetrable bosons. For a general form of interaction, we present a formal calculation based on the two-channel model and draw the same qualitative conclusion of only one confinement-induced resonance. Our findings are inconsistent with a recent experiment by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], where a splitting of confinement-induced resonances has been observed in an anisotropic quasi-one-dimensional quantum gas of Cs atoms.