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Journal of Applied Physics

Optical coherent transient effects in magnetoactive GaAs/AlGaAs quantum well structure

S. Kapoor, Jitendra Kumar, P. K. Sen

Published Apr 14, 2004• 10 citations
Publisher

Abstract

The effect of an external magnetic field on optical coherent transient phenomena has been analyzed for semiconductor quantum well structures (QWS). The Lüttinger Hamiltonian is used to incorporate the complex valence band structure which is modified due to the application of the magnetic field. We have considered a GaAs/AlGaAs QWS with magnetic field applied in the direction perpendicular to the plane of the well. We get two quantum levels due to confinement, and doubly degenerate heavy-hole and light-hole bands corresponding to each quantum level, thus leading to eight hole subbands. This results in an 8×8 Hamiltonian in an appropriately chosen basis. Energy eigenvalues and eigenvectors have been calculated by numerically diagonalizing the above Hamiltonian. The absorption characteristics and the optical coherent transient phenomena have been studied by solving the effective semiconductor Bloch equations in the weak excitation regime. The polarization induced in conjunction with the results obtained by solving the modified Lüttinger Hamiltonian has been used to analyze the transient characteristics. We observe a blueshift in transition energy with an increase in magnetic field. The features are changed dramatically when one includes band mixing. The crossing of subbands in the absence of band-mixing effects changes over to anticrossing behavior when band mixing is included. Multiple oscillations are observed in the optical nutation signal that can be attributed to band-mixing effects. Absorption spectra also show a significant blueshift with an increase in magnetic field and additional peaks appear when band mixing is included.

DOI
10.1063/1.1697621

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The effect of an external magnetic field on optical coherent transient phenomena has been analyzed for semiconductor quantum well structures (QWS). The Lüttinger Hamiltonian is used to incorporate the complex valence band structure which is modified due to the application of the magnetic field. We have considered a GaAs/AlGaAs QWS with magnetic field applied in the direction perpendicular to the plane of the well. We get two quantum levels due to confinement, and doubly degenerate heavy-hole and light-hole bands corresponding to each quantum level, thus leading to eight hole subbands. This results in an 8×8 Hamiltonian in an appropriately chosen basis. Energy eigenvalues and eigenvectors have been calculated by numerically diagonalizing the above Hamiltonian. The absorption characteristics and the optical coherent transient phenomena have been studied by solving the effective semiconductor Bloch equations in the weak excitation regime. The polarization induced in conjunction with the results obtained by solving the modified Lüttinger Hamiltonian has been used to analyze the transient characteristics. We observe a blueshift in transition energy with an increase in magnetic field. The features are changed dramatically when one includes band mixing. The crossing of subbands in the absence of band-mixing effects changes over to anticrossing behavior when band mixing is included. Multiple oscillations are observed in the optical nutation signal that can be attributed to band-mixing effects. Absorption spectra also show a significant blueshift with an increase in magnetic field and additional peaks appear when band mixing is included.
Abstract The energy eigenvalues and eigenfunctions have been obtained for a GaAs/AlGaAs quantum wire structure with multiple valence subbands, subjected to an external magnetic field. The hole wavefunctions are calculated by numerical diagonalization of Luttinger Hamiltonian in an appropriately chosen basis. The electron–hole wavefunctions thus obtained are used in conjunction with effective semiconductor Bloch equations for the study of optical coherent transient effects like optical nutation. The results show squeezing of wavefunctions with increasing magnetic field while band mixing effects lead to overlapping of peaks. The corresponding optical nutation curves show an increase in nutation frequency with magnetic field while band mixing effects are revealed through multiple oscillations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Transient optical nonlinearities of semiconductor quantum dots in the strongly confined regime are studied, in which the exciton, biexciton and magnetic field effects are taken into account. The photo induced band-to-band electronic transitions are considered from both the heavy-hole (hh) and light-hole (lh) valence bands to the lowest (1s) exciton state below the fundamental absorption edge. The time dependent perturbation technique for a three-level system, under the near band gap resonant excitation regime, has been employed; with the incorporation of the relaxation and dephasing mechanisms phenomenologically. The induced polarization is calculated from where the real and imaginary parts of the third-order nonlinear optical susceptibility, responsible for the occurrence of nonlinear refraction and nonlinear absorption respectively, have been derived. The temporal and detuning spectra of nonlinear refraction and absorption; and their dependence on density of biexcitons and a moderately strong magnetic field, have been analyzed. It is observed that the nonlinear refraction and nonlinear absorption enhance with increasing magnetic field in small CdS quantum dots.
The coherent optical response of semiconductor quantum wells is studied theoretically using the multiband semiconductor Bloch equations which include coupling of the heavy- and light-hole bands as well as many-body Coulomb effects. For the case of a two-pulse excitation scheme it is shown how the different rotational symmetries of heavy- and light-hole bands induce a strong polarization dependence of the signal in the photon echo direction. The selection rules are based on the Kane-Luttinger theory while the transition amplitudes are obtained by numerically solving the multiband semiconductor Bloch equations. In addition, the influence of valence-band mixing effects on the optical Stark effect is demonstrated.
We have studied optical nutation and Stark splitting in a GaAs/AlGaAs quantum well with multi valence band structure using effective semiconductor Bloch equations. The individual roles of light and heavy holes in optical nutation have been examined. The analysis shows that both Rabi oscillation frequency and Stark splitting increase with rising electric field strength as observed experimentally. Also it is seen that light hole species dominates over heavy hole species in the transmission characteristics of quantum wells.
We study theoretically the time evolution of nonlinear optical phenomena of a probe electromagnetic field pulse in intersubband transitions of a semiconductor quantum well structure under the influence of a pump electromagnetic field. More specifically, we take into consideration the effects of electron-electron interactions and consider the interaction of a two-subband system with rectangular electromagnetic fields. The spectral form of the linear absorption, dispersion, and nonlinear optical Kerr effect is described, from the time that the external field is applied up until the dynamics of the system has reached a steady state. In order to describe the dynamics of the system, the effective nonlinear Bloch equations are used, in which renormalized terms for the transition energy and the applied field have been added, due to the effects of electron-electron interactions. These equations are properly combined, and the differential equations of the density matrix elements for the several optical phenomena up to third order are derived. These are solved numerically in the whole time range up to the steady state for a GaAs/AlGaAs quantum well structure. We show that the form of the several optical spectra studied here has a significantly altered evolution over time, according to the value of the frequency of the pump field and of electron sheet density. Even in the case in which the spectral form in the steady state case is almost identical for two different sets of parameters, their evolution can be quite different, according to the precise value of these parameters.
In the present work, the optical properties of GaAs/AlGaAs semiparabolic quantum wells (QWs) are studied under the effect of applied electric field and magnetic field by using the compact-density-matrix method. The energy eigenvalues and their corresponding eigenfunctions of the system are calculated by using the differential method. Simultaneously, the nonlinear optical rectification (OR) and optical absorption coefficients (OACs) are investigated, which are modulated by the applied electric field and magnetic field. It is found that the position and the magnitude of the resonant peaks of the nonlinear OR and OACs can depend strongly on the applied electric field, magnetic field and confined potential frequencies. This gives a new way to control the device applications based on the intersubband transitions of electrons in this system.