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Physical review. B, Condensed matter

Simultaneous influence of disorder and Coulomb interaction on photon echoes in semiconductors

F. Jahnke, Martín Koch, T. Meier, Jochen Feldmann, Wilfried Schäfer, P. Thomas, Stephan W. Koch, Ernst Otto Göbel, Heinrich. Nickel

Published Sep 15, 1994• 48 citations
Publisher

Abstract

The effects of disorder and many-body interaction on the four-wave-mixing signal in semiconductor quantum wells are studied experimentally and theoretically. For weakly disordered samples it is shown that the combined influence of Coulomb and disorder effects leads to a characteristic photon-echo signal in time-resolved measurements and to oscillations in the time-integrated signal. Convincing agreement between experiment and theory is demonstrated.

DOI
10.1103/physrevb.50.8114

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•Jan 1, 2003•0 citations
The effects of disorder and many-body interaction on the four-wave-mixing signal in semiconductor quantum wells are studied experimentally and theoretically. For weakly disordered samples it is shown that the combined influence of Coulomb and disorder effects leads to a characteristic photon-echo signal in time-resolved measurements and to oscillations in the time-integrated signal. Convincing agreement between experiment and theory is demonstrated.
The simultaneous influence of pulse propagation and Coulomb many-body interaction in Four Wave Mixing experiments is theoretically studied using the Semiconductor-Maxwell-Bloch equations. In this framework, the propagation of the optical fields and the microscopic interaction of the light with the semiconductor are treated consistently. The Maxwell equation is used as a reduced wave equation and the many-body Coulomb interaction are treated at the level of a screened Hartree-Fock approximation including phenomenological decay terms. We have analyzed the interplay of the propagation and Coulomb effects by calculating the Four Wave Mixing signal (FWMS) for different sample lengths and various excitation conditions, i.e, for pulses with different intensities at the exciton and in the continuum.
We have performed time-integrated as well as time-resolved femtosecond degenerate four-wave-mixing measurements on inhomogeneously broadened (Zn,Cd)Se/ZnSe quantum-well structures. Potential fluctuations due to alloy disorder in the ternary wells give rise to localized quasi-zero-dimensional excitons and biexcitons. For time-integrated detection, they manifest themselves by distinct (disorder-renormalized) quantum beats. Time resolving these transients reveals a free-induction-decay-like emission nature of the biexciton in contrast to the photon-echo exciton contribution. Using a five-level scheme, containing both biexcitons and antibound two-exciton states, this striking emission-type change is explained by fluctuation and correlation effects upon the biexciton binding energy. A combination of time-resolved and time-integrated four-wave mixing is thus a powerful tool to gain information about the disorder in a given kind of quantum structure.
The photon-echo signal in disordered semiconductors is treated including the electron-hole Coulomb attraction. The amplitude of the spontaneous photon echo is calculated up to third order in the external-field amplitude using the semiconductor Bloch equations. Several idealized situations are analyzed showing the significance of a critical correlation of the polarization dynamics in the two time intervals preceding and following the second excitation pulse. Strong photon-echo decay is predicted for short-range disorder without Coulomb interaction. The inclusion of electron-hole attraction leads to a stabilization of the echo signal. For the case of long-range disorder with Coulomb interaction, we predict slow decay in the diffusive limit.
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.
Summary form only given. Four-wave mixing processes in semiconductor quantum wells have been studied intensively for many years, because they allow for a detailed investigation of ultrafast many-body processes such as quantum correlations and quantum coherences. From a theoretical point of view one can roughly divide the existing approaches into two categories: (i) fully microscopic theories based on the bandstructure and on Coulomb interactions between electrons and holes, and (ii) phenomenological few-level models.
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.