Double Slit Question

[dogjones]

Had a quick read of this article: http://news.bbc.co.uk/2/hi/science/nature/8363934.stm

And have a question about just this:

Quote:

A single wave of light, a photon, passes through two slits at the same time and creates an interference pattern.

How small do the slits have to be in order to let only one photon through??

[JohnnyG]

Originally Posted by dogjones

How small do the slits have to be in order to let only one photon through??

They don't filter out photons by making the slit smaller, they use a source that can be "pulsed" in very short durations to only emit one photon at a time.

[dogjones]

Ahhhhhhh! Making more sense. Although how near do the slits have to be to each other to ensure it goes through both at the same time?

[godofpie]

And can you explain the mechanics of being able to fire one photon at a time?

[blutoski]

Originally Posted by dogjones

Ahhhhhhh! Making more sense. Although how near do the slits have to be to each other to ensure it goes through both at the same time?

I'm curious about the result, too, since my understanding is that the distance between slits is dependent on the scale of the wave component of the object passing through.

I was trying to do the math backwards: how far apart do apertures have to be spaced to produce interference with fullerines? How about for planets?

[ben m]

Originally Posted by godofpie

And can you explain the mechanics of being able to fire one photon at a time?

It's possible to do it straightforwardly. Take (say) a green LED emitting 1 microwatt of light---that's enough to see---or 1.5x10^12 photons per second. Put it behind a screen with a tiny pinhole in it; so now 10^6 photons per second come through the pinhole. Now, instead of turning the LED on continuously, turn it on in 10-nanosecond pulses. Each pulse has a 99% chance of launching zero photons through the pinhole, 1% of launching one photon, 0.01% of launching two photons, etc. So that's a reasonable sort of single-photon source. A photon-counting detector (like a PMT) can confirm that this is how it behaves.

Fancier sources can be arranged using quantum physics tricks. There are certain atomic states that are guaranteed to emit exactly one photon; you can prepare one atom at a time, confirm that there's only one of it, and trigger its emission. Certain solid-state quantum systems, like quantum dots, can be made to do the same thing---that's a fairly recent innovation though. The classic single-photon experiments were done with very faint light beams as above.

[Madalch]

I forget how the math works, but I know that if you coat a microscope slide with tar, and put two razor blades together to make a double slit in the tar, they are the right distance apart to diffract light.

[JohnnyG]

Originally Posted by godofpie

And can you explain the mechanics of being able to fire one photon at a time?

They aren't fired exactly, they attenuate a laser beam to a low enough intensity that the mean distance between photons is extremely large (on the order of kilometers), essentially making it a pulsed source. The point is that they slow down the photon rate at the source, not by filtering them using the slit.

[ctamblyn]

Originally Posted by Madalch

I forget how the math works, but I know that if you coat a microscope slide with tar, and put two razor blades together to make a double slit in the tar, they are the right distance apart to diffract light.

If I recall correctly, the result is something like this. If D is the distance from the slits to the screen, d is the slit separation and l is the wavelength then the bright fringes on the screen are a distance Dl/d apart. This assumes that both l and d are much smaller than D. For your molecule beam, the wavelength can be found from the momentum using the basic relation: l = (Planck's constant)/(momentum). Sorry for the rubbish formatting, I'm posting from my phone :-)

[Ziggurat]

Originally Posted by dogjones

Ahhhhhhh! Making more sense. Although how near do the slits have to be to each other to ensure it goes through both at the same time?

There is no maximum. However, the farther apart they are, the more likely that the photon will just hit the wall between them. So it's more of a probability issue: how often do you want the photon to pass through the slits?

As a practical matter, though, the size is generally determined by the size of the diffraction pattern you want to create, not by intensities or probabilities of transmission. The farther apart the slits are, the smaller the separation between diffraction fringes, which can make them hard to see. You can make that distance larger in one of three ways: move the screen farther away from the slits, use longer wavelength light, or move the slits closer together. The first two have obvious limits in any real experiment, which means that you'll end up with a maximum slit separation distance based on the desired diffraction pattern.

[learner]

Originally Posted by dogjones

Ahhhhhhh! Making more sense. Although how near do the slits have to be to each other to ensure it goes through both at the same time?

Just watched a programme on the BBC tonight explaining the experiment. As I understood it the slits and gap may vary. In the instance shown the slits were approximately a hairs width and the spacing the same.

The programme was on measuring a length of string and ranged from using a rule at the shop the string was bought from, to how long it took light to travel its length.
Similar to measuring a coastline, it was not possible. It just became longer the more accurately you measured it.
Very interesting and well explained.

[edd]

Originally Posted by learner

Similar to measuring a coastline, it was not possible.

Tish and fipsy. The UK's Ordnance Survey has long been defying mathematics to do just that.
http://mapzone.ordnancesurvey.co.uk/...s/q_12_69.html
(Despite enquiries, they've never told me how exactly they did that)

[learner]

Originally Posted by edd

Tish and fipsy. The UK's Ordnance Survey has long been defying mathematics to do just that.
http://mapzone.ordnancesurvey.co.uk/...s/q_12_69.html
(Despite enquiries, they've never told me how exactly they did that)

Presumeably, very quickly, before the tide changed, and with a tiny rule!

