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Quantum Electronics and Laser Science Conference

Transient four-wave-mixing lineshapes due to excitation induced shift and excitation induced dephasing

Justin M. Shacklette, Steven T. Cundiff

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. In an optically dense material, such as a semiconductor or a dense vapor, many-body interactions can dramatically modify the results of coherent experiments as compared to the dilute limit. The optical Bloch equations (OBE), which are appropriate in the dilute limit, must be modified to include many-body interactions. Such modified OBE (MOBE) are correct for a dense vapor and a phenomenological approximation for semiconductors, where a full treatment is based on the interacting electron-hole Hamiltonian. Previously, terms describing the local field correction (LFC) and excitation-induced dephasing (EID) have been added to the OBE to describe interactions. We show that an excitation-induced shift (EIS) is equally important. Perturbation calculations demonstrate that EIS gives rise to an additional signal in transient four-wave-mixing (TFWM), a common experiment for probing coherence. Comparison to numerical calculations shows that perturbation theory does not adequately describe either EIS or EID.

DOI
10.1109/qels.2002.1031324

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Summary form only given. In an optically dense material, such as a semiconductor or a dense vapor, many-body interactions can dramatically modify the results of coherent experiments as compared to the dilute limit. The optical Bloch equations (OBE), which are appropriate in the dilute limit, must be modified to include many-body interactions. Such modified OBE (MOBE) are correct for a dense vapor and a phenomenological approximation for semiconductors, where a full treatment is based on the interacting electron-hole Hamiltonian. Previously, terms describing the local field correction (LFC) and excitation-induced dephasing (EID) have been added to the OBE to describe interactions. We show that an excitation-induced shift (EIS) is equally important. Perturbation calculations demonstrate that EIS gives rise to an additional signal in transient four-wave-mixing (TFWM), a common experiment for probing coherence. Comparison to numerical calculations shows that perturbation theory does not adequately describe either EIS or EID.
We numerically calculate the transient-four-wave-mixing (TFWM) response in systems that exhibit either a resonance frequency or a dephasing rate that depends on the level of excitation, which can occur in semiconductors or a dense atomic vapor. These effects change the intensity dependence of the TFWM signal, causing it to display noncubic behavior for significantly lower pulse areas and even a reduction in signal intensity for increasing pulse area. They also qualitatively change both the temporal behavior and spectrum of the TFWM signal in ways that cannot adequately be described in perturbation theory. For time-integrated TFWM, the saturation behavior is also found to depend on the delay between pulses. For comparison, the effects of local fields are also calculated as they produce similar effects. These results can help provide discrimination among the various phenomena.
A transient four-wave-mixing signal is shown to arise from an excitation induced shift. In semiconductors, this signal can be comparable to or stronger than signals arising from saturation, local fields, or excitation induced dephasing. Calculations using modified optical Bloch equations show that multiple peaks in the transient four-wave-mixing spectrum are a signature of an excitation induced shift contributing to the signal. We observe this experimentally from a semiconductor multiple quantum well and confirm the presence of a shift directly using spectrally resolved differential transmission.
Transient four-wave mixing studies of bulk GaAs under conditions of broad bandwidth excitation of primarily interband transitions have enabled four-particle correlations tied to degenerate (exciton-exciton) and nondegenerate (exciton-carrier) interactions to be studied. Real two-dimensional Fourier-transform spectroscopy (2DFTS) spectra reveal a complex response at the heavy-hole exciton emission energy that varies with the absorption energy, ranging from dispersive on the diagonal through absorptive for low-energy interband transitions to dispersive with the opposite sign for interband transitions high above band gap. Simulations using a multilevel model augmented by many-body effects provide excellent agreement with the 2DFTS experiments and indicate that excitation-induced dephasing (EID) and excitation-induced shift (EIS) affect degenerate and nondegenerate interactions equivalently, with stronger exciton-carrier coupling relative to exciton-exciton coupling by approximately an order of magnitude. These simulations also indicate that EID effects are three times stronger than EIS in contributing to the coherent response of the semiconductor.
Summary form only given. Despite recent effort, there are aspects of the transient four-wave-mixing (TFWM) response of semiconductors that remain puzzling. By performing partially nondegenerate TFWM (PND-TFWM) we show that for broadband excitation, the signal emitted at the 1 s exciton is dominated by contributions that correspond to excitation of higher states by the first pulse. The interference of these contributions results in the rapid decay of the excitonic signal. Our results demonstrate that, because TFWM is inherently a many-particle phenomenon, the many-body interactions always couple the excitonic transitions.