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arXiv:1602.01150 · Journal of the Optical Society of America B

Two-dimensional double-quantum spectroscopy: peak shapes as a sensitive probe of carrier interactions in quantum wells

Jonathan Owen Tollerud, Jeffrey A. Davis

Published May 18, 2016• 38 citations
arXivHTMLPDF

Abstract

We identify carrier scattering at densities below that which has previously been observed in semiconductor quantum wells. These effects are evident in the peak shapes of 2D double-quantum spectra, which change as a function of excitation density. At high excitation densities (>109 excitons/cm2), we observe untilted peaks similar to those reported in previous experiments. At low excitation densities (<108 excitons/cm2), we observe narrower tilted peaks. Using a simple simulation, we show that tilted peak shapes are expected in double-quantum spectra when inhomogeneous broadening is much larger than homogeneous broadening, and that fast pure-decoherence of the double-quantum coherence can obscure this peak tilt. These results show that carrier interactions are important at lower densities than previously expected, and that the “natural” double-quantum peak shapes are hidden by carrier interactions at the excitation densities typically used. Furthermore, these results demonstrate that analysis of 2D peak shapes in double-quantum spectroscopy provides an incisive tool for identifying interactions at low excitation density.

DOI
10.1364/josab.33.00c108

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We identify carrier scattering at densities below that which has previously been observed in semiconductor quantum wells. These effects are evident in the peak shapes of 2D double-quantum spectra, which change as a function of excitation density. At high excitation densities (>109 excitons/cm2), we observe untilted peaks similar to those reported in previous experiments. At low excitation densities (<108 excitons/cm2), we observe narrower tilted peaks. Using a simple simulation, we show that tilted peak shapes are expected in double-quantum spectra when inhomogeneous broadening is much larger than homogeneous broadening, and that fast pure-decoherence of the double-quantum coherence can obscure this peak tilt. These results show that carrier interactions are important at lower densities than previously expected, and that the “natural” double-quantum peak shapes are hidden by carrier interactions at the excitation densities typically used. Furthermore, these results demonstrate that analysis of 2D peak shapes in double-quantum spectroscopy provides an incisive tool for identifying interactions at low excitation density.
Double-quantum two-dimensional (2D) coherent spectroscopy (MDCS) is a powerful optical method that is used to study the optical properties of atomic and complex molecular systems and semiconductor materials. Double-quantum 2D spectra and particularly the peak line shapes on the spectra can also provide information about many-body interactions. We model 2D spectra by solving the optical Bloch equations and show the effects of correlation between coupled resonances, which also explains the discrepancies between the experimental results reported by multiple groups.
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.
Abstract Techniques for coherent multidimensional optical spectroscopy have been developed and utilised to understand many different processes, including energy transfer in photosynthesis and many‐body effects in semiconductor nanostructures. Double‐quantum 2D spectroscopy is one variation that has been particularly useful for understanding many‐body effects. In condensed matter systems, however, there are often many competing signal pathways, which can make it difficult to isolate different contributions and retrieve quantitative information. Here, a means of separating overlapping pathways while maintaining the fidelity of the relevant peak/s is demonstrated. This selective approach is used to isolate the double‐quantum signal from a mixed two exciton state in a semiconductor quantum well. The removal of overlapping peaks allows analysis of the relevant peak‐shape and thus details of interactions with the environment and other carriers to be revealed. An alternative pulse ordering identifies a double‐quantum state associated only with GaAs defects, the signature of which has previously been confused with other interaction induced effects. The experimental approach described here provides access to otherwise hidden details of excitonic interactions and demonstrates that the manner in which the double‐quantum coherence is generated can be important and provide an additional control to help understand the many‐body physics in complex systems. image
Multidimensional analysis of coherent signals is commonly used in nuclear magnetic resonance to study correlations among spins. These techniques were recently extended to the femtosecond regime and applied to chemical, biological and semiconductor systems. In this work, we apply a two-dimensional correlation spectroscopy technique which employs double-quantum-coherence to investigate many-body effects in a semiconductor quantum well. The signal is detected along the direction k(1)+ k(2)- k(3), where k(1), k(2) and k(3) are the pulse wave vectors in chronological order. We show that this signal is particularly sensitive to many-body correlations which are missed by time-dependent Hartree-Fock approximation. The correlation energy of two-exciton can be probed with a very high resolution arising from a two-dimensional correlation spectrum, where two-exciton couplings spread the cross peaks along both axes of the 2D spectrum to create a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo (-k(1)+ k(2)+ k(3)).