Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

Abstract

The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass $m$ and a different one of mass $m_1$, which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio $m/m_1$, at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength ${\lambda }_1$ of the identical particles. A number of exact results are enlisted and asymptotic dependences both for $m/m_1\to \infty$ and ${\lambda }_1\to -\infty$ are derived. Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.

References in corpus (16)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Observation of Phase Separation in a Strongly-Interacting Imbalanced Fermi Gas
• Localization of bosonic atoms by fermionic impurities in a 3d optical lattice
• Two-dimensional Bose-Einstein condensate in an optical surface trap
• Spin dynamics in a one-dimensional ferromagnetic Bose gas
• Low-energy three-body dynamics in binary quantum gases
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Molecular superfluid phase in systems of one-dimensional multicomponent fermionic cold atoms
• Composite fermionization of 1-D Bose-Bose mixtures
• Feshbach resonances in mixtures of ultracold ${}^6$Li and ${}^{87}$Rb gases
• Ferromagnetic behaviour in the strongly interacting two-component Bose gas
• Atom-dimer scattering for confined ultracold fermion gases
• Universal low-energy properties of three two-dimensional particles
• Three-Body Recombination in One Dimension
• On the stability of Bose-Fermi mixtures
• One-dimensional Bose chemistry: effects of non-integrability

Cited by in corpus (29)

• Efimov Physics: a review
• Universal 1+2-body bound states in planar atomic wave guides
• Quantum mixtures of ultracold gases of neutral atoms
• Universal bound states of one-dimensional bosons with two- and three-body attractions
• Crossover trimers connecting continuous and discrete scaling regimes
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• A Pure Confinement Induced Trimer in One-Dimensional Atomic Waveguides
• Universal physics of 2+1 particles with non-zero angular momentum
• Diffractive scattering of three particles in one dimension: a simple result for weak violations of the Yang--Baxter equation
• Binding of heavy fermions by a single light atom in one dimension
• Quartet Superfluid in Two-dimensional Mass-imbalanced Fermi Mixtures
• Universality in a one-dimensional three-body system
• Emergence of Crystalline Few-body Correlations in Mass-imbalanced Fermi Polarons
• The three-body pseudo-potential for atoms confined in one dimension
• Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement
• Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice
• Universality of excited three-body bound states in one dimension
• Mass Ratio Dependence of Three-Body Resonance Lifetimes in 1D and 3D
• Competing few-body correlations in ultracold Fermi polarons
• Three-body bound states of two bosons and one impurity in one dimension
• Fermionic trimers in spin-dependent optical lattices
• Three-body bound states in a harmonic waveguide with cylindrical symmetry
• Self-binding of one-dimensional fermionic mixtures with zero-range interspecies attraction
• Universal clusters in quasi-two-dimensional ultracold Fermi mixtures
• Heavy-light $N+1$ clusters of two-dimensional fermions
• Effective theory for strongly attractive one-dimensional fermions
• Shallow Trimers of Two Identical Fermions and One Particle in Resonant Regimes
• Absence of binding of heavy fermions by two light atoms in two dimensions
• From three-body resonances to bound states in a continuum: pole trajectories