  The entanglement properties of the time periodic Kitaev chain with nearest
neighbor and next nearest neighbor hopping, is studied. The cases of the exact
eigenstate of the time periodic Hamiltonian, referred to as the Floquet ground
state (FGS), as well as a physical state obtained from time-evolving an initial
state unitarily under the influence of the time periodic drive are explored.
Topological phases are characterized by different numbers of Majorana zero
($\mathbb{Z}_0$) and $\pi$ ($\mathbb{Z}_{\pi}$) modes, where the zero modes are
present even in the absence of the drive, while the $\pi$ modes arise due to
resonant driving. The entanglement spectrum (ES) of the FGS as well as the
physical state show topological Majorana modes whose number is different from
that of the quasi-energy spectrum. The number of Majorana edge modes in the ES
of the FGS vary in time from $|\mathbb{Z}_0-\mathbb{Z}_{\pi}|$ to
$\mathbb{Z}_0+\mathbb{Z}_{\pi}$ within one drive cycle, with the maximal
$\mathbb{Z}_0+\mathbb{Z}_{\pi}$ modes appearing at a special time-reversal
symmetric point of the cycle. For the physical state on the other hand, only
the modes inherited from the initial wavefunction, namely the $\mathbb{Z}_0$
modes, appear in the ES. The $\mathbb{Z}_{\pi}$ modes are absent in the
physical state as they merge with the bulk excitations that are simultaneously
created due to resonant driving. The topological properties of the Majorana
zero and $\pi$ modes in the ES are also explained by mapping the parent
wavefunction to a Bloch sphere.
