  Employing the time-dependent variational principle combined with the multiple
Davydov $\mathrm{D}_2$ Ansatz, we investigate Landau-Zener (LZ) transitions in
a qubit coupled to a photon mode with various initial photon states at zero
temperature. Thanks to the multiple Davydov trial states, exact photonic
dynamics taking place in the course of the LZ transition is also studied
efficiently. With the qubit driven by a linear external field and the photon
mode initialized with Schr\"odinger-cat states, asymptotic behavior of the
transition probability beyond the rotating-wave approximation is uncovered for
a variety of initial states. Using a sinusoidal external driving field, we also
explore the photon-assisted dynamics of Landau-Zener-St\"{u}ckelberg-Majorana
interferometry. Transition pathways involving multiple energy levels are
unveiled by analyzing the photon dynamics.
