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arXiv:1109.0026

Molecular Response in Coherent vs. Incoherent One Photon Absorption

Paul W. Brumer, Moshe Shapiro

Published Aug 31, 2011• 2 citations
arXivHTMLPDF

Abstract

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.

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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.
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.
The mixed state of an isolated molecule, which results from one-photon absorption using a pulsed laser of arbitrary coherence, is obtained using a simple model for a partially coherent laser source. The relative effect of the pulse time τ, source coherence time τcoh, and field correlation time τc on the prepared state and on its subsequent molecular dynamics are described. Numerical computations on several properties are provided and support obtained for the analytical result showing that under certain circumstances the falloff of the survival probability of the created molecular state depends primarily on the pulse time τ.
Abstract Excitation of molecules by incident incoherent electromagnetic radiation, such as sunlight, is described in detail and contrasted with the effect of coherent (e.g. laser) light. The nature of the quantum coherences induced by the former, relevant to transport processes in nature and in technology, is emphasized. Both equilibrium and steady state scenarios are discussed, three examples: simple models, calcium excitation in polarized light, and the isomerization of retinal in rhodopsin are used to expose the underlying qualitative nature of the established coherences.
Mechanisms of two-photon transitions of a molecular ensemble induced by stationary-phase-incoherent light beams are theoretically studied. The time evolution of the vibronic coherence created by the phase-incoherent light beams is analyzed by using the Liouville-space Feynman diagram properly taking into account vibronic dephasings. It is shown that effects of coherence between sequential transitions make a dominant contribution to the time profile of the pump-probe two-photon transition induced by the phase-incoherent light beams. The time profiles are calculated within a simple model to demonstrate differences in the time evolution of the vibronic coherence between the phase-incoherent and pulsed-coherent light spectroscopy. A theoretical consideration is also given to nonresonant two-photon fluorescence of coumarin 440 in solution excited by incoherent light beams, which shows subfemtosecond oscillation with the incident photon-field frequencies.
Various characteristics of molecules have been clarified by spectroscopic methods in which the interactions of molecules with the radiation field were investigated. A stationary response of a molecule excited by a radiation field appears as a spectral line. Information on molecules may be obtained from position (resonance frequency), intensity, and shape and width of the spectral line. So far the interaction of molecules with the radiation field has been studied primarily in a “frequency domain.” Although molecular spectroscopy is one of the research fields in modern science which has the longest history, a variety of important aspects have been demonstrated very recently in this field as radiation sources have been improved. When the radiation field is “weak,” the photon nature of the radiation field is dominant in the interaction with a molecule, such as in the cases of emission, absorption, and scattering of photons. When the radiation field is “strong,” in the sense that many photons exist in a proper mode of the radiation field, the wave nature of the field plays an important role in the interaction. In this case the radiation may be described in the form of the classical field, say, a sinusoidal function of the time and spatial coordinates, coherently interacting with the molecule, which is described quantum mechanically. Here nonlinear properties would appear in the interactions: saturation in absorption, induced scattering, multiphoton processes, coherent transients, etc.
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.