Avoiding dark states in open quantum systems by tailored initializations

We study the transport of excitations on a network of three coupled two-level systems that are subjected to an environment that induces incoherent hopping between the nodes. The two end nodes are coupled to a source while the central node is coupled to a drain. A common feature of these networks is the existence of a dark state that blocks the transport to the drain. Here we propose a means to avoid this state by a suitable initialization of the system, induced by a source that is common to both coupled nodes.

Figure 1

An illustration of the two different ways of connecting the source(s) to the trimer network: (I) corresponds to the configuration with two independent transitions to the network and (II) corresponds to the configuration with a source that initializes the system in a superposition state of nodes 1 and 2.

Figure 2

Dependence of the EST ${\eta }_{II}\left(\alpha \right)$ on the angle $\phi$ for $\lambda =1$ and $\Gamma =0.5$. On the left we show the general result for all values of $\phi$ and $\alpha$. The right figure shows the cross-sectional curves for $\phi =0,\pi /2$, and $\phi =\pi$, together with the result for ${\eta }_I\left(\alpha \right)$.

Figure 3

The dependence of the EST on the dephasing rate $\lambda$, with $\Gamma =0.5$ and $\gamma =1$. The red curves correspond to ${\eta }_I\left(\alpha \right)$ and the black curves correspond to ${\eta }_{II}\left(\alpha \right)$ with phase $\phi =0$.