7 research outputs found
Coupled-channel pseudo-potential description of the Feshbach resonance in two dimensions
We derive pseudo-potentials that describe the scattering between two
particles in two spatial dimensions for any partial wave m, whose scattering
strength is parameterized in terms of the m-dependent phase shift. Using our
m=0 pseudo-potential, we develop a coupled channel model with 2D zero-range
interactions, which describes the two-body physics across a Feshbach resonance.
Our model predicts the scattering length, the binding energy and the "closed
channel molecular fraction" of two particles; these observables can be measured
in experiments on ultracold quasi-2D atomic Bose and Fermi gases with
present-day technology.Comment: 4 pages, 3 figure
Low-energy resonances and bound states of aligned bosonic and fermionic dipoles
The low-energy scattering properties of two aligned identical bosonic and
identical fermionic dipoles are analyzed. Generalized scattering lengths are
determined as functions of the dipole moment and the scattering energy. Near
resonance, where a new bound state is being pulled in, all non-vanishing
generalized scattering lengths diverge, with the and
scattering lengths being dominant for identical bosons and identical fermions,
respectively, near both broad and narrow resonances. Implications for the
energy spectrum and the eigenfunctions of trapped two-dipole systems and for
pseudo-potential treatments are discussed.Comment: 4 pages, 4 figure
Pseudo-potential treatment of two aligned dipoles under external harmonic confinement
Dipolar Bose and Fermi gases, which are currently being studied extensively
experimentally and theoretically, interact through anisotropic, long-range
potentials. Here, we replace the long-range potential by a zero-range
pseudo-potential that simplifies the theoretical treatment of two dipolar
particles in a harmonic trap. Our zero-range pseudo-potential description
reproduces the energy spectrum of two dipoles interacting through a
shape-dependent potential under external confinement very well, provided that
sufficiently many partial waves are included, and readily leads to a
classification scheme of the energy spectrum in terms of approximate angular
momentum quantum numbers. The results may be directly relevant to the physics
of dipolar gases loaded into optical lattices.Comment: 9 pages, 4 figure
Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement
Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled
successfully using a zero-range delta-function potential, while that of bosonic
3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave
pseudo-potential. Here, we derive the eigenenergies of two spin-polarized 1D
fermions under external harmonic confinement interacting through a zero-range
potential, which only acts on odd-parity wave functions, analytically. We also
present a divergent-free zero-range potential treatment of two spin-polarized
3D fermions under harmonic confinement. Our pseudo-potential treatments are
verified through numerical calculations for short-range model potentials.Comment: 9 pages, 4 figures (subm. to PRA on 03/15/2004
Resonance phenomena in ultracold dipole-dipole scattering
Elastic scattering resonances occurring in ultracold collisions of either
bosonic or fermionic polar molecules are investigated. The Born-Oppenheimer
adiabatic representation of the two-bodydynamics provides both a qualitative
classification scheme and a quantitative WKB quantization condition that
predicts several sequences of resonant states. It is found that the
near-threshold energy dependence of ultracold collision cross sections varies
significantly with the particle exchange symmetry, with bosonic systems showing
much smoother energy variations than their fermionic counterparts. Resonant
variations of the angular distributions in ultracold collisions are also
described.Comment: 19 pages, 6 figures, revtex4, submitted to J. Phys.