Decoherence-Assisted Transport in a Dimer System

The dynamics of a dimer coupled to two different environments, each in a spin star configuration under the influence of decoherence, is studied. The exact analytical expression for the transition probability in the dimer system is obtained for different situations, i.e., independent and correlated environments. In all cases considered, it is shown that there exist well-defined ranges of parameters for which decoherent interaction with the environment assists energy transfer in the dimer system. In particular, we find that correlated environments can assist energy transfer more efficiently than separate baths.

Figure 1

Scheme of the dimer coupled to two decoherent environments in a spin star configuration. A dimer has energy levels ${\epsilon }_1\ne {\epsilon }_2$ and amplitude of transition probability $J$. Each level of the dimer $|1⟩$ and $|2⟩$ is in contact with a bath of spins with coupling constants ${\gamma }_1$ and ${\gamma }_2$, respectively. The dashed double arrow denotes the possibility of correlations between the baths through the Ising-like interaction $\sum _{k,m}{\sigma }_z^{k,1}{\sigma }_z^{m,2}$ with strength $q$.

Figure 2

Probability of transition $P_{1\to 2}(t)$ in the dimer system with the upper level coupled to a spin bath (${\gamma }_1=0$) as a function of time and the coupling constant to the spin bath (${\gamma }_2=\gamma$). The temperature of the spin bath in Fig. 2a is 77 K, while, in Fig. 2b, it is 300 K. For both figures, the parameters are chosen to be $N_2=20$, ${\alpha }_2=250{\mathrm{ps}}^{-1}$, $J=10{\mathrm{ps}}^{-1}$, and ${\epsilon }_2-{\epsilon }_1=20{\mathrm{ps}}^{-1}$.

Figure 3

Maximum of the probability of transition $\mathrm{Max}[P_{1\to 2}(t)]$ for a dimer coupled to two spin baths as a function of the correlations $q$ between the baths and the coupling constants ${\gamma }_1={\gamma }_2=\gamma$ of the interaction with the baths in the non-zero-temperature case. In Fig. 3a, the temperature of the baths is 77 K, while, in Fig. 3b, it is 300 K. For both figures, the parameters are $N_1=22$, $N_2=20$, ${\alpha }_1={\alpha }_2=250{\mathrm{ps}}^{-1}$, $J=10{\mathrm{ps}}^{-1}$, and ${\epsilon }_2-{\epsilon }_1=20{\mathrm{ps}}^{-1}$.