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Physica Scripta

Population transfer in a gold-nanoparticle-coupled Λ -type quantum system using Lewis–Riesenfeld invariant-based shortcuts

Mingjie Lin, Yuewei Xiao, RenDi Luo, Wei Liu, Jingrong Zheng, Changshui Chen

Published Sep 3, 2026• 0 citations
Publisher

Abstract

Abstract Lewis–Riesenfeld (LR) invariant-based inverse engineering is applied to a Λ -type quantum system coupled to a gold nanoparticle, and three auxiliary-angle paths satisfying the same boundary conditions are constructed. By incorporating the local-field modifications and spontaneous-emission decay rates induced by the metal nanoparticle (MNP), the density-matrix equations are solved to compare the final target-state populations of the three LR paths and conventional stimulated Raman adiabatic passage (STIRAP) under different quantum-system–MNP distances, free-space decay rates, Rabi frequencies, and polarization configurations. The results show that, under the first polarization configuration, the α 2 path maintains a lower intermediate-state population and yields a high and stable final target-state population over most of the parameter range. Under the second polarization configuration, conventional STIRAP yields a higher final target-state population in some parameter regions. These results indicate that the final target-state population is affected by both optical-field-driven coherent transfer and spontaneous emission, and that the choice of LR path should be evaluated by considering the intermediate-state population together with the modifications induced by the plasmonic environment.

DOI
10.1088/1402-4896/aea1f1

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Abstract Lewis–Riesenfeld (LR) invariant-based inverse engineering is applied to a Λ -type quantum system coupled to a gold nanoparticle, and three auxiliary-angle paths satisfying the same boundary conditions are constructed. By incorporating the local-field modifications and spontaneous-emission decay rates induced by the metal nanoparticle (MNP), the density-matrix equations are solved to compare the final target-state populations of the three LR paths and conventional stimulated Raman adiabatic passage (STIRAP) under different quantum-system–MNP distances, free-space decay rates, Rabi frequencies, and polarization configurations. The results show that, under the first polarization configuration, the α 2 path maintains a lower intermediate-state population and yields a high and stable final target-state population over most of the parameter range. Under the second polarization configuration, conventional STIRAP yields a higher final target-state population in some parameter regions. These results indicate that the final target-state population is affected by both optical-field-driven coherent transfer and spontaneous emission, and that the choice of LR path should be evaluated by considering the intermediate-state population together with the modifications induced by the plasmonic environment.
Abstract A theoretical investigation on the population transfer in a Λ‐type quantum system near a spherical gold nanoparticle under application of two stimulated Raman adiabatic passage (STIRAP) shortcuts and efficiency comparison with conventional STIRAP. It combines the density matrix approach for system dynamics, with classical electromagnetic calculations used to obtain the modified electric field amplitudes of the applied pulses and the Purcell factor of the quantum system due to the presence of the nanoparticle. The efficiency of population transfer is investigated by varying the distance between the quantum system and the nanoparticle, the free‐space decay rate of quantum states, the mutual polarization, and the Rabi frequencies of each STIRAP shortcut pulses. In all cases, at least one of the applied shortcuts is more efficient than conventional STIRAP, while in most cases both perform better. When the pump and Stokes fields of the shortcuts have radial and tangential polarizations with respect to the nanoparticle surface, respectively, high transfer efficiency is obtained for small distances of the quantum system to the nanoparticle, moderate free space decay rates and large Rabi frequencies of the fields, while when the pulse polarizations are interchanged, the transfer becomes highly efficient only at large distances.
Abstract We investigate theoretically the population transfer process in a Λ-type three-level quantum system (QS) near a metallic nanosphere using the stimulated Raman adiabatic passage (STIRAP) technique. We combine density matrix quantum dynamical calculations with first-principle electromagnetic calculations, which quantify the influence of the plasmonic nanoparticle on the electric field of the pump and Stokes pulses in STIRAP as well as on the spontaneous emission rates within the Λ-type system. We study the population transfer process by varying the free-space spontaneous emission rate, the distance of the QS from the nanosphere, the polarization direction with respect to the nanoparticle surface and the relative strength of the pump and Stokes pulses used in STIRAP. We find that when the pump and Stokes fields have tangential and radial polarizations with respect to the nanosphere surface, the transfer efficiency is improved due to the increase of the decay rate of the excited state to the target state relatively to the decay to the initial state. The optimal population transfer is achieved for small interparticle distances, moderate free space spontaneous decay rate, large values of the pump Rabi frequency and small values of the Stokes Rabi frequency. When we exchange the polarization directions of the pump and Stokes fields we can still find a range of parameters where the population transfer remains efficient, but larger Stokes Rabi frequencies are necessary to overcome the increased decay rate from the excited state back to the initial state.
In this work, we present numerical results on the influence of a spherical metallic nanoparticle to the population transfer in a Λ-type quantum system under conditions of Stimulated Raman Adiabatic Passage (STIRAP). For the study of the system’s dynamics, we use the density matrix approach for the quantum system, where the parameters for the electric field amplitudes and the spontaneous decay rates have been calculated using ab initio electromagnetic calculations for the plasmonic nanoparticle. We present results for the evolution of the populations of the different levels of the quantum system as a function of different parameters, in the presence and the absence of the plasmonic nanoparticle. We find that the presence of the plasmonic nanoparticle and the polarization of the pump and Stokes fields with respect to the surface of the nanoparticle, affect the efficiency of the population transfer inside the three-level quantum system. For the right combination of the values of the modified spontaneous decay rates and the fields intensities, high efficiency population transfer is obtained in the quantum system near a plasmonic nanoparticle using STIRAP process.
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.
The stimulated Raman adiabatic passage (STIRAP) shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity, in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a generally robust approach to speed up STIRAP with invariant-based shortcut to adiabaticity. By controlling the dynamical process, we inversely design a family of Hamiltonians that can realize fast and accurate population transfer from the first to the third level, while the systematic error is largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.
The shortcut to adiabaticity (STA) is a powerful technique to speed up population transfer via quantum coherent control. This paper demonstrates that STA provides a fast, robust, and efficient population transfer compared to the stimulated Raman adiabatic passage. In the ideal situation of a closed system, STA is insensitive to the detunings and Rabi frequencies, and the undesired diabatic transitions could be eliminated by the auxiliary pulses, so the complete population transfer from the initial state to the target state in the designed adiabatic passage can be rapidly achieved against the inevitable amplitude noises of the interactions and systematic errors. When we consider the situation including the environment noises, spontaneous emission from the intermediate state $|2\ensuremath{\rangle}$ in STA can be sufficiently ignored in the cases of the dark-state evolution and quantum overdamping, since the state $|2\ensuremath{\rangle}$ is thoroughly separated from the three-state system. Moreover, the diabatic transitions induced by the spontaneous emission are also sufficiently suppressed in STA.