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JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS

Optical Absorption Line Shape of a Λ-Type Three-Level Semiconductor Quantum Dot: Roles of Transition Dipole Moment and Relaxation Rate

Bintoro Siswo Nugroho, Arik Ramadhan, Asifa Asri

Published Aug 31, 2026• 0 citations
Publisher

Abstract

The optical absorption of an isolated Λ-type three-level semiconductor quantum dot under continuous-wave excitation was investigated theoretically using a semiclassical density-matrix approach. The equations of motion were derived from the master equation within the rotating-wave approximation and solved in the steady-state regime to obtain the optical susceptibility and absorption spectrum. The roles of the transition dipole moment and relaxation rate were examined systematically in both weak- and strong-field regimes. In the weak-field regime, the spectrum was dominated by the ∣1⟩↔∣3⟩ transition, while a weaker secondary feature associated with the ∣2⟩↔∣3⟩ transition emerged through relaxation-assisted population redistribution. Increasing the relaxation rate broadened and suppressed the dominant peak, whereas increasing the transition dipole moment mainly broadened the weaker secondary feature. In the strong-field regime, the two absorption channels merged into a broadened composite profile due to the combined effects of stronger coherent driving, power broadening, and relaxation. These results clarify how transition strength and dissipation govern the absorption line shape of an elementary multilevel semiconductor quantum-dot system.

