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arXiv:1102.5686 · Physical Review A

Resonant d -wave scattering in harmonic waveguides

Panagiotis Giannakeas, Vladimir S. Melezhik, Peter Schmelcher

Published Aug 11, 2011• 13 citations
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Abstract

We observe and analyze $d$-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the $d$-wave resonance emerges in the quasi-1D regime as an imprint of a 3D $d$-wave shape resonance. A scaling relation for the position of the $d$-wave resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from $s$-wave to $d$-wave resonant behavior. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a possibility for studying strongly correlated atomic systems beyond $s$-wave physics.

DOI
10.1103/physreva.84.023618

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We observe and analyze ddd-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the ddd-wave resonance emerges in the quasi-1D regime as an imprint of a 3D ddd-wave shape resonance. A scaling relation for the position of the ddd-wave resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from sss-wave to ddd-wave resonant behavior. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a possibility for studying strongly correlated atomic systems beyond sss-wave physics.
We observe d-wave confinement-induced resonances (CIRs) of bosonic scattering in tightly confining harmonic waveguides. It is shown that the d-wave CIR emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave CIR is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave CIRs. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a novel possibility for studying strongly correlated atomic systems beyond s-wave physics. PACS numbers: 03.75.Be, 34.10.+x, 34.50.-s
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 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.
Low energy scattering amplitudes for two atoms in one- and two-dimensional atomic waveguides are derived for short range isotropic and resonant interactions in high partial wave channels. Taking into account the finite width of the resonance which was neglected in previous works is shown to have important implications in the properties of the confinement induced resonances. For spin polarized fermions in quasi-1D waveguides, it imposes a strong constraint on the atomic density for achieving the Fermi Tonks Girardeau gas. For a planar waveguide, the characteristics of the 2D induced scattering resonances in p- and d-waves are determined as a function of the 3D scattering parameters and of the waveguide frequency.
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 analyze ddd-wave resonances in atom-atom scattering in the presence of harmonic confinement by employing a higher-partial-wave pseudopotential. Analytical results for the scattering amplitude and transmission are obtained and compared to corresponding numerical ones, which employ the Lennard-Jones potential. Qualitative agreement is observed for weak confinement. For strong confinement the pseudopotential does not capture the sss- and ddd-wave interference phenomena, yielding an asymmetric Fano profile for the transmission resonance.