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

Kartavtsev, O. I.; Malykh, A. V.; Sofianos, S. A.

doi:10.1134/s1063776109030017

Cited by 28 publications

(54 citation statements)

References 44 publications

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“…Therefore, we expect a scenario similar to the one discussed in this paper for these systems as well. We also note that a change in dimensionality would make this qualitatively different [33,34], which could be a subject of future study.…”

Section: Discussionmentioning

confidence: 91%

Crossover trimers connecting continuous and discrete scaling regimes

2012

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For a system of two identical fermions and one distinguishable particle interacting via a short-range potential with a large s-wave scattering length, the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of the mass ratio. The Efimov trimers are known to exhibit a discrete scaling invariance, while the Kartavtsev-Malykh trimers feature a continuous one. We point out that a third type of trimers, "crossover trimers", exist universally regardless of short-range details of the potential. These crossover trimers have neither discrete nor continuous scaling invariance. We show that the crossover trimers continuously connect the discrete and continuous scaling regimes as the mass ratio and the scattering length are varied. We identify the regions for the KartavtsevMalykh trimers, Efimov trimers, crossover trimers, and non-universal trimers in terms of the mass ratio and the s-wave scattering length by investigating the scaling property and universality (i.e. independence on short-range details) of the trimers.

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Section: Discussionmentioning

confidence: 91%

Crossover trimers connecting continuous and discrete scaling regimes

2012

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“…This corresponds to the continuum model studied in Ref. 28 . The convergence to the continuum result is studied in Fig.3 where we plot the ratio |E|/E b pair between the trimer and pair energies as a function of t −1/2 ↓ for decreasing values of the interaction strength |U |.…”

Section: Ground State Solutionmentioning

confidence: 99%

“…We also discuss new and unexpected results for the excited bound states. The three-body problem of interacting atoms with unequal mass has already attracted a lot of attention [23][24][25][26][27][28][29][30] . We will make contact with the corresponding results for the continuum model obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

Fermionic trimers in spin-dependent optical lattices

Orso¹,

Jolicœur²

2011

Comptes Rendus. Physique

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We investigate the formation of three-body bound states (trimers) in two-component Fermi gases confined in one dimensional optical lattice with spin-dependent tunneling rates. The binding energy and the effective mass of the trimer are obtained from the solution of the Mattis integral equation generalized to the case of unequal Bloch masses. We show that this equation admits multiple solutions corresponding to excited bound states, which are only stable for large mass asymmetry.

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“…Our full three-dimensional calculations for κ = 1 confirm, as suggested by Refs. [13,14,34], the absence of three-body bound states in the (Π ρ , M rel , Π z , a y ) = (+1, 0, ±1, +1) channels. Our calculations for κ > 1 are summarized in Secs.…”

Section: Three-body Bound States a General Considerationsmentioning

confidence: 99%

“…[13,14]. For unequal masses, the bound states of three particles in a waveguide have been investigated within a strictly onedimensional framework, in which the unlike particles interact through a one-dimensional δ-function potential with effective coupling constant g [33][34][35], and not yet within a full three-dimensional framework. It was found that three-body bound states are only supported if g is negative, corresponding to a ho /a 3D 1/1.03263 ≈ 0.96840, Π z = −1 and κ > 1.…”

Section: Three-body Bound States a General Considerationsmentioning

confidence: 99%

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

Blume

2014

Phys. Rev. A

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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.

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

Cited by 28 publications

References 44 publications

Crossover trimers connecting continuous and discrete scaling regimes

Crossover trimers connecting continuous and discrete scaling regimes

Fermionic trimers in spin-dependent optical lattices

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

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