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arXiv:1309.4954 · Physical Review A

Observing dipolar confinement-induced resonances in quasi-one-dimensional atomic gases

Tao Shi, Su Yi

Published Oct 20, 2014• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.90.042710

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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 develop a nonperturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory and allows us to include accurately long-range anisotropic interactions. For ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization of, e.g., Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases.
We study quasi-one-dimensional atomic gases across wide and narrow confinement-induced resonances (CIRs). We show using the virial expansion that, by tuning the magnetic field, the repulsive scattering branch initially prepared at low fields can continuously go across CIRs without decay; instead, the decay occurs when the noninteracting limit is approached. The interaction properties essentially rely on the resonance width of the CIR. Universal thermodynamics holds for the scattering branch right at a wide CIR, but is smeared out in a narrow CIR due to the strong energy dependence of the coupling strength. In wide and narrow CIRs, the interaction energy of the scattering branch shows different types of strong asymmetry when the decay is approached from opposite sides of the magnetic field. Finally, we discuss the stability of the repulsive branch for a repulsively interacting Fermi gas in different trapped geometries at low temperatures.
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.
Fundamental aspects of ultracold collisions between identical bosonic or fermionic dipoles are studied under quasi-two-dimensional (Q2D) confinement. In the strongly dipolar regime, bosonic and fermion species are found to share important collisional properties as a result of the confining geometry, which suppresses the inelastic rates irrespective of the quantum statistics obeyed. A potential negative is that the confinement causes dipole-dipole resonances to be extremely narrow, which could make it difficult to explore Q2D dipolar gases with tunable interactions. Such properties are shown to be universal, and a simple WKB model reproduces most of our numerical results. In order to shed light on the many-body behavior of dipolar gases in Q2D we have analyzed the scattering amplitude and developed an energy-analytic form of the pseudopotentials for dipoles.