Optical absorption in quantum dots: Coupling to longitudinal optical phonons treated exactly

Optical transitions in a semiconductor quantum dot are theoretically investigated, with emphasis on the coupling to longitudinal optical phonons, and including excitonic effects. When limiting to a finite number of m electron and n hole levels in the dot, the model can be solved exactly within numerical accuracy. Crucial for this to work is the absence of dispersion of the phonons. A suitable orthogonalization procedure leaves only m(m+1)∕2+n(n+1)∕2-2 phonon modes to be coupled to the electronic system. We calculate the linear optical polarization following a delta pulse excitation and, by a subsequent Fourier transformation, the resulting optical absorption. This strict result is compared with a frequently used approximation modeling the absorption as a convolution between spectral functions of electron and hole, which tends to overestimate the effect of the phonon coupling. Numerical results are given for two electron and three hole states in a quantum dot made from the polar material CdSe. Parameter values are chosen such that a quantum dot with a resonant sublevel distance can be compared with a nonresonant one.