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physica status solidi (b)

Wavefunction analysis and optical nutation in magnetized semiconductor quantum wires exhibiting multiple valence subbands

Sheetal Kapoor, Jitendra Kumar, Pranay K. Sen

Published Jun 20, 2005• 5 citations
Publisher

Abstract

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)

DOI
10.1002/pssb.200440056

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IEEE Journal of Quantum Electronics•May 24, 2005•4 citations
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)
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.
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.
This work presents a detailed theoretical study of the linear and third‐order nonlinear optical properties of excitonic δ ‐doped GaAs/AlGaAs multiple quantum wells under an external magnetic field. The electronic structure is modelled within the effective mass approximation, and the correlated excitonic states are obtained by diagonalising the full electron–hole Hamiltonian in a realistic multi‐well potential using a centred finite‐difference method. The Coulomb interaction is treated using a softened potential appropriate for quasi‐one‐dimensional confinement. The model incorporates band offsets, pressure‐ and temperature‐dependent material parameters and magnetic field–induced confinement effects. The linear and third‐order nonlinear optical absorption coefficients, along with the associated refractive index changes, are calculated using the density‐matrix formalism. Magnetic fields (1–5 T) induce blue shifts of 6–12 meV with reduced peak intensity. Increasing barrier width (2–6 nm) produces larger blue shifts (30–40 meV), while pressure and temperature cause characteristic blue and red shifts, respectively. These results demonstrate tuneable excitonic energies and nonlinear optical responses in engineered multiple quantum wells for tuneable photonic device applications. A rigorous theoretical analysis of excitonic linear and third‐order nonlinear optical responses in δ ‐doped GaAs/AlGaAs multiple quantum wells is presented. The electron–hole interaction is treated using a regularised Coulomb potential. The combined influence of magnetic field, hydrostatic pressure, temperature and barrier widths reveals rich and controllable optical behaviour, offering insights for advanced optoelectronic device design.
Abstract We discuss, from a theoretical point of view, the four wave mixing spectroscopy on an ensemble of p‐doped quantum dots in a magnetic field slightly tilted from the in‐plane configuration. We describe the system evolution in the density matrix formalism. In the limit of coherent ultrafast optical driving, we obtain analytical formulas for the single system dynamics and for the response of an inhomogeneously broadened ensemble. The results are compared to the previously studied time‐resolved Kerr rotation spectroscopy on the same system. We show that the Kerr rotation and four wave mixing spectra yield complementary information on the spin dynamics (precession and damping). (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In this work, the influence of an external magnetic field on the refractive index changes and optical absorption coefficients of a typical GaAs/AlxGa1−xAs coaxial cylindrical quantum well wire is studied. Energy eigenvalues and eigenvectors in the presence of a magnetic field are calculated using the fourth-order Runge-Kutta method and optical properties are obtained using the compact density matrix approach. It is found that the resonant peak values of the linear and the third-order nonlinear refractive index changes as well as the optical absorption coefficients of a cylindrical quantum wire decrease with increasing the magnetic field. However, these optical properties of a coaxial cylindrical quantum well wire are nonmonotonic functions of the magnetic field, due to the anticrossing of the subbands. The anticrossing effect leads to a large increase of the resonant peak values of these optical properties. Results also indicate that the resonant peak values of these optical properties decrease with increasing the barrier width.
We calculate the anisotropic two-photon absorption spectra of an AlGaAs-GaAs V-shaped quantum wire with realistic band structure, including excitonic effects. The absorption coefficient is obtained by integrating effective multiband Bloch equations accounting for the Coulomb interaction within the Hartree-Fock approximation. The various excitonic peaks are identified with respect to the involved energy subbands and the symmetry properties. Furthermore, A/sub 2/-excitons, which are dark for one-photon excitation, become bright for two-photon spectroscopy when the light is linearly polarized along a direction that is not a symmetry axis. We show that some of them may be observable.