Influence Of Phonon Bath On The Quantum Dot-microcavity Systems

The main interest of cavity quantum electrodynamics (cQED) is the properties of atom oratom-like emitters in cavities. CQED provides a basic model for the light-matter interaction inquantum optics. Compared with traditional atoms cQED, solid-state cQED systems have someadvantages such as small size of the microcavity and scalability. The microcavity consisting ofquantum dots (QD) and the photonic crystal is a typical solid-state cQED system. A semiconductorquantum dot interacts with bulk phonons in the solid environment besides interacting with the cavitymode. Three effects can be induced by the phonon bath: the coupling renormalization, theoff-resonance assisted feeding and the pure dephasing. Phonon spectrum functions are essential in thecalculation of these effects which are the focus of this study. In this paper, the physics and applicationsof cQED were introduced first. Fabrication techniques of self-assembled quantum dots and opticalmicrocavity systems were presented. Then the theoretical model including the Hamiltonian of thesolid-state cQED systems and the Gaussian wave functions were developed. The difference betweenelectron and hole in the confinement length has been taken into consideration. Spherical (ellipsoidal)Gaussian wave functions were used to simulate the size (shape) of the quantum dot. Two couplingmechanisms between the electron-hole pair and the phonon bath were investigated, and thecorresponding phonon spectrum density functions were calculated analytically. The phonon-introducedpure dephasing rates were calculated numerically from the phonon bath correlation function. Using anapproximate expression, the total decay rates of quantum dots dependence on the QD-cavity detuningat different temperatures were obtained. The results show that both the amplitude and extending rangeof the phonon spectrum increase as the confinement lengths of quantum dots decrease. As aconsequence, the interaction between the electron-hole pair and the acoustic phonon strengthens therenormalization of the QD-cavity coupling factor. Pure dephasing rates increase as the confinementlengths of the quantum dot decrease, and increase as the temperature T increases. At T=4K, the totaldecay rates of the quantum dot dependence on the QD-cavity detuning shows little change for thephonon spectrum of different sizes and shapes. However, the phonon spectrum of4nm size has aspecial behavior. The confinement length of quantum dots dominates the coupling between theelectron-hole and the phonon.