Role of interference in the photosynthetic heat engine

The observation of quantum coherence in pigment-protein complexes has attracted considerable interest. One such endeavor entails applying a quantum heat engine to model the photosynthetic reaction center, but the definition of work used is inconsistent with that defined in quantum thermodynamics. Using the definition of work proposed in Weimer et al. [Europhys. Lett. 83, 30008 (2008)], we investigated two proposals for enhancing the performance of the photosynthetic reaction center. In proposal A, which is similar to that in Dorfman et al. [Proc. Natl. Acad. Sci. USA 110, 2746 (2013)], we found that the power and current-voltage characteristic of the heat engine can be increased by Fano interference but the efficiency cannot. In proposal B, which is similar to that in Creatore et al. [Phys. Rev. Lett. 111, 253601 (2013)], we found that the mechanism of strengthening the performance of the heat engine is invalid; i.e., the dipole-dipole interaction between two electron donors could not increase the power, efficiency, or current-voltage characteristic.

Figure 1

Scheme of the quantum heat engine model of the photosynthetic reaction center. (a) Proposal A, where HTR and LTR1, respectively, represent common high- and low-temperature reservoirs, LTR2 denotes the low-temperature reservoir inducing the transition from $\left|\beta \right.〉$ to $\left|b\right.〉$, and WR is a work reservoir. (b) Proposal B. It differs from proposal A because (1) the corporative transitions from $\left|b\right.〉$ to $\left|a_1\right.〉$ and/or $\left|a_2\right.〉$ and from $\left|a_1\right.〉$ and/or $\left|a_2\right.〉$ to $\left|\alpha \right.〉$ are achieved by a dipole-dipole interaction (whose coupling constant is denoted by $g$) and (2) all the dissipative transitions are induced by an independent reservoir.

Figure 2

(a) Power $P^A$ as a function of the interference, ${\gamma }_{a_1{a}_2}^c$. The thick (${\gamma }_{a_1{a}_2}^h=0$) and dashed (${\gamma }_{a_1{a}_2}^h={\gamma }_h$) lines represent DDES, and the dotted line represents LLS while the interference, ${\gamma }_{a_1{a}_2}^h$, reaches its maximum, ${\gamma }_{a_1{a}_2}^h={\gamma }_h$. In all cases, the coupling constant is chosen to be $\Omega =0.6$ eV. (b) Heat fluxes from the high-temperature reservoir $J_h^A$ corresponding to (a).

Figure 3

Current generated as a function of the voltage $V$ for minimum (${\gamma }_{a_1{a}_2}^h={\gamma }_{a_1{a}_2}^c=0$) (thick line) and maximum (${\gamma }_{a_1{a}_2}^h={\gamma }_h$ and ${\gamma }_{a_1{a}_2}^c={\gamma }_c$) (dashed line) interference. The inset shows the voltage $V$ versus the coupling constant $\Omega$. The other parameters used are the same as those in Fig. 2.