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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Probing many-body interactions in a disordered semiconductor quantum well with electronic two-dimensional Fourier transform spectroscopy

Zheng Sun, Thomas W. Jarvis, Xiaoqin Li, Mikhail Erementchouk, Michael Niklaus Leuenberger

Published Feb 11, 2010• 0 citations
Publisher

Abstract

The interplay between disorder and Coulomb interactions ubiquitously affects the properties of condensed matter systems. We examine its role in the nonlinear optical response of semiconductor quantum wells. In particular, we investigate the coherent coupling strength between exciton resonances that are spectrally split by interface fluctuations. Previous studies yielded conflicting results. In light of rising interest in semiconductor devices that rely on spatial and/or temporal coherence, we revisit this problem by applying a newly developed spectroscopy method: electronic two-dimensional Fourier transform spectroscopy (2DFTS). 2DFTS is a powerful technique for revealing the presence of coupling and for distinguishing the (coherent or incoherent) nature of such coupling, especially in complex systems with several spectrally overlapping resonances. Even the most basic information about such complex systems, including the homogeneous and inhomogeneous linewidths of various resonances, cannot be extracted reliably using conventional spectroscopic tools. In these new 2DFTS measurements, we did not observe any clear cross peaks corresponding to coherent couplings between either heavy-hole or light-hole excitons. These measurements allow us to place a quantitative upper bound on the possible coupling strength in this prototypical system. A modified mean-field theory reveals a simple yet important relation that determines how the coherent coupling strength depends on the disorder correlation length and Coulomb interaction length. © 2010 Copyright SPIE - The International Society for Optical Engineering.

DOI
10.1117/12.840125

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The interplay between disorder and Coulomb interactions ubiquitously affects the properties of condensed matter systems. We examine its role in the nonlinear optical response of semiconductor quantum wells. In particular, we investigate the coherent coupling strength between exciton resonances that are spectrally split by interface fluctuations. Previous studies yielded conflicting results. In light of rising interest in semiconductor devices that rely on spatial and/or temporal coherence, we revisit this problem by applying a newly developed spectroscopy method: electronic two-dimensional Fourier transform spectroscopy (2DFTS). 2DFTS is a powerful technique for revealing the presence of coupling and for distinguishing the (coherent or incoherent) nature of such coupling, especially in complex systems with several spectrally overlapping resonances. Even the most basic information about such complex systems, including the homogeneous and inhomogeneous linewidths of various resonances, cannot be extracted reliably using conventional spectroscopic tools. In these new 2DFTS measurements, we did not observe any clear cross peaks corresponding to coherent couplings between either heavy-hole or light-hole excitons. These measurements allow us to place a quantitative upper bound on the possible coupling strength in this prototypical system. A modified mean-field theory reveals a simple yet important relation that determines how the coherent coupling strength depends on the disorder correlation length and Coulomb interaction length. © 2010 Copyright SPIE - The International Society for Optical Engineering.
Optical two-dimensional Fourier transform (2DFT) spectroscopy has been developed over the last decade as a powerful tool for studying a variety of physical systems, ranging from atoms to molecules to solids. This review covers our use of 2DFT spectroscopy to study exciton dynamics in semiconductor nanostructures. In quantum wells, 2DFT spectroscopy confirms the importance of many-body contributions to the coherent optical response and reveals nonradiative double-quantum and Raman coherences. For natural quantum dots, 2DFT spectroscopy enables ensemble measurements of the homogeneous linewidth, including the temperature and density dependence. Relaxation from quantum well states into the quantum dots can also be studied using 2DFT spectroscopy.
A particular difficulty in studying many-body interactions in a solid is the absence of an experimental technique that can directly probe their key characteristics. We show that two-dimensional (2D) Fourier spectroscopy provides an efficient tool for the measurement of critical parameters describing the effect of many-body interactions on the optical response of semiconductors. We develop the basic microscopic theory of 2D Fourier spectroscopy of semiconductors in the framework of the three-band model (heavy holes, light holes, and electrons). The theory includes many-body correlations nonperturbatively and can be generalized straightforwardly in order to describe 2D Fourier spectra obtained in atomic physics. We establish a relation between the 2D Fourier spectrum and the many-body correlations. It is shown, in particular, that 2D Fourier spectroscopy provides a principal possibility to establish experimentally the origin of the fast decay of the memory term describing the Coulomb interaction between heavy- and light-hole excitons. The theory is applied to an analysis of the available experimental data. Experiments providing more detailed information are suggested.
Correlated electron-hole pairs, or excitons, in semiconductor nanostructures have been studied extensively over the past few decades. The optical response of excitons is complicated due to inhomogeneous broadening, presence of multiple states, and exciton-exciton interactions. In this work we bring new perspectives to exciton physics in semiconductor quantum wells (QWs) through two-dimensional coherent spectroscopy (2DCS).\nThe effect of QW growth direction on the optical properties of excitons is explored by studying (110)-oriented GaAs QWs. The homogeneous and inhomogeneous linewidths of the heavy-hole exciton resonance are measured. By probing the optical nonlinear response for polarization along the in-plane crystal axes [1-10] and [001], we measure different homogeneous linewidths for the two orthogonal directions. This difference is found to be due to anisotropic excitation-induced dephasing, caused by a crystal-axis-dependent absorption coefficient. The extrapolated zero-excitation density homogeneous linewidth exhibits an activation-like temperature dependence.\nSpectral diffusion of excitons in (001)-oriented QWs has been studied. We show that the spectral diffusion characteristics depend strongly on the sample temperature. Spectral diffusion is generally assumed to follow the strong-redistribution approximation, partly because of lack of any evidence to the contrary. We find that this assumption is violated at low sample temperatures for excitons in QWs; high-energy excitons preferentially relax due to a negligible phonon population at low temperatures. The frequency-frequency correlation function is measured through a numerical fitting procedure to quantify spectral diffusion for sample temperatures >20>20>20 K.\nExciton-exciton interactions affect the light-matter interactions in QWs significantly. We present an intuitive and simple model for these interactions by treating excitons as interacting bosons. We show that the polarization-dependent exciton dephasing rate in GaAs quantum wells is due to the bosonic character of excitons. We fit slices from simulated spectra to those from the experimentally measured spectra and show that interference between two different quantum mechanical pathways results in a slower dephasing rate for co-circular and co-linear polarization of optical excitation pulses. This interference does not exist for cross-linearly polarized excitation pulses resulting in a faster dephasing rate. Additionally, we were able to separately quantify inter- and intra-mode interactions between excitons through exciton-density-dependent measurements.
Electronic structure and dynamics are captured by optical 2D-Fourier-transform (2DFT) spectroscopy, which tracks the phase of the nonlinear signal during two time delays of a multi-pulse excitation sequence. These Fourier-transformed spectra separate and isolate overlapping and competing contributions to the coherent response. We have developed an ultra-stable platform consisting of nested interferometers with active phase control, allowing for exploration of single- and two-quantum coherences. Phase-resolved spectra are retrieved by all-optical determination of experimental phase ambiguities. GaAs quantum wells show suppression of many-body interactions in cross-linear polarized 2DFT spectra and many-body two-quantum coherences. Potassium vapor also shows unexpected two-quantum coherences.
Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.