Constructive Interference of Light

[jactor]

TL;DR Summary

When two photons constructively interfere, what is resultant photon/waves' characteristics?

When two photons constructively interfere, what is resultant photon/waves' characteristics?

When we talk about physical waves like sound, the constructive interference results in their amplitudes essentially being added together. But with light, my understanding is that the amplitude of a photon is universal (and that "brightness" generally refers to density of photons).

Further, what do the photons look like that have destructively interfered? Do they get annihilated?

 

[PeroK]

Summary:: When two photons constructively interfere, what is resultant photon/waves' characteristics?

When two photons constructively interfere, what is resultant photon/waves' characteristics?

When we talk about physical waves like sound, the constructive interference results in their amplitudes essentially being added together. But with light, my understanding is that the amplitude of a photon is universal (and that "brightness" generally refers to density of photons).

Further, what do the photons look like that have destructively interfered? Do they get annihilated?

Photons interfere with each other neither constructively nor destructively (although there is some rare photon-photon interactions):

https://en.wikipedia.org/wiki/Two-photon_physics

 

[jactor]

@PeroK Hmm so what are the light and dark spots that you would observe in the double slit experiment? Are those photons getting concentrated into certain places?

 

[Dale]

Photons interfere neither constructively nor destructively (although there is some rare photon-photon interactions):

I think you are thinking of “interaction” rather than “interference”. The wave function of a two-photon state should just be the sum of the wave functions of two one-photon states, right?

 

[PeroK]

@PeroK Hmm so what are the light and dark spots that you would observe in the double slit experiment? Are those photons getting concentrated into certain places?

Diffraction and the double-slit interference pattern are a result of (individual) photons behaving quantum mechanically. Not "interfering with eath other", as it were.

 

[jactor]

@PeroK That, unfortunately, does not aid my understanding.

 

[PeroK]

@PeroK That, unfortunately, does not aid my understanding.

A quantum particle (photon or electron, say) diffracts when it passes though a narrow slit. If we have a double slit, then the wave function of the particle is a superposition of wave functions corresponding to each slit. Quantum interference relates to the behaviour of the superposition of wave functions for each particle. It's not directly two particles interfering with each other.

 

[PeroK]

I think you are thinking of “interaction” rather than “interference”. The wave function of a two-photon state should just be the sum of the wave functions of two one-photon states, right?

I only meant that if quantum interference depended on two particles interfering with each other, then the double-slit interference pattern wouldn't arise if carried out one particle at a time.

 

[PeroK]

PS see also:

https://www.physicsforums.com/threa...t-feel-electromagnetism.1000527/#post-6466177

 

[jactor]

A quantum particle (photon or electron, say) diffracts when it passes though a narrow slit. If we have a double slit, then the wave function of the particle is a superposition of wave functions corresponding to each slit. Quantum interference relates to the behaviour of the superposition of wave functions for each particle. It's not directly two particles interfering with each other.

That is interesting. Is there any intuition behind this explanation or is our best understanding strictly mathematic (i.e. wave functions)?

 

[PeroK]

That is interesting. Is there any intuition behind this explanation or is our best understanding strictly mathematic (i.e. wave functions)?

It's generally accepted that QM is fundamentally different from classical mechanics in ways that would be difficult to imagine were it not for the experimental evidence. In that sense it's not intuitive.

 

[jactor]

@PeroK Got it. Thanks for your help!

 

[Dale]

I only meant that if quantum interference depended on two particles interfering with each other, then the double-slit interference pattern wouldn't arise if carried out one particle at a time.

Sure, but just because a photon does interfere with itself doesn’t mean that two or more photons don’t interfere with each other.

If you have two coherent sources then each source has a wave function with a certain probability of detecting a photon in any given place. The combined wavefunction of both sources will have locations where there is no probability of detecting a photon. So they do interfere.

 

[PeroK]

Sure, but just because a photon does interfere with itself doesn’t mean that two or more photons don’t interfere with each other.

If you have two coherent sources then each source has a wave function with a certain probability of detecting a photon in any given place. The combined wavefunction of both sources will have locations where there is no probability of detecting a photon. So they do interfere.

With photons it gets complicated. If we stick with electrons, so we can apply some basic QM, then two electrons don't "interfere" with each other, in the sense of exhibit quantum interference. You have the exclusion principle, which puts an overall antisymmetric requirement on the two-particle wave-function, but again that's not interference.

The interference term arises in general through different time evolution of the superimposed wave functions representing a single particle. You may have out-of-phase probability amplitudes that cancel.

 

[vanhees71]

@PeroK Hmm so what are the light and dark spots that you would observe in the double slit experiment? Are those photons getting concentrated into certain places?

In leading order you describe the double-slit experiment with single photons, i.e., there the interference pattern is due to single-photon interference.

One should not intuitively think about photons (or also particles) in terms of classical particles, particularly not if you consider interference effects, which is of course a wave phenomenon. Particularly for photons a classical-particle picture is completely misleading since you cannot even define a position observable for them with the usual meaning. Physically photons thus cannot be localized at all in the strict sense. For photons the only known working theory is QED, i.e., quantum fields.

 

[vela]

@PeroK Hmm so what are the light and dark spots that you would observe in the double slit experiment? Are those photons getting concentrated into certain places?

Yeah, pretty much. If you send one photon through at a time, you'll see the photon arriving at random spots on the screen. If you repeat this over and over, you'll find the interference pattern emerges. This idea is illustrated in the figure below from Young and Freedman's textbook.