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arXiv:1002.3795 · Physical Review Letters

Confinement-Induced Resonances in Low-Dimensional Quantum Systems

Elmar Haller, Manfred J. Mark, Russell Hart, Johann Georg Danzl, Lukas Reichsöllner, Vladimir S. Melezhik, Peter Schmelcher, Hanns‐Christoph Nägerl

Published Apr 14, 2010• 252 citations
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Abstract

We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.

DOI
10.1103/physrevlett.104.153203

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We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.
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.
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 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 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.
We consider coherently-coupled bosonic mixtures scattering at low energies in the presence of an external confinement along either one or two directions. We exactly solve the two-body scattering problem, showing that for large Rabi coupling the confinement-induced resonance can be displaced towards scattering lengths values much smaller than the oscillator length. Our results make the observation of confinement-induced resonances more tunable and accessible, offering yet another handle for the efficient control of strong interactions in ultracold quantum gases.
We point out that theories describing s -wave collisions of bosonic atoms confined in one-dimensional (1D) or two-dimensional (2D) geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries.