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arXiv:0706.2241 · Physical Review B

Dynamics-controlled truncation scheme for quantum optics and nonlinear dynamics in semiconductor microcavities

S. Portolan, Omar Di Stefano, Salvatore Savasta, Fausto Rossi, R. Girlanda

Published May 5, 2008• 23 citations
arXivHTMLPDF

Abstract

We present a systematic theory of Coulomb-induced correlation effects in the nonlinear optical processes within the strong-coupling regime. In this paper, we shall set a dynamics controlled truncation scheme microscopic treatment of nonlinear parametric processes in semiconductor microcavities including the electromagnetic field quantization. It represents the starting point for the microscopic approach to quantum optics experiments in the strong-coupling regime without any assumption on the quantum statistics of electronic excitations (excitons) involved. We exploit a previous technique, which was used in the semiclassical context, which, once applied to four-wave mixing in quantum wells, allowed us to understand a wide range of observed phenomena. We end up with dynamical equations for exciton and photon operators, which extend the usual semiclassical description of Coulomb interaction effects in terms of a mean-field term plus a genuine noninstantaneous four-particle correlation to quantum optical effects.

DOI
10.1103/physrevb.77.195305

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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.
A microscopic many-body theory for the optical and electronic properties of semiconductors is reviewed with an emphasis on the role of correlation effects. At the semiclassical level, the semiconductor Bloch equations include many-body effects via bandgap and field renormalization as well as correlation contributions representing two electron-hole pair amplitudes, excitonic populations, and coupled interband and intraband coherences. These Coulomb interaction induced carrier correlations lead to characteristic signatures in nonlinear semiconductor spectroscopy. At the fully quantum mechanical level the dominant light-matter correlations are described by coupled semiconductor Bloch and luminescence equations. Excitonic emission properties of quantum well and microcavity systems are discussed, including effects such as coherent signatures in the secondary emission and coherent control of the emitted light.
Abstract We present an extension of the previous descriptions based on the Dynamics Controlled Truncation Scheme of light‐matter interaction beyond mean‐field, including the microscopic description of the exciton‐photon interaction. This enables the microscopic analysis of the influence of decoherence and noise on the polariton quantum correlations originating from nonlinear optical processes. We expand the operators involved in the dynamics in terms of exact eigenstates of the electron system, the photon and phonon operators and treat phonon‐assisted transitions within the Markov approximation. In particular, we present quantum Heisenberg‐Langevin equations describing light‐induced excitations in semiconductor systems interacting with the phonon bath. This theoretical framework is applied to study the influence of dephasing and noise due to photoluminescence on polariton quantum correlations generated by parametric emission in microcavities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The dynamics of semiconductor quantum wires and wells that are coupled to a single-mode quantum field are analyzed. Within a two-band tight-binding model the Coulomb interaction between electrons and holes is included on a microscopic basis and the light-matter interaction is quantized. The dynamics of the system is described by equations of motion for the relevant set of expectation values of the coupled electronic-photonic system. Starting from the initial condition of a single photon occupying the field mode, we study the dynamics of the mean photon number. To analyze effects arising from the many-body Coulomb interaction, we use an exact truncation of the electronic hierarchy problem by employing the fact that N photons cannot excite more than N electron-hole pairs. We compare Rabi oscillations with and without Coulomb interaction for different excitation conditions. When the quantum field mode is initially occupied by two photons, two interacting electron-hole pairs, i.e., biexcitons, can be generated which characteristically modify the dynamics. Within a consistent and fully-quantized approach we show consequences of biexcitonic many-body correlations that are coupled to a quantum field and discuss the obtained dynamics.