We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a $p$ -wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a $p$-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

arXiv:1407.7664Physical Review ADec 22, 201423 citations

On the Efimov effect in higher partial waves

K. Helfrich, H.‐W. Hammer

Using the framework of effective field theory, we present a detailed study of the Efimov effect in higher partial waves for systems of two identical particles and a third distinguishable particle. Depending on the total angular momentum $L$ , the two identical particles must be bosons or fermions. We derive analytical expressions for the elastic and inelastic atom-dimer scattering cross sections as well as the atom-dimer relaxation rate at the dimer breakup threshold. For the experimentally most relevant case of P-waves, we numerically calculate the atom-dimer scattering cross sections and relaxation rates as a function of the scattering length, three-body parameter, and mass ratio for energies away from the breakup threshold.Using the framework of effective field theory, we present a detailed study of the Efimov effect in higher partial waves for systems of two identical particles and a third distinguishable particle. Depending on the total angular momentum $L$, the two identical particles must be bosons or fermions. We derive analytical expressions for the elastic and inelastic atom-dimer scattering cross sections as well as the atom-dimer relaxation rate at the dimer breakup threshold. For the experimentally most relevant case of P-waves, we numerically calculate the atom-dimer scattering cross sections and relaxation rates as a function of the scattering length, three-body parameter, and mass ratio for energies away from the breakup threshold.

arXiv:1107.0869Journal of Physics B Atomic Molecular and Optical PhysicsOct 18, 201125 citations

The symmetry and Efimov's effect in systems of three-quantum particles

Semjon A. Vugalter, G. M. Zhislin

Communications in Mathematical PhysicsMar 1, 198225 citations

Efimov effect and higher bound states in a three-particle system

A.C.B. Antunes, Vera Lúcia Vieira Baltar, Erasmo M. Ferreira

Nuclear Physics AJul 1, 197617 citations

Bound States in a Quasi-Two-Dimensional Fermi Gas

Jesper Levinsen, Meera M. Parish

We consider the problem of $N$ identical fermions of mass ${m}_{\ensuremath{\uparrow}}$ and one distinguishable particle of mass ${m}_{\ensuremath{\downarrow}}$ interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For $N=2$ and mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}<13.6$, we find non-Efimov trimers that smoothly evolve from 2D to 3D. In the limit of strong 2D confinement, we show that the energy of the $N+1$ system can be approximated by an effective two-channel model. We use this approximation to solve the $3+1$ problem and we find that a bound tetramer can exist for mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions.We consider the problem of $N$ identical fermions of mass ${m}_{\ensuremath{\uparrow}}$ and one distinguishable particle of mass ${m}_{\ensuremath{\downarrow}}$ interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For $N=2$ and mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}<13.6$, we find non-Efimov trimers that smoothly evolve from 2D to 3D. In the limit of strong 2D confinement, we show that the energy of the $N+1$ system can be approximated by an effective two-channel model. We use this approximation to solve the $3+1$ problem and we find that a bound tetramer can exist for mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions.

arXiv:1207.0459Physical Review LettersJan 29, 201342 citations

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a

p

-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

L

, the two identical particles must be bosons or fermions. We derive analytical expressions for the elastic and inelastic atom-dimer scattering cross sections as well as the atom-dimer relaxation rate at the dimer breakup threshold. For the experimentally most relevant case of P-waves, we numerically calculate the atom-dimer scattering cross sections and relaxation rates as a function of the scattering length, three-body parameter, and mass ratio for energies away from the breakup threshold.

We consider the problem of

N

identical fermions of mass ${m}_{\ensuremath{\uparrow}}$ and one distinguishable particle of mass ${m}_{\ensuremath{\downarrow}}$ interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For

N=2

and mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}<13.6$, we find non-Efimov trimers that smoothly evolve from 2D to 3D. In the limit of strong 2D confinement, we show that the energy of the

N+1

system can be approximated by an effective two-channel model. We use this approximation to solve the

3+1

problem and we find that a bound tetramer can exist for mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions.