Quantum Kinetic Theory of Phonon-Assisted Excitation Transfer in Quantum Dot Molecules

We present a quantum-kinetic theory of the excitation transfer in a quantum dot molecule. We derive the consistent Markovian limit for the system kinetics, which leads to a description in terms of a single transfer rate for weak coupling. We show that the transfer rate is a strongly varying, nonmonotonic function of the spatial separation and energy mismatch between the dots.

Figure 1

(a),(b) The Bloch sphere representation of the evolution for two coupling strengths. (c),(d) The corresponding occupation of the “dot 1” as a function of time. The results are calculated at $T=4\mathrm{K}$. Inset in (c): the system geometry. Inset in (d): the correction to the dipole approximation.

Figure 2

The occupation of the higher energy QD as a function of time at $T=4\mathrm{K}$: (a) $D=8\mathrm{nm}$ and $\Delta$ as shown; (b) $\Delta =3\mathrm{meV}$ and $D$ as shown. Dashed line: the Markov approximation with renormalized coupling.

Figure 3

(a) The initial stage of the transfer from “dot 1“ at $T=4\mathrm{K}$, obtained in different approximations: CE (solid line), TCL (dashed line), Markov-RWA (dotted line), and Markov-RWA with renormalized coupling (thick points). (b) The phonon spectral density of the QDM at $T=4\mathrm{K}$.

Figure 4

The rate of phonon-assisted excitation transfer as a function of the energy mismatch for a few values of the QD separation $D$ (a) and as a function of $D$ for a few values of $\Delta$ (b) at $T=4\mathrm{K}$.