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Physical Review B

Relation between phenomenological few-level models and microscopic theories of the nonlinear optical response of semiconductor quantum wells

N. H. Kwong, I. Rumyantsev, Rolf H. Binder, Arthur L. Smirl

Published Dec 9, 2005• 14 citations
Publisher

Abstract

We analyze a generic atomic few-level model for the third-order $({\ensuremath{\chi}}^{(3)})$ optical response of semiconductor quantum wells. The purpose is to seek a good understanding of the physical nature of the model's parameters in terms of the material's microscopic constituents and their motions. The strategy is to bring the algebraic expression of the ${\ensuremath{\chi}}^{(3)}$ interband polarization in the few-level model to a form similar to that derived in microscopic theories. Most importantly, in the coherent limit, we make the ``time evolution structure'' of the interband polarization in the few-level and microscopic formalisms coincide, whereby the atomic model's parameters can be interpreted microscopically through a comparison of terms of similar structure in the two formalisms. We also discuss how the conclusion of this comparison can be changed by the introduction of phenomenological dephasing and decay into both theories.

DOI
10.1103/physrevb.72.235312

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arXiv:cond-mat/0412370•Physical Review B•Jul 7, 2005•7 citations
We analyze a generic atomic few-level model for the third-order (\ensuremathχ(3))({\ensuremath{\chi}}^{(3)})(\ensuremathχ(3)) optical response of semiconductor quantum wells. The purpose is to seek a good understanding of the physical nature of the model's parameters in terms of the material's microscopic constituents and their motions. The strategy is to bring the algebraic expression of the \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) interband polarization in the few-level model to a form similar to that derived in microscopic theories. Most importantly, in the coherent limit, we make the ``time evolution structure'' of the interband polarization in the few-level and microscopic formalisms coincide, whereby the atomic model's parameters can be interpreted microscopically through a comparison of terms of similar structure in the two formalisms. We also discuss how the conclusion of this comparison can be changed by the introduction of phenomenological dephasing and decay into both theories.
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.
Summary form only given.We present a comprehensive theoretical and experimental study of the magnitude and time evolution of the third-order nonlinear polarization on two InGaAs-GaAs MQW Bragg structures with N=10 and N=30 with an In content of 3% and a QW width of 8 nm and on a 8.5-nm InGa-GaAs SQW located at the antinode of a high-quality long microcavity. Theoretically, the optical response of the interband polarization is calculated from the semiconductor Maxwell Bloch equations in Hartree-Fock approximation.
A detailed numerical study of the third-order nonlinear optical susceptibilities (χ(3)) of semiconductor quantum wells is presented. The dependence of χ(3) on material parameters (electron-hole mass ratio and exciton linewidths), on the light polarization configuration (co- and countercircularly polarized) and on the spectral configuration is discussed. The goal of this study is to map out the nonlinear phase shift per quantum well and a related figure of merit caused by quasi-resonant excitonic and biexcitonic nonlinearities induced by picosecond light pulses. The study is based on the dynamics-controlled truncation formalism and evaluated under the assumption that only 1s-heavy-hole excitons contribute to the nonlinearities. It includes all correlation effects (exciton–exciton scattering in the singlet and triplet channels and coherent biexciton formation in the singlet channel) that contribute within the coherent excitonic χ(3) regime.
Summary form only given. While the conceptual realization of "3-level effects" in semiconductors is usually based on one-particle states given by the band structure of the system, we propose the realization of "3-level effects" in semiconductors based on many-particle states. Specifically, we study the quantum coherences related to excitons and biexcitons. Our analysis is based on the dynamics-controlled trunction (DCT) formalism and includes quantum correlations and quantum coherences within the 3rd-order nonlinear optical response. Within the /spl chi//sup (3)/ regime, only one-pair (excitonic) and two-pair (two-exciton) quantum coherences occur. We restrict the analysis to 1s-hh and 1s-lh excitons which dominate the nonlinear response. Results are shown for ZnSe quantum wells.
We present an approach to spin dynamics by extending the optical Bloch equations for the driven two-level system to derive microscopic expressions for the transverse and longitudinal spin-relaxation times. This is done for the six-level system of electron and hole subband states in a semiconductor or a semiconductor quantum structure to account for the degrees of freedom of the carrier spin and the polarization of the exciting light and includes the scattering between carriers and lattice vibrations on a microscopic level. For the subsystem of the spin-split electron subbands we treat the electron-phonon interaction in second order and derive a set of equations of motion for the $2\ifmmode\times\else\texttimes\fi{}2$ spin-density matrix, which describes the electron spin dynamics and contains microscopic expressions for the longitudinal (T1)({T}_{1})(T1​) and transverse (T2)({T}_{2})(T2​) spin-relaxation times. Their meaning will be discussed in relation to experimental investigations of these quantities.