Resonantd-wave scattering in harmonic waveguides

Abstract

We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance 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 resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave resonant behavior. 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.

Analytical treatment of bosonicd-wave scattering in isotropic harmonic waveguides

“…T n in Fig. 1(a) denotes the numerically calculated transmission coefficient, as it was shown in [26,34,35]. We observe the appearance of two minima (T n = 0) due to resonances.…”

“…1(a)-(b)), whereas there is no trace of the DWR, since contributions from higher partial waves are not included in Eq. (26). In Fig.…”

“…Furthermore, in order to go beyond s-wave physics we assume that the momentum k is very small but not equal to zero. Consequently, as it was shown in [26] except for the well known s-wave CIR [5], an additional resonance emerges in this system, the so-called DWR, which is based on the interference of a free space d-wave shape resonance with s-wave scattering. The coexistence of s-and d-wave resonances implies interactions between the bosons of s-and d-wave symmetries (see Fig.1(c) in Ref.…”

“…The coexistence of s-and d-wave resonances implies interactions between the bosons of s-and d-wave symmetries (see Fig.1(c) in Ref. [26]). …”

“…For the case of bosons an analytical description of collisions in a planar waveguide has been derived, where the cross-section possesses s-and d-wave resonances [17]. In harmonic waveguides higher-partial wave interactions were shown to have important impact on bosonic scattering [26] through the interference of d-wave resonances (DWRs) with the underlying continuum. A theoretical treatment of d-wave scattering of bosons in the case of quasi-1D geometries is, however, still needed.…”