Rabi oscillations in spasers during nonradiative plasmon excitation

In the approach to the stationary regime, a surface plasmon amplification by stimulated emission of radiation exhibits complicated and highly nonlinear dynamics with anharmonic oscillations [M. I. Stockman, J. Opt. 12, 024004 (2010)]. We demonstrate that these oscillations are due to Rabi oscillations of the quantum dot in the field of the nanoparticle. We show that oscillations may or may not arise depending on the initial conditions.

Figure 1

The evolution of the spaser. The open circles mark the beginning of the transient regime, then the system moves along either the solid line ($a\left(0\right)=40+25i$,$\sigma \left(0\right)=0.9,$ and $D\left(0\right)=0.05$) or the dashed line ($a\left(0\right)=5$, $\sigma \left(0\right)=0.65,$ and $D\left(0\right)=0.9$) until it reaches the stationary state marked by the solid circle. Dash-dotted and dash-double dotted lines are projections of the trajectories on the plane $\left|\sigma \right|=0.5$. The curves shown were calculated for the time-constants ${\tau }_a={10}^{-14}s$, ${\tau }_{\sigma }={10}^{-11}s$, ${\tau }_D={10}^{-13}s$, and ${\Omega }_R={10}^{13}{s}^{-1}$.

Figure 2

The dependence of the phase mismatch on time. The initial conditions corresponding to solid line and dashed lines are $a\left(0\right)=50i$, $\sigma \left(0\right)=0.25$, and $D\left(0\right)=0.6,$ and $a\left(0\right)=0.1$, $\sigma \left(0\right)=0.5$, and $D\left(0\right)=0.7$, respectively. Values of the time constants and the Rabi frequency are the same as in Fig. 1.

Figure 3

The dependence of the QD polarization on time calculated for the initial conditions$a\left(0\right)=10$, $\sigma \left(0\right)=0.65,$ and $D\left(0\right)=0.2$. All other parameters have the same values as in previous figures.