Dephasing-assisted selective incoherent quantum transport

Selective energy transport throughout a quantum network connected to more than one reaction center can play an important role in many natural and technological considerations in photosystems. In this work, we propose a method in which an excitation can be transported from the original site of the network to one of the reaction centers arbitrarily using independent sources of dephasing noises. We demonstrate that in the absence of dephasing noises, the coherent evolution of the system does not have any role in energy transport in the network. Therefore, incoherent evolution via application of dephasing noises throughout a selected path of the network leads to complete transferring of the excitation to a desired reaction center.

Figure 1

(a) A network of two-level systems coupled to each other as ${\nu }_{3j-2,3j-1}={\nu }_{3j-2,3j}={\nu }_{3j-1,3j+1}=-{\nu }_{3j,3j+1}=J$ and attached to independent dephasing noises. (b) The same network under the change of basis. Invariant subspaces are incoherently connected by the dephasing noises.

Figure 2

Populations of site 1 (solid red line) and the sink (dashed blue line) for $N=4$ corresponding to Fig. 1, with ${\omega }_1={\omega }_2=\cdots ={\omega }_{13}=50$. The network is affected by independent dephasing noises in three different ways: (a) all sites are attached to the noise with optimal rate ${\gamma }_{\text{opt}}=0.95$, (b) the sites $3j-1$ and $3j$ ($j=1,2,3,4$) are attached with ${\gamma }_{\text{opt}}=1.22$, and (c) the sites $3j-1$ ($j=1,2,3,4$) are attached, with ${\gamma }_{\text{opt}}=2.44$. Each inset shows the dependence of $P_{\text{sink}}$ at a fixed time (the respective transfer time) as a function of $\gamma$. The initially sharp rise is due to the increasing rapidity of destruction of invariant subspaces, while the decreasing rate is due to the quantum Zeno effects.

Figure 3

Robustness of $P_{\text{sink}}$ around the optimal value of dephasing noise due to energy mismatch between sites. (a) The energies of sites $3j-2$ with $j=1,3,5$ are $\hslash (\omega -\delta )$ and those with $j=2,4$ are $\hslash \omega$. (b) The energies of sites $3j-2$ with $j=1,3,5$ are $\hslash (\omega -\delta )$ and those with $j=2,4$ are $\hslash (\omega +\delta )$. For both cases, the sites $3j-1$ and $3j$ are attached to dephasing noises.

Figure 4

Selective incoherent quantum transport building block in two dimensions. (a) Incoherent transport from site ${\mu }_1$ to site ${\mu }_2$ and (b) incoherent transport from site ${\mu }_1$ to site ${\mu }_3$. Parts (c) and (d) show invariant subspaces structure of (a) and (b), respectively, and incoherent connection between them through the noises.

Figure 5

A network with three sinks. Energy excitation can be transferred from site 1 to one of the sinks arbitrarily.

Figure 6

Complete transfer of excitation from site 1 (solid red line) selectively to (a) sink 1 (dashed blue line), (b) sink 2 (dashed green line), and (c) sink 3 (dashed pink line).

Figure 7

Extended network with more than three sinks.