How is quantum interference achieved with atoms fired from opposite directions?

[Jilang]

I came across this today, but wasn't quite sure how it worked.
http://www.sciencedaily.com/releases/2015/04/150409081436.htm
Are the two atoms fired from opposite directions?

 

[craigi]

I came across this today, but wasn't quite sure how it worked.
http://www.sciencedaily.com/releases/2015/04/150409081436.htm
Are the two atoms fired from opposite directions?

They travel in the same direction from the Bose-Einstein condensate source towards the Bragg mirror, but with variable spacing. They observe the interference effect when the spacing is very small.

 

[Jilang]

Thanks Craigi, it wasn't clear as it stated they are fired at opposite sides of the mirror. Does it mean one hits the front wall and one hits the back wall then?

 

[craigi]

Thanks Craigi, it wasn't clear as it stated they are fired at opposite sides of the mirror. Does it mean one hits the front wall and one hits the back wall then?

Perhaps I posted too hastily. This should clear it up:
http://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect

This is the effect that they emulated with atoms.

 

[Jilang]

That's exactly what I was looking for! So is the narrative saying that diagrams 1 and 4 can happen and 2 and 3 cannot (for certain momenta/mirror thickness combinations)?
Very cool!

 

[jerromyjon]

So is the narrative saying that diagrams 1 and 4 can happen and 2 and 3 cannot

It appears to me with a 50/50 splitter any of those 4 possibilities are equally likely, just that 2 and 3 are indistinguishable from each other... whether both photons reflect or not the results are the same.

What I am unclear about is how that is related to the dip caused by indistinguishable atoms?

 

[craigi]

It appears to me with a 50/50 splitter any of those 4 possibilities are equally likely, just that 2 and 3 are indistinguishable from each other... whether both photons reflect or not the results are the same.

What I am unclear about is how that is related to the dip caused by indistinguishable atoms?

Indistinguishable atoms undergo interference in the same way as the photons in the original experiment. When the path integral is performed, for the particle pair, the paths for particles in separate directions are cancelled.

The paths for distinguisable particles don't interfere in this way.

 

[jerromyjon]

Instead of destructive interference the atoms come out in pairs, as in molecules?

 

[craigi]

Instead of destructive interference the atoms come out in pairs, as in molecules?

Molecular bonding isn't relevant to the experiment. The atoms are Helium atoms, so they don't form molecules under normal conditions.

 

[jerromyjon]

Molecular bonding isn't relevant to the experiment.

Ok I get it. The lack of bonding is relevant because they are Helium-4 they shouldn't interfere, and only when they are indistinguishable atoms they cause a "pairing" interference where one atom is reflected while the other passes.

The atoms both just stop moving?

 

[Jilang]

So the situations 2 and 3 are identical except for a phase difference, so cannot be observed?

 

[craigi]

So the situations 2 and 3 are identical except for a phase difference, so cannot be observed?

Draw out wave packets for each case to convince yourself that 2 and 3 correspond to destructive interference and 1 and 4 correspond to constructive interference, but don't forget the phase shift.

 

[Jilang]

I am uncertain what you have in mind for me to do next. How would I draw a wave packet? What do they look like? I am not sure how cases 1 and 4 can interference as they are different.

 

[craigi]

I am uncertain what you have in mind for me to do next. How would I draw a wave packet? What do they look like? I am not sure how cases 1 and 4 can interference as they are different.

Have you studied Vibrations and Waves yet?

Are you sure that you understand superposition of waves, constructive interference and destructive interference?

If not, start here:
http://en.wikipedia.org/wiki/Interference_(wave_propagation)

We're not talking about case 1, interfering with case 4. We're talking about of both wavefunctions splitting and taking both outgoing routes. However, interference determines which of the 4 cases result in a non-zero probability of finding an outgoing particle.

 

[Jilang]

I must have got the wrong end of the stick as you mentioned constructive inference of 1 and 4 in post #12. Yes I have studied wave mechanics, but I still don't know what you mean about drawing a wave-packet.

 

[zonde]

So the situations 2 and 3 are identical except for a phase difference, so cannot be observed?

Yes, 2 and 3 have the same destructive interference and are not observed (are observed considerably less frequently). This in experiments is observed as HOM dip in coincidence counts as you change length of one arm.

 

[craigi]

I must have got the wrong end of the stick as you mentioned constructive inference of 1 and 4 in post #12. Yes I have studied wave mechanics, but I still don't know what you mean about drawing a wave-packet.

Wave packet description here:
http://en.wikipedia.org/wiki/Wave_packet

The envelope overlap of the two packets determines the shape of the dip.

 

[Jilang]

Thanks, it must be pretty tricky to get a decent overlap. I found this today which has all the details...

http://arxiv.org/pdf/1501.03065v2.pdf