Coherent state monitoring in quantum dots

We study the dynamics of excitonic states in dimer and trimer arrangements of colloidal quantum dots using a density-matrix approach. The dots are coupled via a dipole-dipole interaction akin to the Förster mechanism. Coherent oscillations of tuned donor dots are shown to appear as plateaus in the acceptor dot, and therefore in its optical response. This behavior provides one with an interesting and unique handle to monitor the quantum state of the dimer, an “eavesdroping arrangement.” A trimer cluster in a symmetrical loop shows steady states in a shorter characteristic time than the typical radiative lifetime of the dots. Breaking the symmetry of the loop results again in damping oscillatory states in the donor dots and plateaus in the eavesdropping∕acceptor dot. The use of realistic parameters allows direct comparison with recent experiments and indicates that coherent-state monitoring is possible in real experiments.

Figure 1

(Color online) Time evolution of occupation probability of lower exciton state in each dot. Parameters used are $V_F^d=-0.05\mathrm{meV}$, $V_F^b=-1\mathrm{meV}$, $V_F^{db}=-0.21\mathrm{meV}$, ${\Gamma }_D=32\mathrm{meV}$, ${\Gamma }_A=30.5\mathrm{meV}$, $\delta =\omega =0.1\mathrm{meV}$, and $R_{ss}=R_e=11\mathrm{\AA }$. Inset (a) shows a diagram of the trimer chain and (b) is the corresponding energy diagram. Donor dot $D_1$ has been excited at $t=0$. Notice plateaus in occupation of dot $A$.

Figure 2

(Color online) Dynamics of exciton lower state occupation of acceptor dot for different $R_{ss}$ values ($R_e=11\mathrm{\AA }$ fixed as in Fig. 1). (a) Initial excitation (pumping) of $D_1$ for $\delta =\omega =0$. (b) Pumping $D_2$, $\delta =0$. (c) Pumping $D_1$, $\delta =0.1\mathrm{meV}$. (d) Pumping $D_2$, $\delta =0.1\mathrm{meV}$. Curves in (a) and (b) are offset vertically for clarity. Notice a large variation in characteristic growth times, as well as plateaus for nearly all conditions.

Figure 3

(Color online) Dynamics of exciton lower-state population at the acceptor dot with varying ${\Gamma }_A$. ${\Gamma }_A^0=30.5\mathrm{meV}$ as in Figs. 1, 2. Notice the absence of oscillation plateaus and the fastest rise time for ${\Gamma }_A=4V_F^{db}$.

Figure 4

(Color online) Evolution of lower exciton state at each dot arranged in an asymmetrical cluster loop as shown in the top left inset. Oscillation plateaus are visible in eavesdropping $A$ dot. The central inset shows results for a symmetrical loop; notice the absence of plateaus in the $A$ response and saturation at quarter filling in this time window.