Non-resonant exponential Nikitin models with decay

Abstract

We analyzed the dissipative time-dependent Schrödinger equation in the frame of the decaying two-state problem with decay rates Γ1,2. We illustrated our vision through the exponential Nikitin model with decay, where the detuning is represented by two parts: the time-dependent exponential part and the static part characterized by the real part and the imaginary part. We studied two cases of the Rabi frequency: in the first case, the Rabi frequency is constant and we denoted this model by EXP1, in the second case the Rabi frequency is a time-dependent exponential function, and this model is denoted by EXP2. Due to its multiple applications, the description of the Nikitin model is extended to the limiting case in the short and rapid time approximation, these variations make possible the assimilation of the Nikitin model to the Rabi and Landau–Zener model in the short time variation, while in the rapid time approximation, this model corresponds only to the Rabi model. The analytical description of the Nikitin model is in perfect agreement with the numerical results. Exact analytical and numerical solutions to dissipative Schrödinger equations with exponential Nikitin models are obtained for all possible initial moments instead of t0=−∞ and t0=0 with the help of the confluent hypergeometric functions.