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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical nutation in semiconductor quantum wells with multiple valence bands

Sheetal Kapoor, Pratima Sen, Pranay K. Sen

Published Sep 25, 2001• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.441311

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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.
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.
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.
A theoretical study of the coherently coupled heavy-hole--light-hole optical Stark effect in semiconductor quantum wells is presented. Based on a detailed investigation of the various many-body contributions to the Stark shifts, we identify a parameter regime in which the existence of intervalence band coherences (analogous to the nonradiative Raman coherence in three-level atoms) can be inferred from the coherently coupled heavy-hole--light-hole excitonic optical Stark shift. The analysis is performed for the third-order nonlinear optical regime $({\ensuremath{\chi}}^{3}$ regime), and is based on the dynamics-controlled truncation (DCT) formalism. It includes the relevant optical selection rules, excitonic and two-exciton-correlation (e.g., biexcitonic) effects.
We report the experimental observation of coherently coupled heavy-hole-light-hole Stark shifts, i.e., light-hole exciton shifts under heavy-hole exciton pumping conditions, in InGaAs quantum wells. The theoretical analysis of the data is based on a full many-body approach (dynamics-controlled truncation formalism) in the third-order nonlinear optical regime. It is shown that the Stark shift data can be interpreted as strong evidence of suitably defined nonradiative intervalence band coherences in a semiconductor quantum well. Hence, the observations establish a semiconductor analog of Raman coherences in three-level atoms.
We observe multiple excitonic optical Rabi oscillations in a semiconductor quantum well. Up to eight oscillation periods of the heavy-hole exciton density on a subpicosecond time scale are observed. An approximate linear dependence of the oscillation frequency on the light field amplitude is established. The experiment is based on a two-color detection scheme which allows for the observation of the heavy-hole exciton density via transmission changes at the light-hole exciton. The observations are in good agreement with theoretical computations based on multiband semiconductor Bloch equations.