The Coulomb correlations between photoexcited charged particles in materials such as photosynthetic complexes, conjugated polymer systems, J-aggregates, and bulk or nanostructured semiconductors produce a hierarchy of collective electronic excitations, for example, excitons, and biexcitons, which may be harnessed for applications in quantum optics, light-harvesting, or quantum information technologies. These excitations represent correlations among successively greater numbers of electrons and holes, and their associated multiple-quantum coherences could reveal detailed information about complex many-body interactions and dynamics. However, unlike single-quantum coherences involving excitons, multiple-quantum coherences do not radiate; consequently, they have largely eluded direct observation and characterization. In this Account, we present a novel optical technique, two-quantum, two-dimensional Fourier transform optical spectroscopy (2Q 2D FTOPT), which allows direct observation of the dynamics of multiple exciton states that reflect the correlations of their constituent electrons and holes. The approach is based on dosely analogous methods in NMR, in which multiple phase-coherent fields are used to drive successive transitions such that multiple-quantum coherences can be accessed and probed. In 2Q 2D FTOPT, a spatiotemporal femtosecond pulse-shaping technique has been used to overcome the challenge of control over multiple, noncollinear, phase-coherent optical fields in experimental geometries used to isolate selected signal contributions through wavevector matching We present results from a prototype GaAs quantum well system, which reveal distinct coherences of biexdtons that are formed from two identical excitons or from two excitons that have holes in different spin sublevels ("heavy-hole" and light-hole" excitons). The biexdton binding energies and dephasing dynamics are determined, and changes in the dephasing rates as a function of the excitation density are observed, revealing still higher order correlations due to exdton-biexciton interactions. Two-quantum coherences due to four-particle correlations that do not involve bound biexciton states but that influence the exciton properties are also observed and characterized. The 2Q 2D FTOPT technique allows many-body interactions that cannot be treated with a mean-field approximation to be studied in detail; the pulse-shaping approach simplifies greatly what would have otherwise been daunting measurements. This spectroscopic tool might soon offer insight into specific applications, for example, in detailing the interactions that affect how electronic energy moves within the strata of organic photovoltaic cells.
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