Analytical solutions for two atoms in a harmonic trap: p-wave interactions

Abstract

We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential, obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a p-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the p-wave Feshbach resonance.

13 pages, 5 figures

References in corpus (22)

• Ultracold heteronuclear molecules in a 3D optical lattice
• Molecules of Fermionic Atoms in an Optical Lattice
• Quantum phase transitions across p-wave Feshbach resonance
• p-Wave Interactions in Low-Dimensional Fermionic gases
• p-wave Feshbach molecules
• Tuning of heteronuclear interactions in a quantum-degenerate Fermi-Bose mixture
• Quantum theory of ultracold atom-ion collisions
• Anisotropic Fermi Superfluid via p-wave Feshbach Resonance
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Collisional Properties of p-Wave Feshbach Molecules
• Binding Energies of 6Li p-wave Feshbach Molecules
• Fermion Superfluids of Non-Zero Orbital Angular Momentum near Resonance
• Multichannel quantum-defect theory for slow atomic collisions
• Pseudopotential method for higher partial wave scattering
• BCS-BEC crossover in a gas of Fermi atoms with a p-wave Feshbach resonance
• Fermions in Optical Lattices across Feshbach Resonance
• Evolution from BCS to BEC superfluidity in p-wave Fermi gases
• Pseudopotential in resonant regimes
• Modeling interactions for resonant p-wave scattering
• Revised Huang-Yang multipolar pseudopotential
• Theory for p-Wave Feshbach Molecules
• A quasi-Hermitian pseudopotential for higher partial wave scattering

Cited by in corpus (25)

• Few-body physics with ultracold atomic and molecular systems in traps
• Experimental Determination of p-wave Scattering Parameters in ultracold 6Li atoms
• Observation of unitary p-wave interactions between fermions in an optical lattice
• The scattering amplitude of ultracold atoms near the p-wave magnetic Feshbach Resonance
• High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap
• Quantitative analysis of $p$-wave three-body losses via cascade process
• Controlled collisions of two ultracold atoms in separate harmonic traps
• Virial expansion coefficients in the harmonic approximation
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Reactive collisions in confined geometries
• Spin-polarized fermions with $p$-wave interactions
• Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices
• Two-body state with p-wave interaction in one-dimensional waveguides under transversely anisotropic confinement
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• Quantum state engineering with a trapped atom and a set of static impurities
• Scattering Hypervolume of Spin-Polarized Fermions
• Universal relations for a spin-polarized Fermi gas in two dimensions
• Miscibility of Binary Bose-Einstein Condensates with $p$-wave Interaction
• Stability of a Fully Polarized Ultracold Fermi Gas near Zero-Crossing of a p-wave Feshbach Resonance
• Analytical treatment of bosonic d-wave scattering in isotropic harmonic waveguides
• Reactive collisions of two ultracold particles in a harmonic trap
• Collective P-Wave Orbital Dynamics of Ultracold Fermions
• Analytical solutions of the Schrödinger equation for two confined atoms with van der Waals interaction
• Probing $p$-wave effects in spin-density separation of Bose mixtures with the dynamic structure factor
• Elastic collision rates of spin-polarized fermions in two dimensions