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Advanced Quantum Technologies

Nonadiabatic Population Transfer In Two‐Level Non‐Hermitian Systems

Yang Liu, Tian‐Xiang Hou, Yuanfeng Jin, Gang Lü, Hong‐Fu Wang

Published Dec 10, 2025• 5 citations

Abstract

ABSTRACT In this study, nonadiabatic population transfer was successfully achieved in a two‐level non‐Hermitian system with non‐conjugation complex Rabi frequencies and a real geometric phase along the superposition of ancillary basis states, by means of the ancillary picture and Lewis‐Riesenfeld (LR) invariant theory. Compared with the quantum adiabatic process, the core advantage of this scheme lies in that the inherent high‐speed characteristic of nonadiabatic evolution can avoid non‐targeted transitions, thus overcoming the limitations of traditional nonadiabatic processes. The Hamiltonian of the system was derived based on the laws of non‐unitary evolution. Time‐dependent complex pulses can be effectively regulated by adjusting control parameters; in the nonadiabatic population transfer process, the target pulses can be obtained simply by determining the relevant parameters in the non‐unitary evolution. Through the analysis of system dynamics via the ancillary picture and LR invariant theory, and verification by numerical simulations, it is shown that population inversion (the core characteristic of nonadiabatic population transfer) exhibits strong anti‐interference ability against system errors. In conclusion, this scheme provides a feasible approach for realizing high‐fidelity nonadiabatic population transfer in the aforementioned two‐level non‐Hermitian system.

DOI: 10.1002/qute.202500814

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ABSTRACT We theoretically study nonadiabatic population transfer in ‐typenon‐Hermitian (NH) three‐level systems with non‐complex‐conjugate Rabi frequencies, focusing on the Lewis‐Riesenfeld (LR)‐auxiliary picture of and perturbation‐induced systematic errors. A theoretical framework is constructed, enabling perfect population transfer under ideal dynamical conditions. Using second‐order approximation theory to quantify the population transfer fidelity, the results show that the scheme achieves high fidelity and exhibits strong robustness against small perturbations. This work provides reliable theoretical support for the dynamical research of such NH systems.

We have studied the population transfer in a three-state system driven by laser beams in terms of the theory of Lewis–Riesenfeld Hermitian invariants for explicitly time-dependent Hamiltonian. The exact solutions obtained allow us to recover two existing schemes producing complete population transfer in the literature, i.e. the π-pulse and stimulated Raman adiabatic passage methods in our unified description. We present a strict formulation of adiabatic conditions and a more accurate expression of the π-pulse method according to the exact time-evolution of state vector.

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.

A stable and fast path linking two arbitrary states of a quantum system is generally required for state-engineering protocols, such as stimulated Raman adiabatic passage, shortcuts to adiabaticity, and holonomic transformation. Such a path is also fundamental to the exact solution of the time-dependent Schr\"odinger equation. We construct a universal control framework using an ancillary picture, in which the time-dependent Hamiltonian can be diagonalized. Multiple desired paths can be derived by the von Neumann equation for parametric ancillary projection operators. No transition exists among the ancillary basis states during the time evolution. Under various conditions, our control framework reduces to the nonadiabatic holonomic transformation, the Lewis-Riesenfeld theory for invariants, and counterdiabatic driving methods. In addition, it is applicable to the cyclic transfer of system populations that could be a hard problem for existing methods. Our work can provide a full-rank time-evolution operator for a time-dependent quantum system with a finite number of dimensions.

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.