Solution to the Landau–Zener problem via Susskind–Glogower operators

We show that, by means of a right-unitary transformation, the fully quantized Landau–Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau–Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau–Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.

► We study a full quantum Landau–Zener model derived from the Jaynes–Cummings model.
► The model within the rotating wave appoximation is diagonalized in the field basis.
► Solutions to the quantum model are presented in terms of well-know solutions to the classical Landau–Zener problem.
► The model without the rotating wave appoximation is diagonalized in the qubit basis.