- #36

rolnor

- 113

- 14

Thanx, I learn a lot. You wright something of the photon being asymptotic, does that mean that it has no real boundary? You can not say really where its "volume" starts or begins? I understand that, when I with my limited knowledge react strongly against this popular science idéa that a conscious is nessecary to collaps the wavefunction, you guys must really puke on what is all over the webb regarding a lot of quantum mechanics theory...vanhees71 said:A photon is a photon, and it does never behave like a particle. It has not even a position observable. The naive photon picture, introduced by Einstein in 1905, is long outdated (in 1926 Born and Jordan and somewhat later Dirac gave the correct description in terms of field quantization).

A photon is a asymptotically free single-quantum Fock state of the electromagnetic field. So the first thing you need is a single-photon source. Today that's provided usually by parametric down conversion, i.e., by shooting with a laser on a birefringent crystal, where you can get entangled photon pairs and use the one photon to "herald" the other photon, which you can then let go through a double slit. Finally you need a single-photon detector, which I guess is the most expensive part.

What you will observe is that for any single photon going through the slit (with some probability) you'll register this photon at one spot at the photodetector. The location of this spot cannot be predicted in any way but only the probability. Now it turns out that quantum electrodynamics predicts that the probability distribution is given by the properly normalized classical energy densit, i.e., the interference pattern you expect from classical diffraction theory.

What's meant by "wave-particle duality" in modern terms just means that on the one hand you have a kind of "particle property" for a single-photon Fock state, i.e., it can be registered either as a whole or not at all. It's, however not some kind of localizable massless particle following a trajectory of any kind. You cannot even define a position observable for a photon (as you can for massive "particles", i.e., field quanta of massive fields)! All you can know is the probability distribution for the "registration events" at any place of the photodetector (you can use a pixel detector, so that you get an interference pattern by registering many equally prepared photons). On the other hand the probability distribution is given in terms of field theory and it thus shows interference effects.

The next thing is that you can also try to figure out through which slit of the double slit each photon came. This is only possible, if you somehow mark each photon behind the slit in such a way that you can say with certainty through which slit it came. One clever way to do this is to use the polarization observable of this photon to mark it accordingly, i.e., you aim for a perfect "entanglement" between the photon's polarization state and the "which-way information".

This can be achieved by using linearly polarized incoming photons (say in ##x##-direction) (this is easily achieved by using a polarization filter) and mount two quarter-wave plates into the slits one oriented in ##+\pi/4## and the other in ##-\pi/4## orientation. Then any photon going through one slit will be left-circular polarized and any photon going through the other slit will be right-circular polarized, i.e., by measuring the polarization state for the photons going through the slits you could figure out exactly through which slit each photon came (but you cannot predict it beforehand, i.e., you have with 50% probability a photon coming from one and 50% from the other slit). Since now the photons going through the one slit are perfectly polarized in a way that the polarization state is perpendicular to the one of the photon going through the other slit, the interference effect is completely done, i.e., now the partial intensities for photon going through the one or the other slit add, i.e., you completely loose the double-slit interference pattern (the single-slit envelope is still visible though).

This example shows that it is very easy to understand, why gaining 100% "which-way information" (or only the possibility to gain it by measuring the polarization state of the outgoing photons) destroys the double-slit interference pattern completely. Again, this is not understandable within the naive photon picture of 1905 but you need quantum-field theory!