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 κ and the free-space s-wave scattering length a3D 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 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 rel | = 1 and positive parity in z. These bound states arise on the positive s-wave scattering length side if the mass ratio κ is sufficiently large. Implications of our results for ongoing cold atom experiments are discussed.

Universal few-body physics and cluster formation

“…Theoretically, the few-body collisions in the presence of external confinement are investigated by (Günter et al, 2005).) (Blume, 2014;Gharashi et al, 2012;Mora et al, 2005aMora et al, , 2004Mora et al, , 2005b addressing the three and four-body aspects of the confinement-induced physics where a detailed discussion can be found in the excellent review by (Blume, 2012a). (Günter et al, 2005) experimentally investigated pwave collisions of spin-polarized fermions in the presence of cigar-shaped and pancake traps.…”

Universality of excited three-body bound states in one dimension

“…However, it is important to keep in mind that experiments employing these confined systems are always performed in quasi-1D. The conditions to reproduce the results predicted by a pure 2D model in a quasi-2D experiment and accordingly by a 1D model in a quasi-1D setup have been discussed in references [47][48][49].…”