Correlated dynamics as a resource in molecular switches

Abstract

Photoisomerization, a photochemical process underlying many biological mechanisms, has been modeled recently within the quantum resource theory of thermodynamics. This approach has emerged as a promising tool for studying fundamental limitations to nanoscale processes independently of the microscopic details governing their dynamics. On the other hand, correlations between physical systems have been shown to play a crucial role in quantum thermodynamics by lowering the work cost of certain operations. Here, we explore quantitatively how correlations between multiple photoswitches can enhance the efficiency of photoisomerization beyond that attainable for single molecules. Furthermore, our analysis provides insights into the interplay between quantum and classical correlations in these transformations.

Figures (10)

• Figure 1: Energy landscape for a typical photoisomer. The system starts in the electronic ground state at $\varphi=0$, and it is photoexcited (wavy arrow) by a light source. It can then relax to the cis ground state $\mathcal{E}(\varphi=\pi)$, while in contact with its environment. Our results are independent of the actual intermediate dynamics of the process. The advantage of a resource-theoretic approach, is precisely that of providing general bounds that are valid regardless of the complicated microscopic details governing the evolution of the system. The four dots represent the states that are considered in the four-level model of halpern2020fundamental.
• Figure 2: Photoisomerization yield for two molecules with uncorrelated and correlated final states. We see that in both cases there is an advantage over the single-molecule yield, which is depicted in black. However, for a final state that is uncorrelated (blue) the yield quickly decreases to the single molecule solution, whereas for a correlated final state (orange), there is a significant improvement of the optimal yield up to $\Delta \approx W/2$. The insert shows a close-up of the small $\Delta$ region where the curves are particularly close and touch at a point. Here, $q=0.5$ and $W=30$.
• Figure 4: Optimal photoisomerization yield for different system sizes. The curves in blue show the maximum yield with an uncorrelated final state hypothesis, while for the orange ones we allow correlations in the final state. The large difference between the two, comparing systems with the same size, shows the positive contribution of correlations on photoisomerization efficiency. The yield is plotted as a function of the energy $\Delta$ fixing $q = 0.5$ and $W = 30$. Appendix \ref{['App:GSMprogram']} shows a similar plot as a function of $q$.
• Figure 5: The top figure shows the optimal yield as a function of the number of molecules $N$, for uncorrelated (blue) and correlated (orange) final states. The bottom figure shows the relative difference $\delta_N = (\gamma_N^c -\gamma_N^u)/\gamma_N^u$. One can notice the non-monotonic behavior of the advantage $\delta_N$ provided by correlations. The system considered has energies $\Delta = 3$, $W = 30$ and initial state population $q = 0.5$.
• Figure 6: Correlated optimal yield for $N=10^4$ molecules, with the typical sequences approximation performed on the initial state. The excellent match shown between $\gamma^c_{N}$ and $\gamma_{TD}$ when $N$ is large suggests that $\gamma_{N \rightarrow \infty}^c = \gamma_{TD}$.