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

Many-body Physics in One-dimensional Ultra-cold Atomic Systems

Bo-Bo Wei

Jan 1, 20110 citations

Low-energy three-body dynamics in binary quantum gases

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 mass m and a particle of mass m 1 with the zero-range two-body interaction in states of 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 dependences 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 ⩾ λ 1 ≈ 8.172 60 and m / m 1 ⩾ λ 2 ≈ 12.917 43, respectively. For m / m 1 ≲ λ 1 and m / m 1 ≲ λ 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 dependences of the cross sections is connected with the rise of the bound states.The universal three-body dynamics in ultra-cold binary Fermi and Fermi–Bose mixtures is studied. Two identical fermions of mass m and a particle of mass m 1 with the zero-range two-body interaction in states of 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 dependences 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 ⩾ λ 1 ≈ 8.172 60 and m / m 1 ⩾ λ 2 ≈ 12.917 43, respectively. For m / m 1 ≲ λ 1 and m / m 1 ≲ λ 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 dependences of the cross sections is connected with the rise of the bound states.

arXiv:physics/0610261Journal of Physics B Atomic Molecular and Optical PhysicsMar 15, 2007125 citations

Collective effects in RF-dressed 39 K ultra-cold gases

Alfred Hammond

Just like Van der Waals gases, quantum gases have some universal thermodynamic properties in deviation to the ideal gas. A dilute quantum fluid of neutral particles has an equation of state involving very few intrinsic parameters. The use of mixtures of two Bose-Einstein condensate allow for the diminution or even cancellation of some terms in the dynamical equation of the fluid. In this context, it was experimentally observed that the physics of an ultra-cold RF-dressed atomic gas (quantum coherent mixture) is much richer than in absence of RF coupling. On the one hand, collective effects usually insignificant - three body elastic interactions - rise and dominate the mean-field properties of the fluid. On the other hand, some beyond-mean field effects - interaction renormalization and quantum vacuum energy - are modified and enhanced. Consequently, We observed novel dynamical properties in potassium 39 RF dressed quantum gases.Just like Van der Waals gases, quantum gases have some universal thermodynamic properties in deviation to the ideal gas. A dilute quantum fluid of neutral particles has an equation of state involving very few intrinsic parameters. The use of mixtures of two Bose-Einstein condensate allow for the diminution or even cancellation of some terms in the dynamical equation of the fluid. In this context, it was experimentally observed that the physics of an ultra-cold RF-dressed atomic gas (quantum coherent mixture) is much richer than in absence of RF coupling. On the one hand, collective effects usually insignificant - three body elastic interactions - rise and dominate the mean-field properties of the fluid. On the other hand, some beyond-mean field effects - interaction renormalization and quantum vacuum energy - are modified and enhanced. Consequently, We observed novel dynamical properties in potassium 39 RF dressed quantum gases.

Sep 27, 20230 citations

Strongly Interacting Mixtures of Ultracold Atoms

Cheng-Hsun Wu, Ibon Santiago, Jee Woo Park +2 more

Bulletin of the American Physical SocietyMay 28, 20100 citations

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.