Quantum Effects in Photosynthesis

Undercover of a heavy first term of my final year at Warwick, I appear to have disappeared from the blogosphere. I assure you though that I am alive and well; finally finding a few minutes spare to write!

The reason I write tonight is because really, honestly, I am really rather stuck. At the beginning of term, I embarked on a super scary theoretical physics project bearing the same title as this post. Five weeks into it, and my brain has been frazzled – in the most positive way possible! My project partner and I have never before encountered Lindblad operators or the Liouville von Neumann equation or even fully been introduced to Dirac notation and density matrices; now I find myself thinking about commutators and why does   {d \over dt} A(t) = {i \over \hbar } [H, A(t)] + e^{iHt / \hbar} \left(\frac{\partial A}{\partial t}\right)e^{-iHt / \hbar} , whilst I am brushing my teeth.

Between frantically catching up on missed lectures and making an impromptu pumpkin pie from Halloween pumpkin leftovers, the entirety of my Saturday has been spent trying to work through a particular chapter in “The Theory of Open Quantum Systems” (H. P. Breuer and F. Petruccione) and repeatedly hitting a brick wall. Maybe that’s what got rid of my morning-post-night-out queasiness, but that’s a story for another day…

So: we are working with Dr. A. Datta, who has been heavily involved in the following research: “Noise-assisted energy transfer in quantum networks and and light-harvesting complexes” and if you click on the link, you can have a friendly video introduction to an otherwise horrendously confusing, albeit fascinating topic.

We are dealing with a highly efficient (99%) energy transportation system, whereby a photon hits the top of a leaf and is transferred through a complex within the leaf, in the form of an energy excitation. In green plants and cyanobacteria, such a complex is called the Fenna-Matthews-Olson (FMO) complex and can be modelled by an open network of 8 sites (or nodes, or bacteriochlorophyll-a molecules), where the excitation “hops” between the sites. The question stands: what makes the process so efficient? We will be looking at something they like to call ‘noise assisted transport’, whereby quantum incoherence within the state of the system (which itself is a linear superposition of other states) is introduced and destroys destructive interference between particular wavefunctions (hey, that was a pun, I made a funny. Please laugh).

As an aside: if a system is in a pure state, its density matrix will have off-diagonal terms which, when the phase between the basis states goes pear-shaped, they will reduce and possibly disappear. As the quantum coherence dwindles, the state becomes more classical, a ‘mixed state’. Or something or other along those lines. The initial quantum coherence is short lived (and short-ranged) and so the question stands: how much of this crazy magical  99% efficiency is due to classical or quantum effects? Why does this destructive intereference actually help exciton transfer? Why should you care, darn it!?

At this fine moment in time, I am afraid I have no answer to any of the above. I do know, however, that the more I read about it, the less sense everything makes. I live by that fine man Feynman’s opinion: “we don’t really understand it“. What is this it? Everything, I think.

Feynman was a truly great teacher. He prided himself on being able to devise ways to explain even the most profound ideas to beginning students. Once, I said to him, “Dick, explain to me, so that I can understand it, why spin one-half particles obey Fermi-Dirac statistics.” Sizing up his audience perfectly, Feynman said, “I’ll prepare a freshman lecture on it.” But he came back a few days later to say, “I couldn’t do it. I couldn’t reduce it to the freshman level. That means we don’t really understand it.”

David L. Goodstein, “Feynman’s Lost Lecture: The Motions of Planets Around the Sun”

If you fancy some bedtime reading, here is an article which introduces the topic beautifully: N. Lambert, et al. Quantum biology. Nat. Phys. 9, 10–18 (2012).

And… I shall only leave you with this:

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