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We explore both pure and mixed states Floquet dynamical quantum phasetransitions (FDQFTs) in the one-dimensional p-wave superconductor with atime-driven pairing phase. In the Fourier space, the model is recast to thenon-interacting quasi-spins subjected to a time-dependent effective magneticfield. We show that FDQFTs occur within a range of driving frequency withoutresorting to any quenches. Moreover, FDQFTs appear in the region wherequasi-spins are in the resonance regime. In the resonance regime, thepopulation completely cycles the population between the spin down and upstates. Additionally, we study the conditions for the appearance of FDQFTsusing the entanglement spectrum and purity entanglement measure. Our resultsimply that the entanglement spectrum can truly capture the resonance regimewhere FDQFTs occur. Particularly, the dynamical topological region results inthe degeneracy of the entanglement spectrum. It is shown that the boundary ofthe driven frequency range, over which the system reveals FDQFTs, signaled bythe purity entanglement measure.

Floquet dynamical phase transition and entanglement spectrum