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Journal of the Optical Society of America B

Coulomb enhancement of ultrafast nonlinearities in quantum-well structures

Jacob B. Khurgin

Published Jan 1, 1992• 11 citations
Publisher

Abstract

The Coulomb interaction among photoexcited virtual carriers or virtual excitons in two-dimensional heterostructures is theoretically considered by using bare-states and the dressed-states approaches. It is shown that, if the wave functions of the ground and the excited states are spatially separated, then the Coulomb interaction causes coherent pulsations of the transition energy. As a result, significant (an order of magnitude) enhancement of the dynamic Stark shift and of other ultrafast nonlinearities can be achieved. The enhancement of ultrafast nonlinearities is evaluated as a function of the geometry, the doping level, broadening, and other parameters. The effects of the Coulomb interaction on coherent transient phenomena is considered. The problem of practical realization of the predicted effects is addressed.

DOI
10.1364/josab.9.000157

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The Coulomb interaction among photoexcited virtual carriers or virtual excitons in two-dimensional heterostructures is theoretically considered by using bare-states and the dressed-states approaches. It is shown that, if the wave functions of the ground and the excited states are spatially separated, then the Coulomb interaction causes coherent pulsations of the transition energy. As a result, significant (an order of magnitude) enhancement of the dynamic Stark shift and of other ultrafast nonlinearities can be achieved. The enhancement of ultrafast nonlinearities is evaluated as a function of the geometry, the doping level, broadening, and other parameters. The effects of the Coulomb interaction on coherent transient phenomena is considered. The problem of practical realization of the predicted effects is addressed.
Recent works in the area of ultrafast nonlinearities due to virtual carriers in semiconductor heterostructures have generated significant interest among researchers. It has been shown that excitons in QW's behave very much like conventional two-level atoms, to the extent that exciton-exciton interaction can be neglected. Therefore, fast coherent phenomena usually associated with two-level system may occur in excitonic QW transitions. Indeed, dynamic (AC) Stark effect in QW's have been demonstrated. When semiconductor QW's were pumped below the absorption edge there were a strong "blue" shift of the exciton resonance, accompanied by a strong bleaching.
Recent works in the area of ultrafast nonlinearities due to virtual carriers in semiconductor heterostructures have generated significant interest among researchers. It has been shown1 that excitons in QW’s behave very much like conventional two-level atoms, to the extent that exciton-exciton interaction can be neglected. Therefore, fast coherent phenomena usually associated with two-level system may occur in excitonic QW transitions. Indeed, dynamic (AC) Stark effect in QW’s have been demonstrated2,3.
Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena. Ultrafast degenerate four-wave mixing is used as a tool to study the coherent exciton dynamics, and the importance of performing transform limited spectroscopy is demonstrated throughout.
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.