coherent motions of excitons in AsGa

In a band structure materials, especially in a semiconductor, an electron-hole pair can be generated by optical means, with a hole moving in the valence band while an electron in the conduction band. These two entities will attract each other due to Coulomb interaction and actually, they form bound state (a state with energy lower than when they are independent). The energy of such bound state is of the order of 0.01~1 ev, which suggests, in comparison with a hydrogen atom, their size of 10~1000 times larger than hydrogen atom. On scales larger than sizes, such pairs behave like bosons, as both of them are fermions. They can condense. At a closer look on smaller scales, their correlations shall be different. Here is an experiment that is aimed at exactly how multi-exciton correlations might be. The writers found that, coherent motions exist for three excitons, but not for four. A review of their work:

Because of the correlations between electrons and holes, photoexcitation results in the formation of collective electronic states that, in turn, contribute significantly to phenomena such as nonlinear optical properties, optical gain in laser media, the dynamics of highly excited states and the production of ‘entangled’ photons. Although the authors’ experiments2 indicate the presence of correlations (Fig. 1), do they reveal how the details or implications of such correlations relate to these kinds of phenomena? It seems not. The energy shifts recorded in the experiments
(the binding energies of biexcitons and triexcitons) arise from a combination of two major effects. The first, which probably dominates, is explained by theories such as the Hartree–Fock method. These theories evaluate the average electron–hole attractions, electron–electron (hole–hole) repulsions and quantum-mechanical exchange corrections to these Coulomb interactions by assuming that the charges are spread out in space according to the probability that the particle could be found there. The second effect, called electron correlation in the quantum-chemical literature7, describes the fascinating way in which electrons and holes tend to coordinate their motions to minimize repulsions. For example, two electrons
might move in such a fashion that they avoid crossing paths. The complexity of this problem scales steeply with the number of particles involved. Although current investigations into many-body effects provide an important first step to understanding how groups of carriers interact collectively, they cannot quantify the average Coulomb repulsions and attractions relative to how these are modified by correlations in multiparticle motions.

Turner, D. B. & Nelson, K. A. Nature 466, 1089–1092