Three-body bound states in a harmonic waveguide with cylindrical symmetry

Abstract

Highly-elongated quasi-one-dimensional cold atom samples have been studied extensively over the past years experimentally and theoretically. This work determines the energy spectrum of two identical fermions and a third distinguishable particle as functions of the mass ratio $\kappa$ and the free-space $s$-wave scattering length $a_{3\text{D}}$ between the identical fermions and the distinguishable third particle in a cylindrically symmetric waveguide whose symmetry axis is chosen to be along the $z$-axis. We focus on the regime where the mass of the identical fermions is equal to or larger than that of the third distinguishable particle. Our theoretical framework accounts explicitly for the motion along the transverse confinement direction. In the regime where excitations in the transverse direction are absent (i.e., for states with projection quantum number $M_{\text{rel}}=0$), we determine the binding energies for states with odd parity in $z$. These full three-dimensional energies deviate significantly from those obtained within a strictly one-dimensional framework when the $s$-wave scattering length is of the order of or smaller than the oscillator length in the confinement direction. If transverse excitations are present, we predict the existence of a new class of universal three-body bound states with $|M_{\text{rel}}|=1$ and positive parity in $z$. These bound states arise on the positive $s$-wave scattering length side if the mass ratio $\kappa$ is sufficiently large. Implications of our results for ongoing cold atom experiments are discussed.

arXiv comment9 figures

References in corpus (26)

• Many-Body Physics with Ultracold Gases
• Feshbach Resonances in Ultracold Gases
• Theory of ultracold Fermi gases
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Universality in Few-body Systems with Large Scattering Length
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Three-body forces: From cold atoms to nuclei
• Exploring an ultracold Fermi-Fermi mixture: Interspecies Feshbach resonances and scattering properties of 6Li and 40K
• Three-body problem in Fermi gases with short-range interparticle interaction
• Quantum degenerate two-species Fermi-Fermi mixture coexisting with a Bose-Einstein condensate
• Few-body physics with ultracold atomic and molecular systems in traps
• Low-energy three-body dynamics in binary quantum gases
• Universal Fermi gases in mixed dimensions
• Broad Feshbach resonance in the 6Li-40K mixture
• Collisional Stability of 40K Immersed in a Strongly Interacting Fermi Gas of 6Li
• Atom-dimer scattering and long-lived trimers in fermionic mixtures
• Spectrum and Dynamics of the BCS-BEC crossover from a few-body perspective
• Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient
• Observation of a Strong Atom-Dimer Attraction in a Mass-Imbalanced Fermi-Fermi Mixture
• Universal 1+2-body bound states in planar atomic wave guides
• Atom-dimer scattering for confined ultracold fermion gases
• Three-body problem for ultracold atoms in quasi-one-dimensional traps
• Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement
• Three s-wave interacting fermions under anisotropic harmonic confinement: Dimensional crossover of energetics and virial coefficients
• Universal physics of 2+1 particles with non-zero angular momentum
• Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions

Cited by in corpus (3)

• Universal few-body physics and cluster formation
• Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
• Universality of excited three-body bound states in one dimension