Influence of a phonon bath in a quantum dot cavity QED system： Dependence of the shape

We present a systematic analysis on the role of the quantum dot （QD） shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes： spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains（≤2 ps）, and the oft-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence.