Effect of spontaneous emission on a tanh model

Abstract

This study examines the impact of spontaneous emission on a tanh model. The effect is characterized by introducing an imaginary term and a shift in the model, resulting in its non-Hermitian nature. This leads to the appearance of light beams in the population evolution, primarily influenced by the coupling strength and the shift. We derive the necessary conditions to identify the allowed and forbidden regions in the diagram of the real part of the energy. Additionally, we analyze how sweep velocity and time affect the imaginary part of the energy. Furthermore, we demonstrate the similarities between our model and the Rabi and Landau-Zener models. Throughout this work, we confirm that our theoretical predictions align well with numerical simulations.