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Origin of long-lived quantum coherence and excitation dynamics in pigment-protein complexes

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ABSTRACT

We explore the mechanism for the long-lived quantum coherence by considering the discrete phonon modes: these vibrational modes effectively weaken the exciton-environment interaction, due to the new composite (polaron) formed by excitons and vibrons. This subsequently demonstrates the role of vibrational coherence which greatly contributes to long-lived feature of the excitonic coherence that has been observed in femtosecond experiments. The estimation of the timescale of coherence elongated by vibrational modes is given in an analytical manner. To test the validity of our theory, we study the pigment-protein complex in detail by exploring the energy transfer and coherence dynamics. The ground-state vibrational coherence generated by incoherent radiations is shown to be long-survived and is demonstrated to be significant in promoting the excitation energy transfer. This is attributed to the nonequilibriumness of the system caused by the detailed-balance-breaking, which funnels the downhill migration of excitons.

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The dynamics of scaled population on pigment B for (a) including and (b) NOT including the incoherent radiation environment. In both (a,b), the blue and purple curves correspond to the non-adiabatic and adiabatic regimes, respectively. (c) Steady-state population on pigment B with respect to the temperature of low-frequency fluctuations; (d) Steady-state quantum coherence varies as a function of the temperature of low-frequency fluctuations. In (d) the purple and blue lines are for electronic (localized) and excitonic (delocalized) coherences, respectively. The parameters are the same as in Fig. 3.
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f4: The dynamics of scaled population on pigment B for (a) including and (b) NOT including the incoherent radiation environment. In both (a,b), the blue and purple curves correspond to the non-adiabatic and adiabatic regimes, respectively. (c) Steady-state population on pigment B with respect to the temperature of low-frequency fluctuations; (d) Steady-state quantum coherence varies as a function of the temperature of low-frequency fluctuations. In (d) the purple and blue lines are for electronic (localized) and excitonic (delocalized) coherences, respectively. The parameters are the same as in Fig. 3.

Mentions: To uncover the effect of incoherent radiation on energy transfer, we need to study the time evolution of population on pigment B, for both adiabatic and non-adiabatic regimes, as shown in Fig. 4, where incoherent radiation is included in 4(a) but not in 4(b). The initial conditions are: (a) ρ(0) = /0, 0〉〈0, 0/ for blue and ρ(0) = /0〉〈0/ for purple; (b) ρ(0) = /A, 0〉〈A, 0/ for blue and ρ(0) = /A〉〈A/ for purple. By comparing Fig. 4(a) and (b), one can conclude that the vibrational coherence, especially ground-state vibrational coherence, facilitates the excitation energy transport by including the incoherent radiations (blue line is higher than purple in Fig. 4(a)). Otherwise, it is unable to promote the energy transfer process (blue line is lower than purple in Fig. 4(b)). In particular, the incoherent environment (radiation) induces the coupling among the dynamics of excitation populations Pi(t); i = A, B and the ground-state vibrational coherence 〈0, 0/ρ/0, 1〉 reflected by the nonvanishing coefficients in Eq. (7). This indeed breaks the secular approximation and results in the considerable enhancement of the population in pigment B as shown in Fig. 4(a) (blue line exceeds much purple line). Thus the excitation energy transfered to pigment B is considerably promoted. In contrast, it should be noted that the dynamics of excitation populations becomes decoupled to that of vibrational coherence without including the incoherent environment, namely , based on the structure of QME Eq. (7) and (S20) in SI. In this case with low-energy noise from protein included only, our results in Fig. 4(b) show that neither excited-state vibrational nor ground-state vibrational coherence can affect much the excitation energy transfer from pigment A to B. These analyses further elucidate the importance of considering the effect of incoherent radiation in addition to the low-energy fluctuations for rendering the long-lived ground-state vibrational coherence to enhance the excitation energy transfer. This in fact, is originated from the nonequilibriumness of the system, which will be discussed later on in the paper. Furthermore, Fig. 4(a) shows that the cumulative population on pigment B: is much larger than the one without including exciton-vibrational coupling. This means that the total energy transport is much enhanced by the vibrational coherence, when including the radiations. This promotion of energy transport, in fact, is natural from the view of point of nonequilibriumness, which will be illustrated later.


