Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : Crossover from Efimovian to Hydrogenoid spectrum

  title={Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : Crossover from Efimovian to Hydrogenoid spectrum},
  author={Yvan Castin and Edoardo Tignone},
  journal={Physical Review A},
We study the quantum three-body free space problem of two same-spin-state fermions of mass $m$ interacting with a different particle of mass $M$, on an infinitely narrow Feshbach resonance with infinite $s$-wave scattering length. This problem is made interesting by the existence of a tunable parameter, the mass ratio $\alpha=m/M$. By a combination of analytical and numerical techniques, we obtain a detailed picture of the spectrum of three-body bound states, within {\sl each} sector of fixed… 

Figures from this paper

General relations for quantum gases in two and three dimensions: Two-component fermions

We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them

Mass-imbalanced fermionic mixture in a harmonic trap

The mass-imbalanced fermionic mixture is studied, where $N\le5$ identical fermions interact resonantly with an impurity, a distinguishable atom. The shell structure is explored, and the physics of a

Efimov Effect for a Three-Particle System with Two Identical Fermions

We consider a three-particle quantum system in dimension three composed of two identical fermions of mass one and a different particle of mass m. The particles interact via two-body short range

Unitary boson-boson and boson-fermion mixtures: third virial coefficient and three-body parameter on a narrow Feshbach resonance

Abstract We give exact integral expressions of the third cluster or virial coefficients of binary mixtures of ideal Bose or Fermi gases, with interspecies interactions of zero range and infinite

Efimov Trimers Near the Zero-crossing of a Feshbach Resonance

Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question

Models of zero-range interaction for the bosonic trimer at unitarity

We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero

Shallow trimers of two identical fermions and one particle in resonant regimes

We consider two identical fermions interacting in the p-wave channel. Each fermion also interacts with another particle in the vicinity of an s-wave resonance. We find that in addition to the

Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures.

The five-body Efimov effect for this system in the regime where any of its subsystem is non-Efimovian is predicted, which is smaller than the corresponding 2+1 and 3+1 thresholds.

A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity

We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the

Three-body problem in a two-dimensional Fermi gas

We investigate the three-body properties of two identical ↑ fermions and one distinguishable ↓ atom interacting in a strongly confined two-dimensional geometry. We compute exactly the atom-dimer



Three fully polarized fermions close to a p-wave Feshbach resonance

We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p-wave channel via a Feshbach resonance represented by a two-channel

Low-energy three-body dynamics in binary quantum gases

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 m1 with the zero-range two-body interaction in

Three-body problem in heteronuclear mixtures with resonant interspecies interaction

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

Evidence for Efimov quantum states in an ultracold gas of caesium atoms

The observation of an Efimov resonance in an ultracold gas of caesium atoms is reported and represents a starting point with which to explore the universal properties of resonantly interacting few-body systems.

Breakdown of universality for unequal-mass Fermi gases with infinite scattering length.

It is found that unequal-mass Fermi gases are, for sufficiently large κ and in the regime where Efimov physics is absent, not universal.

Conventional character of the BCS-BEC crossover in ultracold gases of {sup 40}K

We use the standard fermionic and boson-fermion Hamiltonians to study the BCS-BEC crossover near the 202 G resonance in a two-component mixture of fermionic {sup 40}K atoms employed in the experiment

Universal fermi gas with two- and three-body resonances.

The resulting Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity, is considered, which is scale invariant and has universal properties, and is very strongly interacting.

Excited Thomas-Efimov levels in ultracold gases

Since the early days of quantum physics, the complex behavior of three interacting particles has been the subject of numerous experimental and theoretical studies. In a recent Letter to Nature,