Abstract The Demkov-Kunike (DK) model, characterized by a hyperbolic tangent detuning and a hyperbolic secant coupling, serves as a universal framework for describing driven quantum systems. However, existing research has primarily focused on two-level systems, some gaps still persist in extending the model to three-level configurations to achieve coherent population transfer (CPT). This study constructs exact solutions for both two- and three-level DK models via a canonical transformation, providing a basis for the quantitative analysis of population transfer, and achieves effective regulation of CPT via a finite-time adiabatic driving mechanism under specific parameter constraints. Furthermore, we analyze the impact of pulse truncation—a common experimental constraint—as well as environmental dissipation on quantum state evolution. The results show that the proposed scheme achieves rapid, high-fidelity coherent population transfer not only under ideal conditions, but also in the presence of realistic pulse truncation and even when decoherence induced by system-environment coupling is included. This work achieves CPT in the three-level DK model, offering a promising approach for advancing quantum state control in practical applications.Abstract The Demkov-Kunike (DK) model, characterized by a hyperbolic tangent detuning and a hyperbolic secant coupling, serves as a universal framework for describing driven quantum systems. However, existing research has primarily focused on two-level systems, some gaps still persist in extending the model to three-level configurations to achieve coherent population transfer (CPT). This study constructs exact solutions for both two- and three-level DK models via a canonical transformation, providing a basis for the quantitative analysis of population transfer, and achieves effective regulation of CPT via a finite-time adiabatic driving mechanism under specific parameter constraints. Furthermore, we analyze the impact of pulse truncation—a common experimental constraint—as well as environmental dissipation on quantum state evolution. The results show that the proposed scheme achieves rapid, high-fidelity coherent population transfer not only under ideal conditions, but also in the presence of realistic pulse truncation and even when decoherence induced by system-environment coupling is included. This work achieves CPT in the three-level DK model, offering a promising approach for advancing quantum state control in practical applications.

Physica ScriptaDec 22, 20250 citations

Dynamics of a dissipative two level system

W. Zwerger

The European Physical Journal BMar 1, 198377 citations

Noisy Demkov-Kunike model

Lin Chen, Zhaoxin Liang

The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling $J\phantom{\rule{0.16em}{0ex}}\text{sech}(t/T)$ and on-site detuning ${\mathrm{\ensuremath{\Delta}}}_{0}+{\mathrm{\ensuremath{\Delta}}}_{1}tanh(t/T)$, 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 application in noise-free cases, the exploration of the noisy DK model remains limited. Here we extend the coherent DK model to take into account a noisy coupling term $J\ensuremath{\rightarrow}{J}_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by telegraph noise and Gaussian noise. We present exact solutions for the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ of the noisy DK model, namely, the probability of the system to remain in its initial state. For slow telegraph noise, we identify parameter regimes where the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ , 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 into the control of two-level quantum systems.The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling $J\phantom{\rule{0.16em}{0ex}}\text{sech}(t/T)$ and on-site detuning ${\mathrm{\ensuremath{\Delta}}}_{0}+{\mathrm{\ensuremath{\Delta}}}_{1}tanh(t/T)$, 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 application in noise-free cases, the exploration of the noisy DK model remains limited. Here we extend the coherent DK model to take into account a noisy coupling term $J\ensuremath{\rightarrow}{J}_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by telegraph noise and Gaussian noise. We present exact solutions for the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ of the noisy DK model, namely, the probability of the system to remain in its initial state. For slow telegraph noise, we identify parameter regimes where the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$, 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 into the control of two-level quantum systems.

arXiv:2309.06448Physical Review AFeb 16, 20244 citations

The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling

J\phantom{\rule{0.16em}{0ex}}\text{sech}(t/T)

and on-site detuning ${\mathrm{\ensuremath{\Delta}}}_{0}+{\mathrm{\ensuremath{\Delta}}}_{1}tanh(t/T)$, 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 application in noise-free cases, the exploration of the noisy DK model remains limited. Here we extend the coherent DK model to take into account a noisy coupling term $J\ensuremath{\rightarrow}{J}_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by telegraph noise and Gaussian noise. We present exact solutions for the survival probability

{Q}_{\text{DK}}^{\text{noisy}}

of the noisy DK model, namely, the probability of the system to remain in its initial state. For slow telegraph noise, we identify parameter regimes where the survival probability

{Q}_{\text{DK}}^{\text{noisy}}

is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability

{Q}_{\text{DK}}^{\text{noisy}}

, 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 into the control of two-level quantum systems.