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Physica Scripta

Coherent population transfer dynamics in two-and three-level Demkov-Kunike models

Wenyi Liang, Yuanfeng Jin, Tian‐Xiang Hou, Yang Liu

Published Dec 22, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ae3039

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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.
Coherent population transfer in quantum systems is of fundamental importance in many fields such as atomic and molecular collision dynamics, and information processing for qubit systems. Stimulated Raman nonadiabatic passage technique, when implemented in an externally driven three-level system, provides an efficient approach for realizing accelerated population transfer while maintaining robust quantum coherence, with no need of rotating wave approximation. However, previous protocols employ multiple pulses and imply that Rabi frequencies have a few oscillations during dynamical evolution. In this work, under the condition of two-photon resonance, we use a gauge transformation method to inversely design a Λ-configuration three-level system that can be solved exactly. By using SU(3) transformation, we establish the relationship between Schrödinger representation and gauge representation, where the effective Hamiltonian is an Abelian operator. Subsequently, we construct the desired Hamiltonian and further investigate its dynamic behavior. The result shows that by imposing appropriate boundary conditions on the control parameters, high-fidelity population transfer can be achieved in ideal evolution. In addition, for the practical case with pulse truncation and intermediate state decay, the fidelities of specific models can reach about 99.996% and 99.983%, respectively. Compared with other existing nonadiabatic quantum control schemes, the present scheme has the distinctive advantages. We achieve the required quantum control by applying only a few sets of Stokes and pump pulses without introducing any additional microwave field. This method does not exhibit Rabi oscillations in the dynamic process, nor does it produce singularities in the pulse itself.
We present an analytically exactly soluble two-state model, in which a hyperbolic-secant-shaped pulsed interaction has a phase jump of $\ensuremath{\phi}$ at the time of its maximum. The detuning has a constant part and a hyperbolic-tangent chirp term. For $\ensuremath{\phi}=0$, this model reduces to the Demkov-Kunike model, which in turn contains as particular cases three other well-known models: the Rosen-Zener, Allen-Eberly, and Bambini-Berman models. A nonzero $\ensuremath{\phi}$ induces dramatic changes in the transition probability, ranging from complete population inversion to complete population return. The analytic results are particularly instructive in the adiabatic limit and demonstrate that complete population inversion can always occur for a suitable choice of $\ensuremath{\phi}$. The jump phase $\ensuremath{\phi}$ can therefore be used as a control parameter for the two-state transition probability.
We propose and analyze a robust population-transfer protocol in a driven two-level system based on a sudden sign change of the detuning at the maximum of a smooth coupling pulse. Away from the jump the dynamics is adiabatic, while the sign flip produces a single nonadiabatic kick in the adiabatic basis. Within a simple stepwise adiabatic-sudden approximation we obtain a compact analytic expression for the final transition probability, identify the parameter regimes that yield high-fidelity inversion, and show that the result depends only on the change of the mixing angle across the detuning jump, i.e., solely on the ratio of the peak Rabi frequency to the detuning. Numerical simulations of the full time-dependent Schrödinger equation confirm the validity and robustness of this description over a broad parameter range. We then use the Majorana decomposition to extend the scheme to an SU(2)-symmetric three-state chain driven by the same coupling and detuning functions. In this setting the three-state propagator is expressed in closed form through the two-level Cayley-Klein parameters, which allows us to derive explicit transition probabilities for all three initial states. In particular, we show that for strong coupling the protocol yields almost complete population transfer between the two outer states, with only small transient population of the middle state, while retaining the same intrinsic robustness as in the underlying two-level model.
Exact analytical solutions to the dissipative time-dependent Schrödinger equation are obtained for a decaying two-state system with decay rates Γ1 and Γ2 for the levels with extremal spin projections. The system is coherently driven with a pulse whose detuning is made up of two parts: a time-dependent part (chirp) of hyperbolic-tangent shape and a static part with real and imaginary terms. This gives us a wide range of possibilities to arbitrarily select the interaction terms. We considered two versions which led to decaying Demkov-Kunike (DK) models; the version in which the Rabi frequency (interaction) is a time-dependent hyperbolic-secant function (called decaying DK1 model) and the case when it is constant in time and never turns off (decaying DK2 model). Our analytical solutions account for all possible initial moments instead of only t0 = 0 or t0 = − ∞ as for non-decaying models and may be useful for the experiments on level crossings. Two complementary limits of the pulse detuning are considered and explored: the limit of fast (i) and slow rise (ii). In the case (i), the coupling between level positions in the first DK model collapses, while the second DK model reduces to a Rabi model (constant Hamiltonian), in the case (ii), both DK models reduce to the LZ model. In both cases (i) and (ii), analytical approximated solutions which conveniently approach the exact solutions are derived.
Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangent-pulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by the truncation of the driving pulse.
Abstract We propose a scheme to inverse engineer the Hamiltonian of any general driven three-level system by employing a SU(3) transformation. For special cases, the scheme is then introduced to explore nonadiabatic dynamic evolution of systems with two-photon resonance. We demonstrate that, by selecting the control parameters with explicit function forms, both the ideal process and the practical evolution driving with the truncation of pulses, systematic error and decaying can implement fast population transfer with high fidelity. Moreover, the nonadiabatic passages are not reconstructed by the superadiabatic approach.