Coherent measurements of high-order electronic correlations in quantum wells

Long-range correlations between charge particles (electrons and 'holes') in semiconductors lead to many-body effects, which are of fundamental interest and also of importance in optoelectronic applications. The exciton state, in which an electron and hole are paired, has been extensively studied, but the properties of multiple exciton states involving three or more charge particles are largely unknown as they are challenging to observe experimentally. Daniel Turner and Keith Nelson have extended a spectroscopy technique called multidimensional Fourier transform optical spectroscopy, and demonstrate its ability to generate and characterize bi-excitons, tri-excitons and other unbound correlations in a gallium arsenide nanostructure. This experiment involves controlling the geometry, temporal delays and optical phases of up to seven light fields simultaneously. The findings are of particular interest as it was previously not known whether tri-excitons — involving correlations between six particles — could exist at all. The authors also present clear evidence that four-exciton states do not exist, indicating an upper limit for many-body correlations in this type of semiconductor system. The exciton state in semiconductors, where an electron and hole are paired, has been studied extensively, but the properties of exciton states involving three or more charged particles are largely unknown. These authors use a challenging spectroscopy technique to generate and characterize biexcitons, triexcitons and other, unbound, correlations in a gallium arsenide nanostructure. It was previously unknown whether triexcitons, which involve correlations between six particles, can exist at all. Strong, long-range Coulomb interactions can lead to correlated motions of multiple charged particles, which can induce important many-body effects in semiconductors. The exciton states formed from correlated electron–hole pairs have been studied extensively1,2, but basic properties of multiple-exciton correlations—such as coherence times, population lifetimes, binding energies and the number of particles that can be correlated—are largely unknown because they are not spectroscopically accessible from the ground state. Here we present direct observations of high-order coherences in gallium arsenide quantum wells, achieved using two-dimensional multiple-quantum spectroscopy methods in which up to seven successive light fields were used. The measurements were made possible by the combination of a reconfigurable spatial beam-shaper that formed multiple beams in specified geometries and a spatiotemporal pulse-shaper that controlled the relative optical phases and temporal delays among pulses in all the beams. The results reveal triexciton coherences (correlations of three excitons or six particles), whose existence was not obvious because the third exciton spin is unpaired, and the values of their coherence times and binding energies. Rephasing of biexcitons, triexcitons and unbound two-exciton coherences was demonstrated. We also determined that there are no significant unbound correlations of three excitons and no bound or unbound four-exciton (eight-particle) correlations. Thus, the limits, as well as the properties, of many-body correlations in this system were revealed. The measurement methods open a new window into high-order many-body interactions in materials and molecules3, and the present results should guide ongoing work on first-principles calculations of electronic interactions in semiconductor nanostructures4.