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The Journal of Chemical Physics

Isolating excitonic Raman coherence in semiconductors using two-dimensional correlation spectroscopy

Lijun Yang, Tianhao Zhang, Alan D. Bristow, Steven T. Cundiff, Shaul Mukamel

Published Dec 19, 2008• 76 citations
Publisher

Abstract

We present the experimental and simulation results of two-dimensional optical coherent correlation spectroscopy signals along the phase-matching direction k(I) = -k(1) + k(2) + k(3) projected on the two-dimensional (2D) (Omega(3),Omega(2)) plane corresponding to the second and third delay periods. Overlapping Raman coherences in the conventional (Omega(3),Omega(1)) 2D projection may now be clearly resolved. The linewidths of the heavy-hole (HH) and light-hole (LH) excitonic Raman coherence peaks are obtained. Further insights on the higher-order (beyond time-dependent Hartree-Fock) correlation effects among mixed (HH and LH) two excitons can be gained by using a cocircular pulse polarization configuration.

DOI
10.1063/1.3037217

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We present the experimental and simulation results of two-dimensional optical coherent correlation spectroscopy signals along the phase-matching direction k(I) = -k(1) + k(2) + k(3) projected on the two-dimensional (2D) (Omega(3),Omega(2)) plane corresponding to the second and third delay periods. Overlapping Raman coherences in the conventional (Omega(3),Omega(1)) 2D projection may now be clearly resolved. The linewidths of the heavy-hole (HH) and light-hole (LH) excitonic Raman coherence peaks are obtained. Further insights on the higher-order (beyond time-dependent Hartree-Fock) correlation effects among mixed (HH and LH) two excitons can be gained by using a cocircular pulse polarization configuration.
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)).
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.
Quantum beats involving the light hole (lh) and heavy hole (hh) excitons in GaAs are observed using homodyne detection of the transient four-wave mixing response. Unlike the beats of earlier studies, these beats are detected in a geometry for which the effect would be forbidden in the absence of exciton interactions and arise from coherence induced between the lh and hh excitons. The beats demonstrate the existence of the Raman coherence due to interaction, and the decay of the coherence shows the correlation of exciton dephasing rates to be relatively unaffected by the interaction.
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.
Quantum beats involving the light-hole and heavy-hole excitons in GaAs quantum wells are studied using both conventional and novel temporally gated differential detection techniques. The contributions of the exciton-exciton correlations are separated from those of the intervalence-band Raman coherence and the interband (population) coherence by monitoring the signal in the probe direction and by taking advantage of the polarization selection rules for the excitonic transitions. The results are shown to be in agreement with a theoretical analysis based on the dynamics-controlled truncation formalism.