# Is coherence a single photon phenomenon?

Hello folks. 2-dimensional spectroscopic techniques have been used to investigate biological systems and found that they transfer energy via coherent pathways. However, some have argued that this has no bearing on how these systems behave in nature, as the sun is not a coherent source and the observed coherence is simply an artifact of the coherence properties of the laser. If you make an assumption of a single photon being absorbed by these systems, is there any difference between a photon from a laser and from an incoherent source?

A recent PNAS article got into this and described a photon as a superposition and an incoherent photon as a thermal mixture, but from a semi-classical point of view it's hard to see how a single photon can be "coherent" since coherence is defined through relationships between photons (or at least the waves that describe them).

I obviously don't know much about this stuff, so if anyone has any thoughts, they'd be very much appreciated.

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The difference between "coherent" and "incoherent" in QM is whether you have a pure or mixed state. A single photon may be in, e.g, the pure state ##|\psi\rangle = \frac{1}{\sqrt{2}}(|x\rangle + |y\rangle)##, an equal superposition of x- and y- linear polarizations. This is a coherent superposition. On the other hand, you can have a statistical mixture of x-polarized and y-polarized states which we describe with a density matrix: ##\rho = \frac{1}{2}(|x\rangle\langle x| + |y\rangle\langle y|)##. This is an incoherent mixture and leads to classical probability. Quantum decoherence tells us that a pure state in thermal contact with its environment will tend to evolve (generally quite quickly) into a mixed state.

So, yes, it is sensible to talk about the coherence of a single photon. It's not an exclusively collective thing.

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A helpful illustration might be the quantum double slit experiment. You can do the double slit experiment in such a way that photons are being produced one by one. Over time, an interference pattern builds up. This is because the photons are able to interfere with themselves because they are in a coherent superposition of "left slit" and "right slit", and those two wavefunctions can interfere in the usual way. An incoherent mixture does not produce such an interference pattern (and is what you create when you try to determine which path each photon takes—thus destroying the interference pattern). This is an example of single photon coherence.

Cthugha
Hello folks. 2-dimensional spectroscopic techniques have been used to investigate biological systems and found that they transfer energy via coherent pathways. However, some have argued that this has no bearing on how these systems behave in nature, as the sun is not a coherent source and the observed coherence is simply an artifact of the coherence properties of the laser. If you make an assumption of a single photon being absorbed by these systems, is there any difference between a photon from a laser and from an incoherent source?
First of all, first-order coherence is a phenomenon taking place on the field level. It does not matter at all, whether there is one photon or a gazillion photons there. This is just about the fields being correlated.

I assume you talk about 2D Fourier transform spectroscopy. Indeed there is some debate on whether lasers are adequate for finding out what happens in nature. It should be pointed out that the wording "incoherent" is kind of misleading. There are no completely incoherent light sources. Light from the sun just has a very short coherence time somewhere in the range of several femtoseconds, while laser light can have coherence times up to milliseconds and above. The question that matters is whether the processes in the material happen faster or slower than the coherence time of the light.

Optical excitation will typically create a polarization in the material. This is the point where the coherent vs. incoherent question matters. For optical excitation with short coherence time, there is no long term stable polarization in the material and the carrier population created will also be an incoherent one (what is happening exactly of course depends on your material). There have been people doing 2D Fourier transform spectroscopy on some light harvesting complexes using light behaving light sun light. It is a bit difficult to get the short pulses needed. I have seen a talk on that recently, but I forgot who did that stuff. Might have been David Jonas from CU, but I am not quite sure. I am also not sure whether these results were already published or not.

I like the question.

From a more or less philosophical view, the answer could depend on how you understand the nature of photon.

My understanding is that coherence can be, but not be limited to, a single photon phenomenon.