Self-consistent theory of the biexciton optical nonlinearity

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Abstract
For the low-excitation regime a self-consistent set of equations for excitons (x), exciton molecules (m), and photons (γ) is derived from the electron-hole-photon Hamiltonian, taking the spin explicitly into account. In this approach the creation of m occurs via the Coulombic scattering of two x’s of opposite internal spin structure. This process is resonant due to the polariton effect. Thus, the Coulombic matrix element for the process x+x→m governs the m formation, rather than the optical matrix element for the process x+γ→m, as is usually assumed. At the same time, the scattering process x+x→m gives rise to a ‘‘true two-photon absorption’’ in the sense of Hopfield’s concept of absorption in the polariton theory. Both for the 2γ absorption and for the x-m optical Stark effect, our theory gives measurable differences compared to the usual phenomenological approach. A Schrödinger equation for the m-wave function is derived which includes polariton effects.