Noisy Demkov-Kunike model

The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling J sech(t/T) and on-site detuning Δ₀+Δ_1tanh(t/T), has one of the most general forms of an exactly solvable two-state quantum system, and, therefore, it provides a paradigm for coherent manipulations of a qubit's quantum state. Despite its extensive applications in the noise-free cases, the exploration of the noisy DK model remains limited. Here, we extend the coherent DK model to take into account of a noisy coupling term J→ J_noisy(t). We consider colored Markovian noise sources represented by the telegraph noise and Gaussian noise. We present exact solutions for the survival probability Q^noisy_DK of the noisy DK model, namely the probability of the system to remain in its initial state. For the slow telegraph noise, we identify parameter regimes where the survival probability Q^noisy_DK is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability Q^noisy_DK, due to the absorption of noise quanta across the energy gap. This study not only complements the existing research on the noisy Landau-Zener model, but also provides valuable insights for the control of two-level quantum systems.