Coherent Energy Transfer Dynamics and Photoluminescence of Coupled Quantum Dots: Fully Analytical Approach

Abstract

We theoretically studied coherent excitation energy transfer between self-growth semiconductor quantum dots (QDs) by solving Heisenberg’s equations of motion for density matrix elements in second quantization regime. In a local excitation condition where only one QD electron is optically excited by the pump laser field, coherent excitation energy transfer to the other QD electron can be achieved through Coulomb (Forster) and electron-photon (radiation field) interactions. We calculated three diagonal and one off-diagonal Coulomb coupling constants, which are responsible for the biexcitonic frequency renormalization and the coherent energy transfer between QDs, respectively, and radiation field coupling coefficients by using electron and hole wave functions derived from eight-band kp-theorem, whose validity has already been tested by comparison with experiment. In linear optical regime where the occupation densities of electrons at higher energy level are negligibly small, we could successfully derive fully analytical behaviors of temporal dynamics of the interband polarizations and level occupation densities of both QDs by using Hartree-Fock approximation (HFA), in eventual, the stationary photoluminescence of the coupled QDs in an analytical form. Additionally, the validity of the HFA was examined by comparing the numerical results with those obtained from the exact correlation expansion model for different values of the pump field intensity.