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Journal of the Optical Society of America B

Quantifying spectral diffusion by the direct measurement of the correlation function for excitons in semiconductor quantum wells

Rohan Singh, Galan Moody, Mark E. Siemens, Hebin Li, Steven T. Cundiff

Published Jun 3, 2016• 40 citations
Publisher

Abstract

The phenomenon of spectral diffusion is common to a variety of inhomogeneously broadened systems. Spectral diffusion can be quantified through the frequency–frequency correlation function (FFCF), which is often approximated using observables from a variety of experimental techniques. We present a direct measurement of the temperature-dependent FFCF for excitons in semiconductor quantum wells using two-dimensional coherent spectroscopy. This technique enables the FFCF to be quantified without making any assumptions of the FFCF dynamics. Our results show that the Gauss–Markov approximation, which assumes exponential decay dynamics of the FFCF, is only valid for sample temperatures above 50 K. We compare our results with those obtained by the ellipticity and center-line slope measurements.

DOI
10.1364/josab.33.00c137

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The phenomenon of spectral diffusion is common to a variety of inhomogeneously broadened systems. Spectral diffusion can be quantified through the frequency–frequency correlation function (FFCF), which is often approximated using observables from a variety of experimental techniques. We present a direct measurement of the temperature-dependent FFCF for excitons in semiconductor quantum wells using two-dimensional coherent spectroscopy. This technique enables the FFCF to be quantified without making any assumptions of the FFCF dynamics. Our results show that the Gauss–Markov approximation, which assumes exponential decay dynamics of the FFCF, is only valid for sample temperatures above 50 K. We compare our results with those obtained by the ellipticity and center-line slope measurements.
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.
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A new method to measure the coherence of inhomogeneously broadened optical excitations in semiconductor nanostructures is presented. The secondary emission of excitons in semiconductor quantum wells is investigated. The spectrally-resolved coherence degree of resonantly-excited light emission is deduced from the intensity fluctuations over the emission directions (speckles). The spectral correlations of the speckles give direct access to the homogeneous line width as function of spectral position within the inhomogeneously broadened ensemble. The combination of static disorder and phonon scattering leads to a partially coherent emission. The temperature dependence of the homogeneous line width is well explained by phonon scattering.
Three-pulse four-wave mixing is used to observe the loss of system memory for excitons confined in quantum wells. By measuring the photon echo peak shift with pulse delay, we obtain the two-time exciton frequency fluctuation correlation function. Spectral diffusion of localized excitons gives rise to exponential decay of the correlation function, while static inhomogeneity gives an offset. Nonmonotonic behavior during the first few picoseconds indicates complex memory effects due to the interaction of excitons with acoustic phonons.
Solid-state quantum emitters are playing a crucial role in the development of photonic quantum technologies. However, several decoherence mechanisms are known to impact the device performances and scalability. In various quantum emitter materials the fluctuation of the two-level system has been investigated by different methods to capture the evolution of coherence reduction. However, resolving the dynamics of spectral diffusion in the fundamental framework of on-demand single-photon generation remained unsolved. Hereby, the challenge is to observe with high time and energy resolution the impact of fluctuations directly in the properties of the emitted photons. In this Rapid Communication, we demonstrate the use of dispersion in a slow-light medium to map the photons frequency domain into time domain, observed as frequency-dependent time-of-flight. This allows for the measurement of the emission spectrum and the quantification of the spectral diffusion dynamics in one intensity correlation measurement. On exemplary semiconductor quantum dots, the impact of charge and spin noise on the spectral diffusion are revealed to follow an Ornstein-Uhlenbeck process. By a single measurement, broadening from the excitation repetition up to the stationary limit is resolved. This enables one to extract time-dependent two-photon interference visibilities for various timescales, which is a key performance measure for quantum emitters.
A linear optical method to measure coherence and dephasing of excitations in solids is presented. The spectrally resolved degree of coherence of resonantly scattered light is deduced from the intensity fluctuations over its emission directions (speckles). The spectral intensity correlation gives a direct measure of the dephasing rate within the inhomogeneously broadened ensemble. For localized excitons in semiconductor quantum wells, the combination of static disorder, phonon scattering, and radiative decay leads to a spectral dependence of the emission coherence and the dephasing rate, which is well described by model calculations.