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Exploiting the possibility of temporal variation of the winding number, wehave prepared a SSH chain in its {\it stroboscopic} topological state, startingfrom the trivial one, by application of a periodic perturbation. The periodicdriving, we employ here, is adiabatically switched on to break theparticle-hole symmetry and generate a chiral mass term in the effective FloquetHamiltonian; consequently the Floquet Hamiltonian also gets deformed withoutcrossing the gapless quantum critical point. The particle hole symmetry issubsequently restored in the Floquet Hamiltonian by adiabatically switching offa part of the periodic potential. Thereafter, the Floquet Hamiltonian developsa symmetry protected non-trivial topological winding number. Furthermore, wealso observe stroboscopic topologically protected localised edge states in along open chain and show that a bulk boundary correspondence survives a unitarynon-equilibrium situation in 1D BDI Hamiltonians. Moreover, considering anextended SSH chain with higher neighbour hoppings, we dynamically prepare thesystem in a stroboscopic out-of-equilibrium topological insulator statestarting from a metallic regime. At the same time, we establish the dynamicalpreparation of higher winding phases in an extended SSH chain with stroboscopicbulk-boundary correspondence in the non-equilibrium state of the system.

Dynamical preparation of a topological state and out of equilibrium bulk boundary correspondence in a SSH chain under periodic driving