  We consider the model of a single optical cavity mode interacting with
two-level systems (spins) driven by a linearly time-dependent field. When this
field passes through values at which spin energy level splittings become
comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ)
transitions leads to co-flips of spins in exchange for photons of the cavity.
We derive exact transition probabilities between different diabatic states
induced by such a sweep of the field.
