In a previous post, we described the coherent transfer of energy from sunlight in photosynthetic systems. What it shows there is some indication of quantum effects playing a useful role in organic processes. What it does not show is whether there exists a different mechanism for explaining the same effect without using quantum mechanics.

To convince anyone that quantum effects play an important function in biological processes such as photosynthesis, we must show that a classical explanation is not sufficient to account for the efficient transport of energy. In a paper by O'Reilly and Olaya-Castro, they demonstrate this using methods in the quantum theory of light.

Light is a form of electromagnetic radiation, where the term is reserved mainly for radiation that is visible to our eyes. It is composed of electromagnetic waves that vibrate at different frequencies, which we perceive as different shades of colors. Much of how light waves behave can be explained using a classical theory of waves, which describes how waves can be combined to produce various patterns of interference.

Quantum mechanics refines the classical description of light mainly by saying that the light waves are composed of particles called photons. In this way, energy lost or gained through electromagnetic radiation must come in lumps, like money comes in units of pennies.

This lends itself to a way of describing the state of light in terms of modes that can be populated by different numbers of photons, quite similar to having several boxes that hold different number of balls. (However, photons are quantum particles, the superposition principle allows them to be found in many different modes at the same time, something impossible with classical balls in boxes.)

Even if we think of light as particles, it should be possible to recover the simpler classical light wave when we consider a large number of photons. This happens for a single mode of light when the number of photons measured in it follows a Poisson distribution (the average number is the same as its variance), it means light in that mode is in what is called a coherent state. Lasers are a good example of photons in a coherent state. (The Poisson distribution for the number of photons describes the probability of finding a certain number of photons in a given light mode when the average photon count is known and the counts are independent of each other.)

Light is said to be non-classical if its state can not be written as a proper mixture of coherent states. Mathematically, if A, B, C represent coherent states and suppose that S = a A + b B + c C where S represents the state of light. Then S is a proper mixture of A, B, and C if the numbers a, b, and c are bigger than or equal to zero.

In pretty much the same way we describe light in terms of photons, we can describe vibrational motion in terms of quantum particles called phonons. In photosynthesis, phonons play a significant role in the coherent transfer of energy between pigments in a light harvesting system.

A simple model of energy transfer between photosynthetic pigments (blue ovals) mediated by a particle of vibration or phonon (yellow ball) in a low-energy thermal bath of proteins. |

In what is called vibration-assisted electronic energy transfer, the energy received from sunlight is transmitted from one pigment to another through modes of vibrations with the right amount of energy. As shown above, consider two neighboring chlorophyll pigments (blue ovals) with compatible energy levels, with vibrational motions that weakly interact in a protein environment acting as a room-temperature thermal bath. We start with the top left pigment carrying an excitation, represented by the red ball on the top energy level. This excitation is transferred to the bottom right pigment through a phonon, which helps the excitation bridge the gap between pigments. For the transfer to work, the phonon must have energy levels that match that of the pigments. We actually know of phycoerythrin pigments in algae and chlorophyll pigments in spinach that have roughly this kind of energy levels.

The Mandel Q-parameter is a measure of non-classical behavior and is given by Q = V/M - M - 1, where M is the mean number of phonons and V is the variance. If Q = 0, then the state of the phonons can be expressed as a mixture of coherent states, which means the phonons behave like a classical wave. In this way, non-classical behavior is indicated by Q < 0.

A numerical simulation of the dynamics between the vibrations and the excitation in pigments in algae with parameters matched to biological values show that for some time as the transfer occurs, the Q value dips to the negative region, indicating that non-classical effects are taking place. We note that the data involves short time scales (picoseconds) since contact with a room temperature thermal bath leads to classical behavior when the interaction takes longer.

The observations made here apply to a vibrational mode for a pair of pigment molecules found in a majority of light harvesting structures. To rigorously assess the efficiency achieved with non-classical effects will require studying the dynamics of energy transfer across the whole structure, which involves interaction with many vibrational modes.

**Reference:**

E. J. O'Reilly, A. Olaya-Castro, "Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature," Nature Communications 5:3012 (2014).

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