# How two photons interfere in a double slit experiment

I have a very basic question about photons in double-slit experiment. I am not good at math, and have some Quantum mechanics knowledge. Math free explanation would be very good to me.

When we do double slit experiment with single photon at a time, it will be detected at some location of screen. Over the time period the accumulation of detected locations show interference pattern. The reason for the interference pattern is that photon's location in not well defined, the presence of photon in particular place can be determined by prbability and this probability is presented as a wave. that probability wave is splitted in to two while passing the two slits, collide with each other and causes interference pattern.

Question 1: Is this reason for single photon interference correct?

Question 2: How is the probability wave behaving while two-photons passing double-slit at a time? Are 4 probability waves (2 for each) interfering?

• 'location [...] is a probability' ????
– Danu
Jan 31, 2014 at 2:57
• I have improved my question. please check now. Jan 31, 2014 at 5:25

Question 1: Is this reason for single photon interference correct?

The most intuitive way of looking at interference that I have encountered is Feynmann's Path Integral Formulation. Loosely speaking, if you have a photon (or anything, really) in location A and want to work out its chance of moving to B, you imagine it taking every possible path between the two at the same time. All of these paths interfere with each other resulting in some final amplitude from which you can extract the probability of the particle moving from from A to B. This sounds kind of like what you were trying to say when you said that the 'probability wave is split in to two'. All particles do this when moving, not just photons, however in the classical (i.e. large) limit, you can show mathematically that only one particular path will contribute to the particle's motion, which is why when you throw a tennis ball across the room you don't see it taking every possible path at once.

Question 2: How is the probability wave behaving while two-photons passing double-slit at a time? Are 4 probability waves (2 for each) interfering?

For a double slit experiment, the interference pattern does not change with light intensity. I believe you can think of each photon as behaving independently in this case.

• Fine. somehow I got answer. let me confirm it. two photons are travelling independent path to each other, and not colliding with each other. Jan 31, 2014 at 16:12
• Yes, we generally think of photons as interfering rather than colliding. It is like if two waves of water 'impact', they just travel through each other. Jan 31, 2014 at 23:48
• Classically, in "line-of-sight" radio communication, the radio wave does not travel on a thin geometric line. Rather, it occupies the Fresnel Zone--and anything in the zone can cause interference. The central zone is basically the region of stationary phase, a la the Feynman path integral.
– JEB
Dec 7, 2017 at 18:32

The reason for the interference pattern is that photon's location in not well defined, the presence of photon in particular place can be determined by probability and this probability is presented as a wave.

Probability distributions have the same meaning classically and quantum mechanically.There is a distribution for life expectancy for example, giving the probability of dying if one is a certain age. This can be plotted in a histogram . The only information it gives is that one event, a person at 90, has a probability of dying within the year of 0.17. The curve was measured from a large sample of population.

In a similar way, the probability curve of a photon impinging on the two slits that it will hit at a certain (x,y) on the screen can be measured by a large sample of photons and one will have the two dimensional histogram of that probability, and then can give a probability for the next photon. Fortunately though mathematical solutions help us to get the probability curve, and those solutions contain sines and cosines which are solutions of wave equations in general, like energy waves and sound waves which have been studied for centuries. The mathematics of quantum mechanics has similar differential equations, but the solutions are identified differently.

that probability wave is splitted in to two while passing the two slits, collide with each other and causes interference pattern.

Question 1: Is this reason for single photon interference correct?

The above preamble is to stress that there is no splitting , there is just a computed/observed probability pattern. There is nothing to collide. It is just a representation that has sine and cosine solutions and a single event will appear according to the probability so that it adds up to the interference pattern. Similar that a single death seems random unless a large number of deaths are plotted and probabilities can be gauged. So no, it is not correct. No splits and interference

Question 2: How is the probability wave behaving while two-photons passing double-slit at a time? Are 4 probability waves (2 for each) interfering?

No, even if you manage to pass two photons at a time (photons are very fast point particles) they do not interact with each other. Quantum mechanical calculations that fit experiments much more sophisticated than the two slits show that photons interfere with each other with tiny probabilities, calculated by higher order feynman diagrams.

BUT two photons can give an interference pattern if superimposed, superposition means adding of wavefunctions so that the measured values show the interference of the wavefunctions. This video is instructive for monochromatic interference patterns.

Yes, the two waves of one photo interfere with each other and the two waves of another interfere with each other. The waves of the first photon do not interfere with the waves of the second photon.