A model study on a pair of trapped particles interacting with an arbitrary effective range

Abstract

We study the effects of the effective range of interaction on the eigenvalues and eigenstates of two particles confined in a three-dimensional (3D) isotropic as well as one- or quasi-one dimensional harmonic (1D) traps. For this we employ model potentials which mimic finite-range s-wave interactions over a wide range of s-wave scattering length $a_s$ including the unitarity limits $a_s\to \pm \infty$. Our results show that when the range is larger than the 3D or 1D harmonic oscillator length scale, the eigenvalues and eigenstates are nearly similar to those of noninteracting two particles in the 3D or 1D trap, respectively. In case of 3D, we find that when the range goes to zero, the results of contact potential as derived by Busch {\it et al.} [Foundations of Physics, {\bf28}, 549 (1998)] are reproduced. However, in the case of 1D, such reproducibility does not occur as the range goes to zero. We have calculated the eigenvalues and eigenstates in 1D harmonic trap taking one-dimensional finite- range model potential. We have also calculated bound state properties of two particles confined in a highly anisotropic quasi-1D trap taking three-dimensional finite-range model potential, and examined whether these quasi-1D results approach towards 1D ones as the aspect ratio $\eta$ of the radial to axial frequency of the trap increases. We find that if the range is very small compared to the axial size of the trap, then one can reach 1D regime for $\eta \ge 10000$. However, for large range, one can nearly get 1D results for smaller values of $\eta$. This study will be important for exploration of two-body or many body physics of trapped ultracold atoms interacting with narrow Feshbach resonance for which the effective range can be large.

References in corpus (29)

• Feshbach Resonances in Ultracold Gases
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Production of cold molecules via magnetically tunable Feshbach resonances
• Realization of Bose-Einstein condensates in lower dimensions
• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Regimes of quantum degeneracy in trapped 1D gases
• Interatomic collisions in a tightly confined Bose gas
• Confinement induced molecules in a 1D Fermi gas
• Observation of scale invariance and universality in two-dimensional Bose gases
• Atom-molecule coherence in Bose gases
• The transverse breathing mode of an elongated Bose-Einstein condensate
• Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps
• Resonant Fermi gases with a large effective range
• Scale invariance and viscosity of a two-dimensional Fermi gas
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Cold Atoms and Molecules in Self-Assembled Dipolar Lattices
• Two atoms in an anisotropic harmonic trap
• Three-dimensional strong localization of matter waves by scattering from atoms in a lattice with a confinement-induced resonance
• Realization of a Resonant Fermi Gas with a Large Effective Range
• Pseudopotential model of ultracold atomic collisions in quasi-one- and two-dimensional traps
• Supercurrent Stability in a Quasi-1D Weakly Interacting Bose Gas
• Alternative Route to Strong Interaction: Narrow Feshbach Resonance
• Bose-Einstein condensate in a harmonic trap decorated with Dirac delta functions
• Quantum scattering in one dimension
• Optical Control of the Scattering Length and Effective Range for Magnetically Tunable Feshbach Resonances in Ultracold Gases
• The two-body problem of ultra-cold atoms in a harmonic trap
• Breakdown of scale invariance in a quasi-two-dimensional Bose gas due to the presence of the third dimension
• Observation of transverse condensation via Hanbury Brown--Twiss correlations
• Finite-range model potentials for resonant interactions

Cited by in corpus (3)

• Modeling atom-atom interactions at low energy by Jost-Kohn potentials
• Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential
• Fermionic vs. bosonic two-site Hubbard models with a pair of interacting cold atoms