# What happens when a photon hits a beamsplitter?

Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (Wheeler's delayed choice experiment). Part of what is puzzling me is the beam-splitter. Are the individual photons actually being split into two new photons of lesser energy?

This question implies that you cannot split a photon but it seems that beam splitters do exactly that.

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The crucial word is "beam", in "beam splitter". Beam means an ensemble, in contrast to "photon" which is an individual particle.

A light beam is an ensemble of photons and if it is of a single frequency nu, all photons have energy E= h*nu. A light beam can be split in a beam spliter, i.e. the ensemble of photons can be split into two streams of photons: the intensity of the beam goes down, but the individual photons still have frequency h*nu.

Now one can think of impinging photons one by one on a beam splitter. A photon is described by a wavefunction which when squared will give the probability of finding the photon in a particular (x,y,z). It will go either where one stream went or the other according to the probabilities, but it will be seen as a whole photon of energy E=h*nu.

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A single photon is a quantised packet of Electromagnetic energy, the smallest indivisible unit imposed by boundary conditions according to quantum mechanics. In this regime I find it easier to think of the photon as a particle with a 'polarization' degree of freedom which can be horizontal $\left|H\right>$,vertical $\left|V\right>$ or in any linear superposition of the two.

When the photon meets a beam splitter it acts like a quantum particle and takes both paths with probabilities determined by the polarization. Much like the electron taking both paths in Young's famous double slit experiment.

It is not the actual photon being split into two new ones, only the 'particle-like' position wavefunction holds the information about where the photon is. Quantum mechanically, we can treat photons exactly like any other bosonic particle.

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Very short and "axiomatic" answer: You indeed can "split" one particle. In QM particles are treated as a "wave functions", maybe it will be more easy for you to imagine a splitting wave. However, only at the point when the photon is detected the particle is measured in one point of space. This is the very foundation of QM and I agree that it's hard to grasp the concept.

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I would define "splitting a particle" to mean that the energy of the particle was split into two pieces. When you fire a single photon at a beam splitter, there's no evidence that this sort of splitting happens. A beam splitter doesn't split an incident photon this way, but rather it splits the wavefunction giving two alternatives which can interfere with each other. –  twistor59 May 30 '13 at 19:08
Jan, yes this is a difficult one to wrap my head around. Let me ask a different but related question. If the individual photon is split and then later detected will it have the same energy as when it left the emitter? –  CramerTV May 30 '13 at 19:42

Photon is quantum. Experiences with photons are quantum experiences. In quantum experiences, you are calculating transitions probabilities .

To calculate transitions probabilities $p$, you will have to use quantum complex amplitudes probabilities $A$, with $p$ = $|A|$

To calculate transition amplitudes $A$, you will have to consider all the paths that are available to the photon field, and sum other them :

$A$ = $\sum_{paths} A_{path} = \sum_{paths} e^{- i S_{path}}$,

where $S_{path}$ is the action of the photon on the considered path.

So, you will have to get rid of the classical view of the particle, localized in space-time, indivisible, and so on.

You are now in the quantum world, which has its own rules.

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