Analytical solution of the bosonic three-body problem

Abstract

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modelling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schrödinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

4 pages, published version

References in corpus (8)

• Universality in Few-body Systems with Large Scattering Length
• Production of cold molecules via magnetically tunable Feshbach resonances
• Evidence for Efimov quantum states in an ultracold gas of cesium atoms
• Three-boson problem near a narrow Feshbach resonance
• Efimov Physics in Cold Atoms
• Excited Thomas-Efimov levels in ultracold gases
• The few-body problem for trapped bosons with large scattering length
• Three-body problem for ultracold atoms in quasi-one-dimensional traps

Cited by in corpus (93)

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• Four-body Efimov effect
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• Few-body physics in resonantly interacting ultracold quantum gases
• Universal van der Waals Physics for Three Ultracold Atoms
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• Two-body and Three-body Contacts for Identical Bosons near Unitarity
• Testing universality of Efimov physics across broad and narrow Feshbach resonances
• Symmetries of Three Harmonically-Trapped Particles in One Dimension
• Polaronic atom-trimer continuity in three-component Fermi gases
• Precision Test of the Limits to Universality in Few-Body Physics
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• Functional renormalization for trion formation in ultracold fermion gases
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• Efimov Physics and Connections to Nuclear Physics
• Three Resonant Ultra-Cold Bosons: Off-Resonance Effects
• New type of crossover physics in three-component Fermi gases
• $N$-boson spectrum from a Discrete Scale Invariance
• Three-body recombination in heteronuclear mixtures at finite temperature
• Isotropic contact forces in arbitrary representation: heterogeneous few-body problems and low dimensions
• Observation of Efimov Universality across a Non-Universal Feshbach Resonance in \textsuperscript{39}K
• Electric dipole induced universality for Dirac fermions in graphene
• Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : Crossover from Efimovian to Hydrogenoid spectrum
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• Resonant atom-dimer collisions in cesium: Testing universality at positive scattering lengths
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• Ultracold three-body collisions near narrow Feshbach resonances
• Efimov Physics in 6Li Atoms
• Crossover in the Efimov spectrum
• Pinpointing Feshbach Resonances and Testing Efimov Universalities in ${}^{39}$K
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• Efimov physics and the three-body parameter for shallow van der Waals potentials
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• FFLO vs Bose-Fermi mixture in polarized 1D Fermi gas on a Feshbach resonance: a 3-body study
• Ultracold bosons in the vicinity of a narrow resonance: shallow dimer and recombination
• Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities
• Universal three-body physics at finite energy near Feshbach resonances
• Reshaped Three-Body Interactions and the Observation of an Efimov State in the Continuum
• Efimov Trimers in a Harmonic Potential
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• QCD-like phase diagram with Efimov trimers and Cooper pairs in resonantly interacting SU(3) Fermi gases
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• Efimov scenario for overlapping narrow Feshbach resonances
• Many Bosons in a Narrow Magnetic Feshbach Resonance
• Emergent inflation of the Efimov spectrum under three-body spin-exchange interactions
• An impurity immersed in a double Fermi Sea
• Two- and three-body problem with Floquet-driven zero-range interactions
• Few-body physics of ultracold atoms and molecules with long-range interactions
• Efimovian three-body potential from broad to narrow Feshbach resonances
• Three-body systems in physics of cold atoms and halo nuclei
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• Exact solution of the three-boson problem at vanishing energy
• Weakly bound molecules trapped with discrete scaling symmetries
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• Topological origin of universal few-body clusters in Efimov physics
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• Critical behavior for point monopole and dipole electric impurities in uniformily and uniaxially strained graphene
• Ultracold-atom collisions in atomic waveguides : A two-channel analysis
• The universality of the Efimov three-body parameter
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• Universality in Ultra-Cold Few- and Many-Boson Systems
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• Observation of an Efimov resonance in an ultracold mixture of atoms and weakly bound dimers
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• Universality in Ionic Three-body Systems Near an Ion-atom Feshbach Resonance
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