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The Journal of Chemical Physics

Realistic vs sudden turn-on of natural incoherent light: Coherences and dynamics in molecular excitation and internal conversion

Timur A. Grinev, Paul W. Brumer

Published Dec 28, 2015• 16 citations
Publisher

Abstract

Molecular excitation with incoherent light is examined using realistic turn-on time scales, and results are compared to those obtained via commonly used sudden turn-on, or pulses. Two significant results are obtained. First, in contrast to prior studies involving sudden turn-on, realistic turn-on is shown to lead to stationary coherences for natural turn-on time scales. Second, the time to reach the final stationary mixed state, known to result from incoherent excitation, is shown to depend directly on the inverse of the molecular energy level spacings, in both sudden and realistic turn-on cases. The S0 → S2/S1 internal conversion process in pyrazine is used as an example throughout. Implications for studies of natural light harvesting systems are noted.

DOI
10.1063/1.4938028

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Molecular excitation with incoherent light is examined using realistic turn-on time scales, and results are compared to those obtained via commonly used sudden turn-on, or pulses. Two significant results are obtained. First, in contrast to prior studies involving sudden turn-on, realistic turn-on is shown to lead to stationary coherences for natural turn-on time scales. Second, the time to reach the final stationary mixed state, known to result from incoherent excitation, is shown to depend directly on the inverse of the molecular energy level spacings, in both sudden and realistic turn-on cases. The S0 → S2/S1 internal conversion process in pyrazine is used as an example throughout. Implications for studies of natural light harvesting systems are noted.
The excitation of molecular systems by incoherent light is studied primarily using a V-system model in the Partial Secular Bloch-Redfield formalism. First, the dynamical regimes are characterized for a system irradiated by suddenly turned on light and the relevant timescales are defined in terms of system parameters. Then excitation by slowly turned-on light is studied, showing a decay in the magnitude of noise-induced coherences with increasing turn-on times, leading to their disapearance in the very slow turn-on limit relevant to many natural systems.
Under natural conditions, excitation of biological molecules, which display nonunitary open system dynamics, occurs via incoherent processes such as temperature changes or irradiation by sunlight or moonlight. The dynamics of such processes is explored analytically in a non-Markovian generic model. Specifically, a system S in equilibrium with a thermal bath TB is subjected to an external incoherent perturbation BB (such as sunlight) or another thermal bath TB${}^{\ensuremath{'}}$, which induces time evolution in (S+TB\text{S}+\text{TB}S+TB). Particular focus is on (i) the extent to which the resultant dynamics is coherent, and (ii) the role of ``stationary coherences'' established in the (S+TB\text{S}+\text{TB}S+TB) equilibration in response to the second incoherent perturbation. Results for systems with parameters analogous to those in light-harvesting molecules in photosynthesis show that the resultant dynamical behavior is incoherent beyond a very short response to the turn on of the perturbation.
Light-induced processes in nature occur by irradiation with slowly turned-on incoherent light. The general case of time-dependent incoherent excitation is solved here analytically for V-type systems using a newly developed master equation method. Clear evidence emerges for the disappearance of radiatively induced coherence as turn-on times of the radiation exceed characteristic system times. The latter is the case, in nature, for all relevant dynamical time scales for other than nearly degenerate energy levels. We estimate that, in the absence of non-radiative relaxation and decoherence, turn-on times slower than 1 ms (still short by natural standards) only induce Fano coherences between energy eigenstates that are separated by less than 0.9 cm−1.
One of the most pertinent problems in the debate on non-trivial quantum effects in biology concerns natural photosynthesis. Since sunlight is composed of thermal photons, it was argued to be unable to induce quantum coherence in matter, and that quantum mechanics is therefore irrelevant for the dynamical processes following photoabsorption. Our present analysis of a toy 'molecular aggregate'—composed of two dipole–dipole interacting two-level atoms treated as an open quantum system—however shows that incoherent excitations indeed can trigger persistent, coherent dynamics in both the site and the exciton bases: we demonstrate that collective decay processes induced by the dipole–dipole interactions create coherent intermolecular transport—regardless of the coherence properties of the incoming radiation. Our analysis shows that the steady state coherence is mediated by the population imbalance between the molecules and, therefore, increases with the energy difference between the two-level atoms. Our results establish the importance of collective decay processes in the study of ultrafast photophysics, and especially their potential role to generate stationary coherence in incoherently driven quantum transport.
The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level V system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in the long time limit, with rates dictated by the adjacent level spacings and the coherence time of the light, and via a mechanism that is distinctly different from traditional decoherence. These two excitation scenarios are also explored for a minimal "toy" model of the electronic levels in pigment protein complex PC645 by both a collisionally broadened CW laser and by a noisy pulse, where unexpectedly long transient coherence times are observed and explained. The significance of environmentally induced decoherence is noted.
Photoinduced biological processes occur via one photon absorption in natural light, which is weak, CW and incoherent, but are often studied in the laboratory using pulsed coherent light. Here we compare the response of a molecule to these two very different sources within a quantized radiation field picture. The latter is shown to induce coherent time evolution in the molecule, whereas the former does not. As a result, the coherent time dependence observed in the laboratory experiments will not be relevant to the natural biological process. Emphasis is placed on resolving confusions regarding this issue that are shown to arise from aspects of quantum measurement and from a lack of appreciation of the proper description of the absorbed photon.