Functional renormalization for trion formation in ultracold fermion gases

Abstract

The energy spectrum for three species of identical fermionic atoms close to a Feshbach resonance is computed by use of a nonperturbative flow equation. Already a simple truncation shows that for large scattering length $|a|$ the lowest energy state is a "trion" (or trimer) bound state of three atoms. At the location of the resonance, for $|a|\to \infty$, we find an infinite set of trimer bound states, with exponentially decreasing binding energy. This feature was pointed out by Efimov. It arises from limit cycle scaling, which also leads to a periodic dependence of the three body scattering coupling on $\ln |a|$. Extending our findings by continuity to nonzero density and temperature we find that a "trion phase" separates a BEC and a BCS phase, with interesting quantum phase transitions for T=0.

9 pages, 4 figures, minor changes, reference added

References in corpus (7)

• Collisional stability of a three-component degenerate Fermi gas
• Three-boson problem near a narrow Feshbach resonance
• Analytical solution of the bosonic three-body problem
• BCS pairing in Fermi systems with several flavors
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Particle-hole fluctuations in the BCS-BEC Crossover
• Three-body scattering from nonperturbative flow equations

Cited by in corpus (3)

• Exact flow equation for composite operators
• Efimov effect from functional renormalization
• Three-body loss in lithium from functional renormalization