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Physical review. B, Condensed matter

Effects of intervalence band coherences on the coherently coupled heavy-hole–light-hole Stark shift in semiconductor quantum wells

I. Rumyantsev, N. H. Kwong, Ryu Takayama, Rolf H. Binder

Published Jun 24, 2002• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.65.245325

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Physical review. B, Condensed matter•Jun 15, 1993•22 citations
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 (\ensuremathχ3({\ensuremath{\chi}}^{3}(\ensuremathχ3 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.
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. The optical Stark shift in semiconductors transient nonlinearity which helps to understand fundamental ultrafast microscopic processes. Studies of similarities and differences between optical Stark shifts in atomic two-level systems and those observed in semiconductors led to the understanding of semiconductor-specific many-body effects such as biexcitons and Coulomb memory effects. While the two-level analogies of Stark shifts in semiconductors have been successfully exploited, the question of what one can learn from a comparison of coherent atomic three-level effects with optical Stark shifts in semiconductors using the coherent coupling between heavy-hole (hh) and light-hole (lh) excitons has not been addressed so far. In atomic three-level systems, nonradiative or Raman coherences are the foundation of important nonlinear optical effects such as electromagnetically-induced transparency and lasing without inversion. We investigate these coherences in an InGaAs multiple quantum well utilizing coherently-coupled Stark shift measurements of the hh- and lh-exciton resonances.
A theoretical analysis of intervalence-band coherences is presented. These optically created non-radiative coherences are generalizations of non-radiative coherences in atomic and molecular three-level systems. Whereas in three-level systems these coherences are the basis of important and well-established nonlinear effects, the interpretation of experimental evidence for such coherences in semiconductors needs to be supported by many-body theory. Based on the dynamics-controlled truncation formalism, the respective contributions of intervalence-band coherences and coherent biexcitonic correlations in time-integrated differential transmission spectroscopy is investigated. It is found that the contribution of the biexcitonic correlations to the observable heavy-hole–light-hole beats can be eliminated, either by reducing the light pulse duration or by choosing the central frequency of the light pulses at the heavy-hole exciton.
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.
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.