Origin of long-lived quantum coherence and excitation dynamics in pigment-protein complexes
The dynamics of scaled population on pigment B for (a) including and (b) NOT including the incoherent radiation environment. In both (a,b), the blue and purple curves correspond to the non-adiabatic and adiabatic regimes, respectively. (c) Steady-state population on pigment B with respect to the temperature of low-frequency fluctuations; (d) Steady-state quantum coherence varies as a function of the temperature of low-frequency fluctuations. In (d) the purple and blue lines are for electronic (localized) and excitonic (delocalized) coherences, respectively. The parameters are the same as in Fig. 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5120302&req=5

f4: The dynamics of scaled population on pigment B for (a) including and (b) NOT including the incoherent radiation environment. In both (a,b), the blue and purple curves correspond to the non-adiabatic and adiabatic regimes, respectively. (c) Steady-state population on pigment B with respect to the temperature of low-frequency fluctuations; (d) Steady-state quantum coherence varies as a function of the temperature of low-frequency fluctuations. In (d) the purple and blue lines are for electronic (localized) and excitonic (delocalized) coherences, respectively. The parameters are the same as in Fig. 3.
Mentions: To uncover the effect of incoherent radiation on energy transfer, we need to study the time evolution of population on pigment B, for both adiabatic and non-adiabatic regimes, as shown in Fig. 4, where incoherent radiation is included in 4(a) but not in 4(b). The initial conditions are: (a) ρ(0) = /0, 0〉〈0, 0/ for blue and ρ(0) = /0〉〈0/ for purple; (b) ρ(0) = /A, 0〉〈A, 0/ for blue and ρ(0) = /A〉〈A/ for purple. By comparing Fig. 4(a) and (b), one can conclude that the vibrational coherence, especially ground-state vibrational coherence, facilitates the excitation energy transport by including the incoherent radiations (blue line is higher than purple in Fig. 4(a)). Otherwise, it is unable to promote the energy transfer process (blue line is lower than purple in Fig. 4(b)). In particular, the incoherent environment (radiation) induces the coupling among the dynamics of excitation populations Pi(t); i = A, B and the ground-state vibrational coherence 〈0, 0/ρ/0, 1〉 reflected by the nonvanishing coefficients in Eq. (7). This indeed breaks the secular approximation and results in the considerable enhancement of the population in pigment B as shown in Fig. 4(a) (blue line exceeds much purple line). Thus the excitation energy transfered to pigment B is considerably promoted. In contrast, it should be noted that the dynamics of excitation populations becomes decoupled to that of vibrational coherence without including the incoherent environment, namely , based on the structure of QME Eq. (7) and (S20) in SI. In this case with low-energy noise from protein included only, our results in Fig. 4(b) show that neither excited-state vibrational nor ground-state vibrational coherence can affect much the excitation energy transfer from pigment A to B. These analyses further elucidate the importance of considering the effect of incoherent radiation in addition to the low-energy fluctuations for rendering the long-lived ground-state vibrational coherence to enhance the excitation energy transfer. This in fact, is originated from the nonequilibriumness of the system, which will be discussed later on in the paper. Furthermore, Fig. 4(a) shows that the cumulative population on pigment B: is much larger than the one without including exciton-vibrational coupling. This means that the total energy transport is much enhanced by the vibrational coherence, when including the radiations. This promotion of energy transport, in fact, is natural from the view of point of nonequilibriumness, which will be illustrated later.

View Article: PubMed Central - PubMed

ABSTRACT

We explore the mechanism for the long-lived quantum coherence by considering the discrete phonon modes: these vibrational modes effectively weaken the exciton-environment interaction, due to the new composite (polaron) formed by excitons and vibrons. This subsequently demonstrates the role of vibrational coherence which greatly contributes to long-lived feature of the excitonic coherence that has been observed in femtosecond experiments. The estimation of the timescale of coherence elongated by vibrational modes is given in an analytical manner. To test the validity of our theory, we study the pigment-protein complex in detail by exploring the energy transfer and coherence dynamics. The ground-state vibrational coherence generated by incoherent radiations is shown to be long-survived and is demonstrated to be significant in promoting the excitation energy transfer. This is attributed to the nonequilibriumness of the system caused by the detailed-balance-breaking, which funnels the downhill migration of excitons.

No MeSH data available.


Related in: MedlinePlus