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

Abstract

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 total angular momentum $l$. For $\alpha$ increasing from 0, we find that the trimer states first appear at the $l$-dependent Efimovian threshold ${\alpha }_c^{(l)}$, where the Efimov exponent $s$ vanishes, and that the {\sl entire} trimer spectrum (starting from the ground trimer state) is geometric for $\alpha$ tending to ${\alpha }_c^{(l)}$ from above, with a global energy scale that has a finite and non-zero limit. For further increasing values of $\alpha$, the least bound trimer states still form a geometric spectrum, with an energy ratio $\exp (2\pi /|s|)$ that becomes closer and closer to unity, but the most bound trimer states deviate more and more from that geometric spectrum and eventually form a hydrogenoid spectrum.

26 pages, 8 figures; small improvements

References in corpus (22)

• The Unitary Fermi Gas: From Monte Carlo to Density Functionals
• Resonantly-paired fermionic superfluids
• Observation of an Efimov spectrum in an atomic system
• Exploring an ultracold Fermi-Fermi mixture: Interspecies Feshbach resonances and scattering properties of 6Li and 40K
• Three-boson problem near a narrow Feshbach resonance
• Observation of universality in ultracold 7Li three-body recombination
• Number of closed-channel molecules in the BEC-BCS crossover
• Radio Frequency Association of Efimov Trimers
• Low-energy three-body dynamics in binary quantum gases
• Analytical solution of the bosonic three-body problem
• Adiabatic association of ultracold molecules via magnetic field tunable interactions
• Three fully polarized fermions close to a p-wave Feshbach resonance
• Excited Thomas-Efimov levels in ultracold gases
• Crystalline phase of strongly interacting Fermi mixtures
• Study of Efimov physics in two nuclear-spin sublevels of 7Li
• Universal Fermi Gas with Two- and Three-Body Resonances
• Breakdown of universality for unequal-mass Fermi gases with infinite scattering length
• Single-Particle Momentum Distribution of an Efimov trimer
• Total control over ultracold interactions via electric and magnetic fields
• Three fermions in a box at the unitary limit: universality in a lattice model
• Crossover in the Efimov spectrum
• Exact solution of the three-boson problem at vanishing energy

Cited by in corpus (22)

• Efimov Physics: a review
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures
• Three-body recombination in heteronuclear mixtures at finite temperature
• Crossover trimers connecting continuous and discrete scaling regimes
• Third virial coefficient of the unitary Bose gas
• A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Three-body problem in a two-dimensional Fermi gas
• The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold
• Efimov effect for a three-particle system with two identical fermions
• Multichannel effects in the Efimov regime from broad to narrow Feshbach resonances
• Energy lower bound for the unitary N+1 fermionic model
• Scattering of universal fermionic clusters in the resonating group method
• Models of zero-range interaction for the bosonic trimer at unitarity
• The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas
• Mass-imbalanced fermionic mixture in a harmonic trap
• Three-body contact for fermions. I. General relations
• Efimov Trimers near the Zero-crossing of a Feshbach Resonance
• Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio
• Mass-ratio condition for non-binding of three two-component particles with contact interactions
• Shallow Trimers of Two Identical Fermions and One Particle in Resonant Regimes