# Can a group of electrons act as one and deflect a photon as a group?

There are interactions between electrons and photons.

But do they always happen on a one-to-one basis? Or can an ensemble of electrons act as a single entity? Especially, are there parts of the electromagnetic spectrum that interact with a sort of collective electronic behavior but would not with lone electrons?

Note: Originally I asked this question because I suspected mirrors are not reemissions of single photons by individual electrons, rather they are reflected by a surface of electrons acting as one, so having a normal component.

• Google coherent scattering. – Lewis Miller Mar 18 at 15:28

Yes, a single photon can interact with multiple electrons. And it does so in most light-matter interactions.

The simplest example is the scattering of a photon by any atom/molecule with more than one electron. In many introductory textbook on quantum light-matter interaction the absorption of a photon is described to cause a single electron to "jump to a higher shell" or transition into a different orbital. This is a useful approximation for most practical cases, when the exact state of the atom is irrelevant. But a more accurate description of multi-electron systems does not treat the electrons as independent entities, but as part of a non-separable multipartite wavefunction $$\Psi \left( \vec{r}_{e_1}, \vec{r}_{e_2}, ... \vec{r}_{e_N} \right) \neq \prod_{i=1}^N \psi \left( \vec{r}_{e_i} \right) \text{.}$$ So when a photon is absorbed by the multi-electron system it changes the state of the whole system, with all of its electrons.
A different way to look at it is the following: Imagine the photon would change the orbital of only a single electron. Because the probability distribution of the "active" electron changes, the other electrons feel its repulsion in a different shape and therefore adjust their own orbitals. This in turn makes the "active" electron feel a different potential, so it readjusts its orbital, and so on.

Even for systems with well-separated electrons, like a cloud of Hydrogen atoms, collective absorption of a single photon is likely to occur. Compared to the case, where $$1$$ atom absorbs $$1$$ photon $$|g\rangle |1\rangle \to |e\rangle |0\rangle$$, collective absorption of $$1$$ photon by $$N$$ atoms happens at a $$N$$ times faster rate and is therefore the dominating process in an atomic cloud. The resulting state is a coherent superposition of all possible states in which one particular atom absorbed the photon:[1] $$|g_1 g_2 ... g_N\rangle |1\rangle \to \frac{1}{\sqrt{N}} \left( e^{i \varphi_1} |e_1 g_2 \cdots g_N\rangle + e^{i \varphi_2} |g_1 e_2 \cdots g_N\rangle + \,\, ... \,\, + e^{i \varphi_N} |g_1 g_2 \cdots e_N\rangle \right) |0\rangle$$ A more general treatment of this case, including multiple excitations, was first given in R. H. Dicke, Phys. Rev. 93(1) (1953) – Coherence in Spontaneous Radiation Processes.

You can observe photons interacting with many electrons at the same time also in an everyday object – a mirror. This was discussed already in some other questions here,[2 and duplicates] but in a nutshell: If a photon would only interact with $$1$$ electron of the mirror it would be scattered in all directions. But since the photon extends over many electrons the scattering interferes destructively for most directions. Calculating the direction of positive interference results in the macroscopic law of reflection.

There are also various processes in which a single emitter interacts with multiple photons, but this is another topic.

• +1. Nice answer. How does collective absorption differ from an electron in a vacuum chamber striking a phosphor covered screen, where 1 atom lights up? What makes many atoms participate in the absorption vs one atom? – mmesser314 Mar 22 at 1:11
• @mmesser314 The electron hitting the phosphor screen leading to the emission of one or more photons is a projective measurement in the sense that it's practically not reversible. In contrast the collective excited state can re-emit the photon and thereby erase all the information about it stored in the atoms. For a good example of such an experiment, see Afzelius et al. NJoP 9 (2007). – A. P. Mar 22 at 8:21
• @mmesser314 You can imagine the reason why many atoms participate in the absorption as the photon being extended over a certain region. All the charges in this region are affected by the photon, so as long as you don't perform a measurement, all atoms interact with it. – A. P. Mar 22 at 8:27
• @A. P.: thank you for this interesting answer. Originally I asked this question because I suspected mirrors are not reemissions of single photons by individual electrons, rather they are reflected by a surface of electrons acting as one, so having a normal component. Is this linked to what you say or completely unrelated? – Winston Mar 22 at 12:00
• @Exocytosis A mirror is another very excellent example. I've added it to the answer. – A. P. Mar 22 at 13:50