Spontaneous emission in an exponential model

The phenomenon of spontaneous emission can lead to the creation of an imaginary coupling and a shift. To explore this, we utilized the renormalized first Nikitin model, revealing an exponential detuning variation with a phase and an imaginary coupling along with the shift. By employing the time-dependent Schr\"odinger equation, we investigated the behavior of our system. Our findings indicate that the imaginary coupling provides specific information, while the shift generates allowed and forbidden zones in the energy diagram of the real part of the energy. In the diagram of the imaginary part of the energy, time dictates order or chaos in the system and identifies the information transmission zone. Notably, the first Nikitin model exhibits similarities to the Rabi model in the short-time approximation. Our theoretical conclusions are consistent with numerical solutions.