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

TL;DR

This work analyzes a two-dimensional spin-polarized attractive Fermi-Hubbard model on a square optical lattice under a Zeeman field to study FFLO order. By computing density and spin dynamical structure factors within Random Phase Approximation, it identifies a phonon mode in the density channel and a bogolon mode in the spin channel, with a roton feature that evolves from a point at $[{\pi},{\pi}]$ to a ring of radius $|\mathbf Q|$, enabling a roton-based protocol to extract the Cooper-pair momentum. The results reveal strong anisotropy in dynamical excitations due to finite ${\bf Q}$ and show that the roton mode’s displacement provides a direct measure of $|\mathbf Q|$ at half-filling, while doping modulates the roton gap and structure. These findings offer concrete signatures for FFLO superfluidity and guidance for experimental detection via Bragg spectroscopy in ultracold atoms on optical lattices.

Abstract

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.

Figures (12)

• Figure 1: Free energy $F=\Omega+{\mu}N$ as a function of $h$ for $t/U=0.3$, respectively. The vertical dotted line marks the BCS-FFLO superfluid phase transition at $h_{\rm c}/U=0.202$.
• Figure 2: Density dynamical structure factor $S_{D}({\bf q},{\omega})$ for (a) $h/U=0.19$ (BCS superfluid) and (b) $h/U=0.1978$ (FFLO superfluid) along $[0,0]\rightarrow [\pi,0]\rightarrow [\pi,\pi]\rightarrow [0,\pi]\rightarrow[0,0]$ in the BZ with $n=1.0$. The white dashed lines exhibit the solution of ${\rm Re}\Sigma=0$ as a function of ${\bf q}$.
• Figure 3: Spin dynamical structure factor $S_{S}({\bf q},{\omega})$ (a) $h=0.19$ (BCS superfluid) and (b) $h/U=0.1978$ (FFLO superfluid).
• Figure 4: (a) $S_{D}({\bf q},{\omega})$ and (b) $S_{S}({\bf q},{\omega})$ of an FFLO superfluid in the low transferred momentum region along $[0,0]\rightarrow [\pi,0]$. (c) $S_{D}({\bf q}=[0.1,0],{\omega})$ (red solid line) and $S_{S}({\bf q}=[0.1,0],{\omega})$ (blue dashed line) as a function of $\omega$; (d) peak positions of two collective modes extracted from $S_{D}({\bf q},{\omega})$ and $S_{S}({\bf q},{\omega})$. Here, the parameters $h/U=0.1978$, $t/U=0.3$, and $n=1$.
• Figure 5: $S_{D}({\bf q},{\omega})$ along the path $[\pi,0]\rightarrow [\pi,\pi]\rightarrow [\pi,2\pi]$ for (a) $t/U=0.3$, (b) $0.35$, (c) $0.4$, and (d) $0.43$.