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D-wave confinement-induced resonances in harmonic waveguides

Panagiotis Giannakeas, Vladimir S. Melezhik, Peter Schmelcher, Russian Federation

Published Feb 28, 2011• 1 citation
OpenAlex

Abstract

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

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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.
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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 investigated the quantum dynamics of two ultracold bosons inside an atomic waveguide for two different confinement geometries (cigar-shaped and toroidal waveguides) by quantum Monte Carlo methods. For quasi-1D gases, the confining potential of the waveguide leads to the so-called confinement induced resonance (CIR), results in the phase transition of the gas to the impenetrable bosonic regime (known as TG gas). In this regime the bosons repel each other strongly and behave like fermions. We reproduce CIR for a cigar-shaped waveguide and analyze the behavior of the system for different conditions. Moreover, our analysis demonstrates appearance of CIR for a toroidal waveguide. Particularly, we show that the resonance position is dependent on the size of the waveguide, which is in contrast to the cigar shaped waveguides for which it is universal.
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.
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.