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We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluidat a finite effective Zeeman field $h$, and study entire dynamical excitationsrelated to density perturbation. By calculating the density dynamic structurefactor, we find anisotropic dynamical excitations in both collective modes andsingle-particle excitations. Along the direction of centre-of-mass momentum$p$, there are two obvious gapless collective modes with different speed. Thelower collective modes is from the usual gauge symmetry breaking and has alarger speed than the one in the negative direction of $p$. The higher one isdue to the direction spontaneous symmetry breaking of centre-of-mass momentum$p$, and separates two kinds of single-particle excitations in the positive $p$direction. However, this higher mode disappears in the opposite direction of$p$, where two single-particle excitations overlap with each other. Thesesignals of dynamical excitations can do help to distinguish Fulde-Ferrellsuperfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in thefuture experiment.

Dynamical excitations of one-dimensional Fulde-Ferrell pairing Fermi superfluid