Comparative study of quartet superfluid state: Quartet Bardeen-Cooper-Schrieffer theory and generalized Nambu-Gor'kov formalism

TL;DR

This paper develops a theoretical framework for quartet superfluidity in fermionic matter, demonstrating the validity of the quartet BCS theory and analyzing spectral evolution across coupling regimes.

Contribution

It introduces a successful quartet BCS variational approach and generalized Nambu-Gor'kov formalism for four-body superfluid states, validated against exact results.

Findings

Quartet BCS theory reproduces exact four-body results in 1D Fermi gas.

The superfluid order parameter remains finite across the BCS-BEC crossover.

Single-particle spectra evolve from coherent quasiparticles to damped continuum with increasing interaction.

Abstract

We theoretically investigate a quartet superfluid state in fermionic matter by using the quartet Bardeen-Cooper-Schrieffer (BCS) variational theory and the Green's function method. We demonstrate that the quartet BCS theory with the multiple-infinite-product ansatz successfully reproduces an exact four-body result in a one-dimensional four-component Fermi gas at the dilute limit, in contrast to the single-infinite-product ansatz. To see the validity of the quartet BCS state, we derive the self-consistent equation for the quartet superfluid order parameter within the generalized imaginary-time Nambu-Gor'kov formalism, which is found to be consistent with the quartet BCS variational equation. Moreover, by numerically computing the momentum-resolved single-particle spectral function in a one-dimensional system, we discuss how the single-particle spectra evolve with increasing the strength of the four-body cluster formation. We show that a coherent BCS-like quasiparticle branch on the weak-coupling side evolves into a strongly damped, continuum-dominated spectrum in the strong-coupling side, while nonzero quartet superfluid order parameter persists throughout the crossover regime. Our results would be useful for understanding beyond-BCS pairing effects and four-body cluster formations in fermionic systems in an interdisciplinary way.