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Journal of Applied Physics

The third-order nonlinear optical susceptibility of the quantum dot as a three-level system in a hybrid structure

Neda Biranvand, Ali Bahari

Published Mar 17, 2023• 8 citations
Publisher

Abstract

To increase the optical nonlinearity effects in hybrid structures comprising a quantum dot and a nanoparticle, a quantum dot is taken as a three-level system. Under the dipole–dipole interactions between the quantum dot and the nanoparticle, the density matrix elements are derived within the rotating approximation. Under the quasi-static approximation by taking the nanoparticle polarization as a function of its geometry, the induced fields around the quantum dot in the presence of one/two nanoparticle(s) are obtained and the increasing factors of the local fields are calculated. The third-order nonlinear optical susceptibility of quantum dot is achieved by using the perturbation expansion theory of density matrix for different geometries of the nanoparticle, and the effects of the structural parameters are investigated to optimize the nonlinear optical response of the system. It can be seen that the presence of two nanorods results in great optical nonlinearities in the hybrid structure, being suitable for on/off switches, quantum communication, and quantum computing applications.

DOI
10.1063/5.0142081

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To increase the optical nonlinearity effects in hybrid structures comprising a quantum dot and a nanoparticle, a quantum dot is taken as a three-level system. Under the dipole–dipole interactions between the quantum dot and the nanoparticle, the density matrix elements are derived within the rotating approximation. Under the quasi-static approximation by taking the nanoparticle polarization as a function of its geometry, the induced fields around the quantum dot in the presence of one/two nanoparticle(s) are obtained and the increasing factors of the local fields are calculated. The third-order nonlinear optical susceptibility of quantum dot is achieved by using the perturbation expansion theory of density matrix for different geometries of the nanoparticle, and the effects of the structural parameters are investigated to optimize the nonlinear optical response of the system. It can be seen that the presence of two nanorods results in great optical nonlinearities in the hybrid structure, being suitable for on/off switches, quantum communication, and quantum computing applications.
The optical response of a hybrid structure consisting of a metal nanoparticle in the vicinity of a quantum dot under an external field is studied. The effect of the nanoparticle shape as it evolves from a sphere to a rod is investigated for various structural parameters. Significant changes are observed in the phase diagram of the optical response at the borders between Fano, exciton-induced transparency, suppression, and bistable regions. In the appropriate limits, the configuration exhibits a response where notable variations are particularly observed in suppression and bistable regions. In the presence of the nanorod, the suppression region is found as the beginning of bistability. Our calculations show that the nanorod can generate significant nonlinearities at the site of quantum dot in the bistable region, making the hybrid structure suitable for devices involving optical switching or information transfer. By considering the effect of other structural parameters, for example the configuration state, background dielectric constant, and interparticle distance, one can obtain additional control of the optical response of the system, engineering it to achieve particular objectives.
In recent years,the subject of optical nonlinearity in semiconductor quantum confined structures such as quantum wires and quantum dots has attracted a considerable attention because of their relevance for studying practical applications and as a probe for the electronic structure of media.It has been shown that the low dimensional quantum systems present very large nonlinear optical susceptibilities .Theoretically,most of the studies on quantum dots are focused on spherical quantum dots for simplicity.The shape of quantum dot depends on growth conditions.In fact,quantum dots are better described as thin disk or cylinder.In the present work third order nonlinear optical susceptibilities in disk shaped quantum dots due to resonant intersubband transition are analyzed by a compact density matrix approach.It has rarely been discussed in literatures.Firstly,we consider an electron moving in a quantum disk whose radius R is very large compared to its thickness d .For simplicity,we assume that the isotropic effective mass approximation is valid within the disk and that the inner potential is null while the outer confining potential is approximately infinite.Using the adiabatic approximation we solve the three dimensional Schrdinger equation and obtain the analytical expressions of wave functions and energy levels in cylindrical coordinates.Secondly,we consider the system is excited by an electromagnetic field with frequency ω. The electromagnetic field is incident with a polarization vector normal to the disk.We treat H′=ezE(t) as a perturbation term.By using the compact density matrix method,we derive a general formula for third order nonlinear optical susceptibilites employing a four level model in quantum disk.Finally,numerical results are illustrated for a typical GaAs quantum disk.We calculate the third order nonlinear optical susceptibilities as a function of the disk thickness.It is shown that the third order nonlinear optical susceptibilities in quantum disk are 10～100 times larger than that in quantum well for various disk thickness.Furthermore,if we choose an optimized thickness of quantum disk,we could obtain a quite large refractive index with a comparatively small absorption coefficient.Therefore,we suggest that the quantum dots would be an excellent system in the field of optical communications and optical switching.
In the present work, we theoretically/numerically study the optical second-order sideband generation in a hybrid structure consisting of a semiconductor quantum dot (QD) conjugated with DNA molecules, and coupled to a solid metallic nanoparticle (MNP) or a metallic nanoshell (MNS) with core-shell geometry. The hybrid system is driven by a strong control (pump) laser field and a weak signal (probe) field. The dynamics of the system is analyzed using the Heisenberg equation of motion in the frame of rotating wave approximation. We discuss the role of plasmon-exciton interaction in enhancing third- and fifth-order nonlinear susceptibilities through the nonlinear optical response of the system and the effects of the presence of a MNP or a MNS near the QD-DNA system on the nonlinear optical absorption spectrum is investigated. We demonstrate that the second-order sideband is generated, and the hybrid system considered here enables robust control and tunability of the second-order sidebands. It is shown that the second-order sideband spectrum (or absorption) is significantly affected by plasmonic nanoparticle size, the interparticle distance, the control field (Rabi frequency ), and the control-exciton detuning.
We study optical effects in a hybrid system composed of a semiconductor quantum dot and a spherical metal nanoparticle that interacts with a weak probe electromagnetic field. We use modified nonlinear density matrix equations for the description of the optical properties of the system and obtain a closed-form expression for the linear susceptibilities of the quantum dot, the metal nanoparticle, and the total system. We then investigate the dependence of the susceptibility on the interparticle distance as well as on the material parameters of the hybrid system. We find that the susceptibility of the quantum dot exhibits optical transparency for specific frequencies. In addition, we show that there is a range of frequencies of the applied field for which the susceptibility of the semiconductor quantum dot leads to gain. This suggests that in such a hybrid system quantum coherence can reverse the course of energy transfer, allowing flow of energy from the metallic nanoparticle to the quantum dot. We also explore the susceptibility of the metal nanoparticle and show that it is strongly influenced by the presence of the quantum dot.
We study the optical response of a coupled asymmetric semiconductor quantum dot-spherical metal nanoparticle structure. The asymmetric quantum dot has permanent electric dipole moments that also interact with light. We derive the density matrix equations for the system including the modification of the electric field and the exciton-plasmon coupling. We emphasize on the effects of the nonlinear optical rectification and controlled optical bistability and analyze these phenomena for different values of the light intensity and different distances between the quantum dot and the metal nanoparticle. We show that when the system is set in a situation where optical bistability can be produced, the optical rectification of the hybrid system is bivalued. We also analyze the slow-down to reach the steady state when the system is driven close and far from the turning points.