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arXiv:0802.3682 · Physical Review A

Multichannel atomic scattering and confinement-induced resonances in waveguides

Shahpoor Saeidian, Vladimir S. Melezhik, Peter Schmelcher

Published Apr 25, 2008• 46 citations
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Abstract

We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\ensuremath{\omega}$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.

DOI
10.1103/physreva.77.042721

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We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency \ensuremathω\ensuremath{\omega}\ensuremathω permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.
We perform an analytical investigation in the framework of generalized KKK-matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular, we present the unitarity bounds which emerge when considering a quasi-one-dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de)excitations by means of CIRs. We analyze the CIR for ddd waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.
We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [Phys. Rev. A 79, 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of sss-, ddd-, and ggg-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of sss-wave resonant scattering.
We have developed the general grid method for multichannel scattering of bosonic atoms inside a harmonic waveguide with transverse anisotropy. This approach is employed to analyze elastic as well as inelastic multichannel confined scattering. For the elastic scattering, the effects of the range and form of interatomic potential and the waveguide anisotropy on the confinement-induced resonance are studied. We have also investigated quantitatively the reactive rate constant in confined atom-atom collisions. It is found that a slight anisotropy to the confining trap considerably enhances the reactive rate constant in multichannel regime.
A wave-packet propagation method is developed and applied to investigate the quantum dynamics of scattering processes of identical and distinguishable atoms in harmonic waveguides. The quantum dynamics of the confinement-induced resonances (CIRs) for ultracold collisions of identical particles, sss-wave CIRs for bosons and ppp-wave CIRs for fermions, is explored in detail. Our multigrid approach allows us to fully take into account the coupling between the center-of-mass (c.m.) and relative motions in the case of distinguishable atoms. The latter includes, in particular, sss- and ppp-partial-wave mixing, caused by the confining trap, which acts differently on the different atomic species. Specifically, we explore in detail the recently discovered [J. I. Kim, V. S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 (2006)] dual CIR, which is based on a destructive interference mechanism leading to complete transmission in the waveguide, although the corresponding scattering in free space exhibits strong sss- and ppp-wave scattering.
We have developed a method for treating ultracold pair collisions in confined geometry of tight atomic waveguides. With this approach we have predicted and analyzed a few novel resonant and multichannel effects induced by confining traps in ultracold atomic collisions. In this report we discuss our model yielding the shifts and widths of magnetic Feshbach resonances in tight atomic waveguides. We also briefly discuss a resonant mechanism of molecule formation in atomic traps with transferring the energy release to the center-of-mass excitation while forming molecule and dipolar confinement-induced resonances in waveguides. These results could potentially be used experimentally.