arXiv:cond-mat/0209246 · Physical Review A

Three-body problem in Fermi gases with short-range interparticle interaction

Dmitry S. Petrov

Published Jan 29, 2003• 294 citations

Abstract

We discuss three-body processes in ultracold two-component Fermi gases with short-range intercomponent interaction characterized by a large and positive scattering length a. It is found that in most cases the probability of three-body recombination is a universal function of the mass ratio and a, and is independent of short-range physics. We also calculate the scattering length corresponding to the atom-dimer interaction.

DOI: 10.1103/physreva.67.010703

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arXiv:cond-mat/0209246 · Physical Review A

Three-body problem in Fermi gases with short-range interparticle interaction

Dmitry S. Petrov

Published Jan 29, 2003• 294 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.67.010703

Related papers

Effective-range corrections to three-body recombination for atoms with large scattering length

H.‐W. Hammer, Timo A. Lähde, Lucas Platter

Few-body systems with large scattering length $a$ have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass $m$ into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to $^{4}\mathrm{He}$ atoms as a test case.Few-body systems with large scattering length $a$ have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass $m$ into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to $^{4}\mathrm{He}$ atoms as a test case.

arXiv:cond-mat/0611769Physical Review AMar 22, 200722 citations

Three-Body Recombination of Ultracold Atoms to a Weakly Bound s Level

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O. I. Kartavtsev, A. V. Malykh

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass $m$ and a particle of the mass $m_1$ with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio $m/m_1$ for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at $m/m_1 \\ge \\lambda_1 \\approx 8.17260$ and $m/m_1 \\ge \\lambda_2 \\approx 12.91743$ , respectively. For $m/m_1 \\alt \\lambda_1$ and $m/m_1 \\alt \\lambda_2$ , the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass $m$ and a particle of the mass $m_1$ with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio $m/m_1$ for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at $m/m_1 \\ge \\lambda_1 \\approx 8.17260$ and $m/m_1 \\ge \\lambda_2 \\approx 12.91743$, respectively. For $m/m_1 \\alt \\lambda_1$ and $m/m_1 \\alt \\lambda_2$, the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.

Oct 28, 200655 citations

Atom-Dimer Scattering for Confined Ultracold Fermion Gases

Christophe Mora, Reinhold Egger, Alexander O. Gogolin +1 more

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.

arXiv:cond-mat/0406627Physical Review LettersOct 22, 200451 citations

Few-body systems with large scattering length

a

have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass

m

into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to

^{4}\mathrm{He}

atoms as a test case.

We discuss three-body recombination of ultracold atoms to a weakly bound

s

level. In this case, characterized by large and positive scattering length

a

for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: ${\ensuremath{\alpha}}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.9\ensuremath{\Elzxh}{a}^{4}/m$, where

m

is the atom mass.

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass

m

and a particle of the mass

m_1

with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio

m/m_1

for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at

m/m_1 \\ge \\lambda_1 \\approx 8.17260

and

m/m_1 \\ge \\lambda_2 \\approx 12.91743

, respectively. For

m/m_1 \\alt \\lambda_1

and

m/m_1 \\alt \\lambda_2

, the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.