Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement

Abstract

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.

9 pages, 4 figures (subm. to PRA on 03/15/2004)

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• One-dimensional mixtures of several ultracold atoms: a review
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• Pseudopotential method for higher partial wave scattering
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Ground-state properties of one-dimensional anyon gases
• Probing many-body interactions in an optical lattice clock
• Generalized Pseudopotentials for Higher Partial Wave Scattering
• Mixed partial-wave scattering with spin-orbit coupling and validity of pseudo-potentials
• Universal One-dimensional Atomic Gases Near Odd-wave Resonance
• Modeling interactions for resonant p-wave scattering
• Pseudo-potential treatment of two aligned dipoles under external harmonic confinement
• Coupled-channel pseudo-potential description of the Feshbach resonance in two dimensions
• Quantum Scattering in Quasi-1D Cylindrical Confinement
• Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions
• Modeling light shifts in optical lattice clocks
• Observation of unitary p-wave interactions between fermions in an optical lattice
• Low-energy resonances and bound states of aligned bosonic and fermionic dipoles
• Feshbach resonance scattering under cylindrical harmonic confinement
• Optical Feshbach resonances of Alkaline-Earth atoms in a 1D or 2D optical lattice
• Analytical solutions for two atoms in a harmonic trap: p-wave interactions
• Tunneling dynamics of two interacting one-dimensional particles
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Stretching p-wave molecules by transverse confinements
• High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap
• Evaporative cooling of reactive polar molecules confined in a two-dimensional geometry
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Probing open- and closed-channel p-wave resonances
• Reactive collisions in confined geometries
• Effective super Tonks-Girardeau gases as ground states of strongly attractive multi-component fermions
• Trap-induced resonances in controlled collisions of cesium atoms
• Universality of internal correlations of strongly interacting p-wave fermions in one-dimensional geometry
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• A quasi-Hermitian pseudopotential for higher partial wave scattering
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• Scattering Hypervolume of Spin-Polarized Fermions
• Ground-state properties of dilute spinless fermions in fractional dimensions
• Excitation spectrum and effective interactions of highly-elongated Fermi gas
• Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules
• p-wave phase shift and scattering length of ${}^6$Li
• K-matrix formulation of two-particle scattering in a wave guide in the presence of one-dimensional spin-orbit coupling
• Controlling ultracold $p$-wave collisions with non-resonant light: Predictions of an asymptotic model for the generalized scattering volume
• Analytical treatment of bosonic d-wave scattering in isotropic harmonic waveguides
• Reactive collisions of two ultracold particles in a harmonic trap
• Temperature dependence of $p$-wave contacts in a harmonically trapped Fermi gas
• Correlations in many-body systems with the Stochastic Variational Method
• Analytical solutions of the Schrödinger equation for two confined atoms with van der Waals interaction
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement