Can two single particles interfere with each other?

Question

Groups of particles can interfere with one another; In the double slit experiment when measuring single photons at the screen each one arrives at the screen in a random manner and they only show the interference pattern once several particles are detected.

Obviously two waves can obviously interfere with one another, but can two single particles interfere with one another? Cohen-Tannoudji writes that

light simultaneously behaves like a wave and like a flux of particles

But do two particles constitute a flux of particles? I doubt that this could be tested experimentally but if it were so would this constitute a measurement for each particle?

Here was my thought (Disclaimer:I do not have a good idea of what the interference of two single particle states is): To have interference of two single particles you would have to know something about there position to be able to describe their interference pattern hence the measurement.

Answer 1

When we are talking of elementary particles we are talking of quantum mechanics.

The wave nature of quantum mechanics comes because the equations are wave equations and the solutions of these wave equations squared have been defined , Born rule, as the probability of observing the particle at an (x,y,z,t). Thus interference in a quantum mechanical setup means: interference patterns in a probability density distribution, not in energy or mass .

The photons, as elementary particles, due to the peculiarity of their masslessness and the Maxwell equations have the same frequency in the single photon double slit interference patterns ( probability distributions) as the frequency displayed by the electromagnetic wave that may emerge from a huge number of photons. (The classical EM wave does display interference patterns in its energy distribution, hence the confusion between classical and quantum interferences).

Now two single particles quantum mechanically will also have a single solution in quantum mechanics that will be defined by the boundary conditions. These solutions will be different than if they are far apart and can be considered independent. Thus the probability of their manifesting in an (x1,y1,z1) (x2,y2,z2) at time t will be different and thus they may be considered to interfere with each other.

Consider an electron and a proton, many boundary conditions could exist:

a) a bound state governed by their potential

b) a resonance if the relative energy is higher than the hydrogen bound state

c) an elastic scattering both changing directions

d) inelastic scattering emitting a photon in each other's field

e) if the energy is high enough a generation of new particles due to the scatter

Different boundary conditions will show different dependances, but yes, they will interfere/change the probabilities for each other.

Answer 2

Don't over interpret Cohen-Tannoudji's sentence. It describes two situations very far apart. Either a single photon or a very very large number of photons, all doing the same thing. It touches on a feature of the world that is very hard to understand. For example, the difference between the stream of photons and a single photon has (in most cases) nothing to do with interactions between the photons.

Take the double slit experiment as an example. Suppose that it is set up so that the screen where the light is observed, we have a very sensitive measurement device sensitive enough to record a the position where a single photon hits it. Sending of a single photon through the double slit will then give rise to the recording of one precise position on the screen.

Sending a trillion of photons but with a distance between them, so that the next is not sent until the previous is recorded by the screen detector, will result in the well known intensity pattern. The number of photons that were recorded at a specific spot is given by the standard expression for the intensity distribution on the screen. Normally the double slit experiment is performed with a laser. The photons are then much closer to each other and could interact, but such interactions are not responsible for the interference pattern. On the contrary, I imagine that a sufficiently intense beam could show deviations from the usual interference pattern.

The well known double split intensity pattern, if appropriately normalized, is simply the probability distribution of where photon will be recorded on the screen.

So, the wave description applies to a single photon as well as the beam from a light source. Now, we have entered a quite deep and complicated aspect of quantum physics. So complex that there is no complete agreement on how it works. There are different interpretations.

My understanding of these situations is based upon the notion of entanglement of quantum states, and of the chaos that photon creates in the measurement apparatus. These two ingredients creates a separation of the quantum state of the combined system of the photon and the measurement device to separate into different parts that have nothing to do with each other any more, thus effectively separating the world into different alternatives. In these different worlds our photon have been recorded at a different locations as the wave description dictates. This is the multiworld interpretation. To my mind this is just an analysis of what the quantum equations say. Anyone coming up with other interpretations have to prove that the real physics deviate from what the quantum equations give. Then they have to come up with some new physics that we can test. I can assure you that there is not yet any experiment that can not be understood using the quantum equations.

Answer 3

Classical particles such as electron, proton and neutron of course interfere with each over. No doubt. Photons interfere too. See https://en.wikipedia.org/wiki/Photon_bunching. If you ask about the double slit experiment with single photons the common answer is yes. A single photon interfere at the position of the slits with itself and that is the reason why on an observation screen appears fringes.

But please take in attention that even a single slit and every edge too produces fringes near the shadow. Every edge interfer with particels in the region between the edges material and the free space. A second fact for the influence of edges to the particles is the fact that if you place two crossbred polarizers no light is coming through. Now place a third one under 45° between the overs and you see light behind all the polarizers. The double slit experiment was made with single electrons too. As result we get the fringes too what was interpreted as interference of the electron with itself. This is a little bit strange because there are the sciences about QED etc. where the fields between the particles (and the edges are made in first line from electrons ergo particles) is part of the calculations.