DOI
10.25077/jif.18.2.158-168.2026

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The optical absorption of an isolated Λ-type three-level semiconductor quantum dot under continuous-wave excitation was investigated theoretically using a semiclassical density-matrix approach. The equations of motion were derived from the master equation within the rotating-wave approximation and solved in the steady-state regime to obtain the optical susceptibility and absorption spectrum. The roles of the transition dipole moment and relaxation rate were examined systematically in both weak- and strong-field regimes. In the weak-field regime, the spectrum was dominated by the ∣1⟩↔∣3⟩ transition, while a weaker secondary feature associated with the ∣2⟩↔∣3⟩ transition emerged through relaxation-assisted population redistribution. Increasing the relaxation rate broadened and suppressed the dominant peak, whereas increasing the transition dipole moment mainly broadened the weaker secondary feature. In the strong-field regime, the two absorption channels merged into a broadened composite profile due to the combined effects of stronger coherent driving, power broadening, and relaxation. These results clarify how transition strength and dissipation govern the absorption line shape of an elementary multilevel semiconductor quantum-dot system.
Semiconductor quantum dots (SQDs) exhibit optical responses that are strongly influenced by their internal level structure, relaxation pathways, and excitation intensity. This study investigates the time- and intensity-dependent population dynamics of a continuously driven single -type three-level SQD using the density-matrix formalism within the rotating-wave approximation. Dissipative processes are incorporated through Lindblad-type relaxation terms, while the transient and stationary responses are obtained, respectively, by numerical time integration and steady-state solution of the density-matrix equations. Special attention is given to the relaxation channel and the off-resonant transition dipole moment . The results show that primarily controls the transient redistribution route and the timescale required to reach the stationary regime, whereas the early oscillatory behavior remains dominated by the resonantly driven transition. In the steady-state regime, mainly determines how population leaving the upper state is partitioned between the two lower states, while governs how readily the off-resonant branch becomes active as the driving intensity increases. Consequently, the crossover from predominantly resonant two-level-like behavior to genuine three-level population redistribution is controlled by the combined action of relaxation-path asymmetry and off-resonant coupling strength. These findings provide a clearer mechanism-based interpretation of driven population redistribution in effective multilevel SQD systems.
I recent years, significant attention has been given to nonlinear optical phenomena, such as nonlinear optical absorption and dispersion, derived from a driven quantum transition of semiconductor nanostructures, such as semiconductor quantum wells, quantum disks and mainly quantum dots. An important issue that is widely studied is the effect of probe electromagnetic field intensity on the total (nonlinear) absorption coefficient and on the total (nonlinear) index of refraction. Some of the phenomena that are commonly found for large electromagnetic field intensities are the creation of a strong dip in the absorption spectrum near or at resonance (the so-called bleaching effect), negative absorption near or at resonance that leads to optical gain and the change of the slope of the total index of refraction near or at resonance from negative to positive that changes the behavior of the system from fast to slow light. Unfortunately, these phenomena do not exist and are artifacts of a common abuse of the theoretical methodology for the study of the total absorption coefficient and the total index of refraction. The main error is that the total absorption coefficient and the total index of refraction was initially derived from density matrix equations using perturbation theory and includes first-order (linear) as well as third-order (nonlinear) terms. This method gives correct results for small electromagnetic field intensities and it leads to saturation of absorption and dispersion in this regime. However, for larger intensities it gives the misleading results mentioned above due to either failure of the order of perturbation theory considered in the derivation of the total absorption coefficient and the total index of refraction or even failure of perturbation theory at all in the treatment of the problem. In this work, we revisit the problem of the total absorption coefficient and the total index of refraction in a symmetric semiconductor quantum dot structure (we choose the example of a core-shell quantum dot) under a strong probe field excitation. We use the two-level model, solve the relevant density matrix equations under the rotating wave approximation and under steady state conditions, and obtain the correct form of the nonlinear optical susceptibility that is then used for the derivation of the formulae of the total absorption coefficient and the total index of refraction under the interaction with a strong probe field. Actually, the commonly used perturbation theory formulae can be obtained by our formulae using a series expansion and keeping terms up to second order in electric field amplitude. We also derive the electronic structure of the quantum dot system by solving numerically the time-independent Schrodinger equation, under the effective mass approximation, using the potential morphing method and obtain the energy difference and the electric dipole matrix element for the relevant transitions of the quantum dot system. Then, for the specific quantum dot system we compare the results of the total absorption coefficient and the total index of refraction for the two methodologies (the perturbation result and our result) for different electromagnetic field intensities.
Abstract The optical properties of the CdSe/ZnS spherical core/shell quantum dot (CSQD), related to the laser-driven transitions 1 s → 1 p − 1 and 1 s → 2 p − 1 , are the subject of this study. We investigate in detail how transition energies, oscillator strengths, imaginary and real parts of the total, linear and third-order susceptibilities change with the variation of the model parameters, such as CSQD radius, core radius, relaxation rates and laser intensity. The energy levels and wave functions, needed for the calculations of the model parameters, were obtained by solving the radial Schrödinger equation in the effective mass approximation with the corresponding boundary conditions. The interaction of CSQD with laser light was studied in a density matrix approach using a two-level model and, for the first time, a five-level model. Optical Bloch equations were derived under dipole and rotating wave approximations and solved in the steady-state regime to obtain an analytic expression for susceptibility. Special attention was paid to the cases in which nonlinear susceptibility prevailed over linear susceptibility, leading to the appearance of the window in the absorption peak. It was found that susceptibility is more sensitive to the change in the core radius than to the change in the CSQD radius and that a greater laser intensity is needed to change the nature of the absorption and dispersion curves for 1 s → 2 p − 1 then for 1 s → 1 p − 1 transition.
Exciton-biexciton coherent coupling effects are examined in semiconductor quantum dots. The exciton absorption spectrum is measured with the microphotoluminescence excitation technique in a single InGaAs quantum dot. The spectrum changes from a Lorenztian-type line shape to an unusual dip-shaped line shape with increasing excitation intensities in a higher exciton state where there is a large oscillator strength between the exciton and biexciton states. The intensity dependence of the dip energy width clearly indicates that coherent Rabi oscillation occurs between the exciton and biexciton states. The absorption properties with excitation light of different polarizations show that the dip-shaped spectra only appear when there is a large biexciton state population with linear polarization. A theoretical analysis undertaken with the density matrix method agrees well with experimental results. This agreement reveals that exciton-biexciton coherent interactions lead to unusual absorption spectra and contribute crucially to the optical properties of quantum dots. The exciton-biexciton coherent effects provide a scheme for controlling four distinguishable states, which can be applied to a demonstration of quantum gate operations.
The density matrix approach has been employed to study analytically the property of dispersion and absorption in semiconductor single quantum dot under the confinement regime.The numerical simulation results show that under the condition of weak probe field and adjusting the two coupling field relative magnitude,the magnitude of normal dispersion is changed and the abrupt change of normal and anomalous dispersion takes place.Enhancement the magnitude of probe field and change the angle between probe field and dipole,the steep change of dispersion states occur.Comparing the absorption curves we find the absorption under weak probe is more power than the strong case.The stronger probe field and change the angle between probe field and dipole,the absorption peak is higher between the resonance point and the space increases.
We study nonlinear optical absorption and nonlinear optical rectification in an asymmetric semiconductor quantum dot structure under a strong probe field excitation. We apply a form of the rotating wave approximation for asymmetric quantum systems, solve the relevant density matrix equations under steady state conditions, and derive the formulae for nonlinear optical absorption and nonlinear optical rectification under the interaction with a strong probe field. The differences between our formulae and those of a previous study are also presented for the case of an electron confined in an asymmetric double quantum dot nanostructure.