We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation, and the three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well-controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation, and the three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well-controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.

arXiv:1001.4371Physical Review AApr 28, 201095 citations

Three-Body Recombination in One-Dimensional Systems

Nirav P. Mehta, Chris H. Greene, Brett D. Esry

Bulletin of the American Physical SocietyMay 18, 20061 citation

Three-body losses of a polarized Fermi gas near a p -wave Feshbach resonance in effective field theory

Marcel Schmidt, H.‐W. Hammer, Lucas Platter

We study three-body recombination of fully spin-polarized $^{6}\mathrm{Li}$ atoms that are interacting resonantly in relative $p$ waves. Motivated by a recent experiment, we focus on negative scattering volumes where three atoms recombine into a deep dimer and another atom. We calculate the three-body recombination rate using a Faddeev equation derived from effective field theory. In particular, we study the magnetic field and temperature dependences of the loss rate and use the recombination data to determine the effective range of the $p$ -wave atom-atom interaction. We also predict the existence of a shallow three-body resonance state that manifests itself as a prominent feature in the energy-dependent three-body recombination rate.We study three-body recombination of fully spin-polarized $^{6}\mathrm{Li}$ atoms that are interacting resonantly in relative $p$ waves. Motivated by a recent experiment, we focus on negative scattering volumes where three atoms recombine into a deep dimer and another atom. We calculate the three-body recombination rate using a Faddeev equation derived from effective field theory. In particular, we study the magnetic field and temperature dependences of the loss rate and use the recombination data to determine the effective range of the $p$-wave atom-atom interaction. We also predict the existence of a shallow three-body resonance state that manifests itself as a prominent feature in the energy-dependent three-body recombination rate.

arXiv:1911.05749Physical Review AJun 1, 202024 citations

Three-body recombination of two-component cold atomic gases into deep dimers in an optical model

Mathias Mikkelsen, A. S. Jensen, D. V. Fedorov +1 more

Abstract We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering length is usually related to the non-equal two-body systems. We account for temperature smearing which tends to wipe out the higher-lying Efimov peaks. The range and the strength of the imaginary potential determine positions and shapes of the Efimov peaks as well as the absolute value of the recombination rate. The Efimov scaling between recombination peaks is calculated and shown to depend on both scattering lengths. Recombination is predicted to be largest for heavy–heavy–light systems. Universal properties of the optical parameters are indicated. We compare to available experiments and find in general very satisfactory agreement.Abstract We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering length is usually related to the non-equal two-body systems. We account for temperature smearing which tends to wipe out the higher-lying Efimov peaks. The range and the strength of the imaginary potential determine positions and shapes of the Efimov peaks as well as the absolute value of the recombination rate. The Efimov scaling between recombination peaks is calculated and shown to depend on both scattering lengths. Recombination is predicted to be largest for heavy–heavy–light systems. Universal properties of the optical parameters are indicated. We compare to available experiments and find in general very satisfactory agreement.

arXiv:1501.05137Journal of Physics B Atomic Molecular and Optical PhysicsMar 20, 201526 citations

We study three-body recombination of fully spin-polarized

^{6}\mathrm{Li}

atoms that are interacting resonantly in relative

p

waves. Motivated by a recent experiment, we focus on negative scattering volumes where three atoms recombine into a deep dimer and another atom. We calculate the three-body recombination rate using a Faddeev equation derived from effective field theory. In particular, we study the magnetic field and temperature dependences of the loss rate and use the recombination data to determine the effective range of the

p

-wave atom-atom interaction. We also predict the existence of a shallow three-body resonance state that manifests itself as a prominent feature in the energy-dependent three-body recombination rate.