The few-body problem for trapped bosons with large scattering length

Abstract

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm{o}sc}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\theta$. For large positive $a/a_{\mathrm{o}sc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\theta$. For other states the $\theta$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm{o}sc}|\gg 1$.

4 pages, 3 figures

References in corpus (7)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Controlled Collapse of a Bose-Einstein Condensate
• Strongly enhanced inelastic collisions in a Bose-Einstein condensate near Feshbach resonances
• Fermi systems with long scattering lengths
• Three-body recombination in Bose gases with large scattering length
• Cold Bose gases with large scattering lengths
• The Dilute Bose-Einstein Condensate with Large Scattering Length

Cited by in corpus (49)

• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Few-body physics with ultracold atomic and molecular systems in traps
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Observation of the Second Triatomic Resonance in Efimov's Scenario
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Analytical solution of the bosonic three-body problem
• Universal properties of a trapped two-component Fermi gas at unitarity
• Effective Theory for Trapped Few-Fermion Systems
• Virial theorems for trapped cold atoms
• Excited Thomas-Efimov levels in ultracold gases
• Symmetries of Three Harmonically-Trapped Particles in One Dimension
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Two-component Fermi gas with a resonant interaction
• Single-Particle Momentum Distribution of an Efimov trimer
• The Hyperspherical Four-Fermion Problem
• Production of three-body Efimov molecules in an optical lattice
• The Unitary Gas and its Symmetry Properties
• Third virial coefficient of the unitary Bose gas
• Efimov trimers under strong confinement
• Energy and structural properties of $N$-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator
• Three-fermion problems in optical lattices
• On Non-Relativistic Conformal Field Theory and Trapped Atoms: Virial Theorems and the State-Operator Correspondence in Three Dimensions
• The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold
• The few scales of nuclei and nuclear matter
• Efimov physics and the three-body parameter for shallow van der Waals potentials
• Correlated N-boson systems for arbitrary scattering length
• Non-universal bound states of two identical heavy fermions and one light particle
• Universal few-body physics in a harmonic trap
• Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap
• Lieb-Thirring Inequality for a Model of Particles with Point Interactions
• Occupation numbers of the harmonically trapped few-boson system
• Efimov Trimers in a Harmonic Potential
• Broken scale-invariance in time-dependent trapping potentials
• Harmonically Trapped Four-Boson System
• Temperature-dependence of small harmonically trapped atom systems with Bose, Fermi and Boltzmann statistics
• Universal and non-universal effective $N$-body interactions for ultracold harmonically-trapped few-atom systems
• D-dimensional three-body bound-state problem with zero range interactions
• Convergence Properties of the Effective Theory for Trapped Bosons
• Hyperspherical-LOCV Approximation to Resonant BEC
• Quench dynamics of mass-imbalanced three-body fermionic systems in a spherical trap
• Efimov states with strong three-body losses
• Universality in Ultra-Cold Few- and Many-Boson Systems
• Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity
• Effects of Efimov states on quench dynamics in a three-boson trapped system
• Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
• Triviality of a model of particles with point interactions in the thermodynamic limit
• Energetics and structural properties of two- and three-boson systems in the presence of 1D spin-orbit coupling