  We analyze the formation of maximally entangled Rydberg atom pairs subjected
to Landau-Zener sweeps of the atom-light detuning. Though the populations reach
a steady value at longer times, the phases evolve continuously, leading to
periodic oscillations in the entanglement entropy. The local unitary
equivalence between the obtained maximally entangled states and the Bell states
is verified by computing the polynomial invariants. Finally, we study the
effect of spontaneous emission from the Rydberg state of rubidium atoms on the
correlation dynamics and show that the oscillatory dynamics persists for
high-lying Rydberg states. Our study may offer novel ways to generate maximally
entangled states, quantum gates and exotic quantum matter in arrays of Rydberg
atoms through Landau Zener sweeps.
