Novel dynamical excitations and roton-based measurement of Cooper-pair momentum in a two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov superfluid on optical lattices

Determining the center-of-mass (COM) momentum of Cooper pairs in unconventional superconductors or superfluids is a topic of great interest in condensed matter physics and ultracold atomic gases. Theoretically, we investigate the dynamical excitations of a two-dimensional spin-polarized attractive Hubbard model on a square optical lattice under an effective Zeeman field by computing the density and spin dynamical structure factors, focusing on phase transition from a Bardeen-Cooper-Schrieffer (BCS) superfluid to an Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. In the FFLO superfluid, besides the phonon mode in the density channel, a low-energy bogolon mode emerges in the spin channel, which is associated with Bogoliubov quasiparticles on a Bogoliubov Fermi surface. Moreover, the dynamical excitations exhibit pronounced anisotropy in momentum space due to the finite COM momentum. At half filling, the roton mode around $[π,π]$ evolves from a point-like minimum into a ring structure shifted by the COM momentum across the BCS-FFLO transition, providing a roton-based protocol to extract the COM momentum. These predictions provide key insights for confirming the existence of FFLO superfluids and understanding their dynamical excitation spectra.

💡 Research Summary

This paper presents a comprehensive theoretical study of dynamical excitations in a two‑dimensional spin‑polarized attractive Hubbard model on a square optical lattice, focusing on the transition from a conventional Bardeen‑Cooper‑Schrieffer (BCS) superfluid to a Fulde‑Ferrell‑Larkin‑Ovchinnikov (FFLO) superfluid induced by an effective Zeeman field. Using a mean‑field treatment, the authors derive the quasiparticle spectra, the pairing gap Δ, and the center‑of‑mass (COM) momentum Q self‑consistently from the thermodynamic potential. When the Zeeman field exceeds a critical value h_c, the free energy minimum shifts from Q = 0 to a finite Q, signalling a first‑order BCS‑FFLO transition accompanied by a discontinuous drop in Δ.

To capture collective fluctuations beyond mean‑field, the random phase approximation (RPA) is employed. Four coupled density operators—spin‑up density, spin‑down density, pair‑creation, and pair‑annihilation—are assembled into a 4 × 4 response matrix χ₀(q,iωₙ). The RPA resummation χ = χ₀