Functional renormalization for trion formation in ultracold fermion gases

TL;DR

This paper uses a nonperturbative flow equation approach to study three-atom bound states in ultracold fermionic gases near a Feshbach resonance, revealing Efimov states and a trion phase separating BEC and BCS phases.

Contribution

It introduces a nonperturbative flow equation method to analyze trion formation and Efimov states in ultracold fermions, extending understanding of quantum phase transitions.

Findings

Existence of Efimov trimer states at resonance

Infinite set of trimer bound states with decreasing binding energy

Identification of a trion phase separating BEC and BCS phases

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.