Ginzburg-Landau Formalism for 2n-Body Condensation

TL;DR

This paper develops a Ginzburg-Landau formalism for 2n-body condensation in Fermi superfluids, predicting stable multi-particle condensed states in cold atomic gases like ytterbium isotopes.

Contribution

It introduces a compact Ginzburg-Landau approach for 2n-body condensation, simplifying transition temperature calculations and predicting possible multi-particle superfluid states in atomic gases.

Findings

2n-body condensation transition temperature derived from quadratic coefficient

Stability of 2n-body states in intermediate/strong coupling regimes

Prediction of sextet superfluid state in $^{173}$Yb atomic gas

Abstract

The Ginzburg-Landau formalism is constructed for Fermi superfluidity based on the 2n-body condensation in parallel with the usual Ginzburg-Landau formalism for the Cooper pair condensation. By this formalism, the transition temperature of the 2n-body condensation is given compactly by the zero of coefficient of the quadratic term in the 2n-body condensed order parameter without counting complicated Feynman diagrams for the 2n-body condensation susceptibility. It is shown that the 2n-body condensed state is stabilized in the intermediate- or strong-coupling regime against the BCS state based on the Cooper pair condensation. This theory is applied to the case of the possible superfluid state of cold atomic gases such as $^9$Be and $^{173}$Yb; the quartet state is possible in the former case, while the sextet state is expected in the latter case. It is predicted that the $^{173}$Yb atomic gas so far attained satisfies the condition for the sextet condensed state to be realized.