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.
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.
An exact analytic solution to the time-dependent Schrödinger equation is presented for a two-state quantum system coherently driven by a nonresonant pulsed external field. The pulse has a hyperbolic-secant shape, with a sign jump (i.e. a phase step of π) at its maximum, which nullifies the overall pulse area. It is shown that off resonance, for detunings larger than the pulse bandwidth, the transition probability approaches unity as the field intensity increases. The population inversion is robust against small-to-moderate variations in the detuning and the intensity, a feature reminiscent of adiabatic passage. The population inversion, however, is not of adiabatic nature; it is induced by δ-function-shaped nonadiabatic coupling with an area of nearly π. An estimate of the required experimental resources shows that implementation with shaped femtosecond pulses is feasible.
Population inversion from an initial quantum state to a desired quantum state represents an exciting new frontier for quantum manipulation; that frontier is endowed with a strong interdisciplinary character and connections to other scientific fields, including atomic, molecular, and optical physics, as well as in solid-state devices, for fundamental studies, nuclear magnetic resonance and other spectroscopic techniques, metrology, interferometry, optical control of chemical reactions or quantum-information applications. Two-level systems are ubiquitous in these areas, and the driving of a population inversion is an important operation. So far various schemes for population transfer to a target state from an initial state have been proposed in theory and implemented in experiment. To be useful, such methods must, of course, be reliable, fast, and robust. Most literatures on two-level models investigated population inversion, which could be modelled by infinite-time processes. In this paper, by using a composite adiabatic passage (CAP) technique—in which the single pulse driving the quantum transition is replaced by a sequence of pulses with well-defined control phases, we investigate the population inversion problem of two-level quantum system with a finite duration. We take a sinusoidally varying pulse model that continuously vanishes at the beginning and the end of the finite duration as an example. The high-fidelity population inversion of the two-level system with finite duration is achieved. We discuss the effects of both coupling strength and detuning strength on the transition probability. It is found that this protocol could suppress the oscillations in the transition probability and reduce the admissible error bellow the 10 -4 quantum computation benchmark. The fidelity can arrive at 1, even with simple three- and five-composite pulse sequences. The protocol combines the advantages of adiabatic passage and composite pulses techniques. By choosing the composite phases appropriately, a high-fidelity, fast, stable and extremely robust complete population inversion is achieved for the finite-time two-level model. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp as long as the latter satisfy the symmetry property. Furthermore, the classical Hamiltonian is applied to describe the dynamic properties of the quantum system and further verify the effectiveness and feasibility of the proposed CAP technique. The results we present here are general and in principle apply to any two- and multi-level quantum systems. The accuracy of the CAP technique and its robustness against parameter variations make the protocol suitable for ultrahigh-fidelity quantum manipulation. We believe that the protocol can be widely used in many different areas of science, ranging from the quantum information, the quantum chemical, and the quantum optics to the ultracold atomic and molecular physics.
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.
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.
We propose a controlled-Z gate scheme for Rydberg atoms based on level-crossing-free echoing rapid adiabatic population transfer. We design antisymmetric Rabi frequency pulses and symmetric detuning pulses, enabling the system to completely avoid level-crossing points throughout the evolution, and the dynamical phase is naturally eliminated by the time-reversal symmetry of the double-pulse sequence. We incorporate dissipative effects through the Lindblad master equation. The numerical simulation yields a two-qubit CZ gate fidelity of 0.9999. When the Rabi-frequency fluctuation is within ±2%, and the detuning offset is within ±1%, the fidelity can still remain above 0.999. Under the same dissipative model, the three-qubit CCZ gate achieves a fidelity of 0.999. When a single-parameter fluctuation does not exceed ±3%, the fidelity is always higher than 0.997. Our scheme requires no laser phase jumps or fast switching operations. The zero-area pulse structure suppresses first-order intensity noise, and the symmetric double-pulse sequence avoids spatially resolved laser switching, making it suitable for parallel gate operations in large-scale neutral-atom arrays.
Adiabatic passage induced by chirped laser pulses in three-level $\ensuremath{\Lambda}$ systems is investigated. Two different strategies for efficient population transfer (equal and opposite sign of the chirp) are analyzed. The role of detuning, crucial for the attempt to reduce the population of the intermediate state, is demonstrated. The scheme of adiabatic passage by laser pulses with chirps of different sign is not symmetric with respect to the sign of the one-photon detuning. Blue detuning results in a smaller transient population of the intermediate state than does red detuning. The results are explained on the basis of dressed states. Numerical results for a fully off-resonant adiabatic passage scheme, based on two pulses with the same sign of the chirps, are also considered. The robustness of the schemes in terms of the Rabi frequency, chirp rate, detuning, and time delay of the pulses is explored.