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arXiv:1809.05351 · Physical Review A

Confinement-induced resonances in two-center problem via a pseudopotential approach

Sara Shadmehri, Vladimir S. Melezhik

Published Mar 13, 2019• 5 citations
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Abstract

We study confined scattering of a quantum particle by two centers fixed on the longitudinal axis of a harmonic-waveguide-like trap. The conditions of confinement-induced resonances (CIRs) appearing in these systems, when scattering cross section approaches the unitary limit, are derived for a regularized pseudopotential describing particle interaction with scattering centers. In the limit of a single center, the position of CIR for an even state tends to the well-known result obtained by Olshanii [Phys. Rev. Lett. 81, 938 (1998)]. Our result can be applicable to confined atomic scattering by fixed impurities, such as ions or Rydberg atoms, with possible extension to $N$ impurities, or by two-atomic molecules.

DOI
10.1103/physreva.99.032705

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We study confined scattering of a quantum particle by two centers fixed on the longitudinal axis of a harmonic-waveguide-like trap. The conditions of confinement-induced resonances (CIRs) appearing in these systems, when scattering cross section approaches the unitary limit, are derived for a regularized pseudopotential describing particle interaction with scattering centers. In the limit of a single center, the position of CIR for an even state tends to the well-known result obtained by Olshanii [Phys. Rev. Lett. 81, 938 (1998)]. Our result can be applicable to confined atomic scattering by fixed impurities, such as ions or Rydberg atoms, with possible extension to NNN impurities, or by two-atomic molecules.
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 investigate confinement-induced resonances in a system composed of a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region---from the ``long-wavelength'' limit to the opposite case when the typical length scale of the atom-ion polarization potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the ``long-wavelength and zero-energy'' limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semianalytic formula for the resonance position in the long-wavelength and zero-energy limit and we investigate numerically the dependence of the resonance condition on the finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, to determine the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi-one-dimensional atomic quantum gas.
It was recently predicted [Phys. Rev. Lett. 81, 938 (1998)]] that atom-atom scattering under transverse harmonic confinement is subject to a "confinement-induced resonance" where the effective one-dimensional coupling strength diverges at a particular ratio of the confinement and scattering lengths. As the initial prediction made use of the zero-range pseudopotential approximation, we now report numerical results for finite-range interaction potentials that corroborate this resonance. In addition, we now present a physical interpretation of this effect as a novel type of Feshbach resonance in which the transverse modes of the confining potential assume the roles of "open" and "closed" scattering channels.
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 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 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.