Just had a daunting thought. I am planning a walk around the coast of Ireland (as near as i can get to it) If its gona take an infinite length of time im not going. Think I will take a rule and assess at half way.
Doh! theres no half way!

[Soapy Sam]

Sure, if you're not going, den it'll take forever sure enough.

[Fontwell]

Originally Posted by learner

Just watched a programme on the BBC tonight explaining the experiment.

Me too. I've known of the experiment for years and never really understood how you could make things small enough, especially considering when it was first done. It was therefore quite a surprise to see it being done and using stuff that was all pretty big. The target was about the size of a postage stamp and it just had two thin slits in it, thin but not microscopicly thin. The laser was a meter or so away from the target and the wave pattern was projected onto a wall!

[rjh01]

Do not worry. If you take steps that are almost a meter long then the length of a coast is finite. However if you want to produce an infinite length try answering this problem.

Give the total length of the triangle produced by this process.

1. Generate a triangle with each side of length one.
2. For every straight length add another triangle in the middle such that all four lines are of equal length (the four lines are the two sides of the triangle and the two parts of the remaining original line).
3. Repeat infinitely step 2 for every straight line

NB Step 2 turns a straight line into this shape: _/\_ Now you have four straight lines. For each one of those four lines you need to repeat the step.

The result is a simulated coastline.

I hope the above makes sense. It is bedtime for me and I am rather tired.


Edit. This is in response to posts 12,13,14.

[dogjones]

Originally Posted by rjh01

Do not worry. If you take steps that are almost a meter long then the length of a coast is finite. However if you want to produce an infinite length try answering this problem.

Give the total length of the triangle produced by this process.

1. Generate a triangle with each side of length one.
2. For every straight length add another triangle in the middle such that all four lines are of equal length (the four lines are the two sides of the triangle and the two parts of the remaining original line).
3. Repeat infinitely step 2 for every straight line

NB Step 2 turns a straight line into this shape: _/\_ Now you have four straight lines. For each one of those four lines you need to repeat the step.

The result is a simulated coastline.

I hope the above makes sense. It is bedtime for me and I am rather tired.


Edit. This is in response to posts 12,13,14.

Um, I'm not really sure what's going on here. This seems an elaborate way of saying "if you want to produce an infinite length, then keep drawing?"

[ctamblyn]

Originally Posted by dogjones

Um, I'm not really sure what's going on here. This seems an elaborate way of saying "if you want to produce an infinite length, then keep drawing?"

It's a Koch curve - en (dot) wikipedia (dot) org/wiki/Koch_snowflake

[rjh01]

Thanks ctamblyn. Here is the link http://en.wikipedia.org/wiki/Koch_snowflake.

And welcome. I owe you one.

[dogjones]

I don't get it. It's a foreign concept, and I'm Zenophobic.

[JohnnyG]

Originally Posted by rjh01

3. Repeat infinitely step 2 for every straight line

The result is a simulated coastline.

Why infinitely? Surely the recursion must stop before the characteristic length reaches the atomic scale.

[dogjones]

I could make a pirate joke about walking the Planck here, but I won't.

[learner]

I think Il just take big strides and see if I make it home.

[MattusMaximus]

Originally Posted by Madalch

I forget how the math works, but I know that if you coat a microscope slide with tar, and put two razor blades together to make a double slit in the tar, they are the right distance apart to diffract light.

Visible light.

And yes, this works. It's a low-tech trick I've used before in the lab when money was tight.

[alexi_drago]

Possibly stupid question time again.

What's hitting the detector, a photon? the same photon that was emitted? how far did it travel to get there or how long did it take as the distances for each path are different?

[Ziggurat]

Originally Posted by alexi_drago

What's hitting the detector, a photon?

Yes.

Quote:

the same photon that was emitted?

Yes.

Quote:

how far did it travel to get there or how long did it take as the distances for each path are different?

The photon is not a point particle. As such, it is neither emitted nor detected at an instant of time, but over a period of time. This makes any path length difference irrelevant: the difference will be less than the "length" of the photon. If that is not the case, you won't get interference.

[ctamblyn]

Indeed, any measurement that could reveal which path the particle took will wash away the interference. This is most definitely one of my favourite experiments in physics.

[ctamblyn]

Originally Posted by rjh01

Thanks ctamblyn. Here is the link...(snip)

And welcome. I owe you one.

My pleasure! Thank you for posting a proper link for me.

[Fontwell]

Hijacking this thread to ask another double slit question

When they use 'a detector' to tell which slit a photon went through I can see several problems and I'd be interested to know how they are resolved: If the detector interacts with photons to the extent of detecting them then presumably photons that get detected never make it to the screen? Is it possible to detect a photon and still have it travel to the screen? Similarly, If the detector is close to a slit, wouldn't it be effectively blocking that slit? But if it is far away from the slits how can you tell which slit the photon came through at all?

[rjh01]

Originally Posted by Ziggurat

<snip>
The photon is not a point particle. As such, it is neither emitted nor detected at an instant of time, but over a period of time. This makes any path length difference irrelevant: the difference will be less than the "length" of the photon. If that is not the case, you won't get interference.

This is not quite right. The photon goes through both slits (how good is that a single photon goes though two different paths. It can do this because it is a wave not a particle). It then travels to the photon detector. Now then what happens next depends on the distance the wave took on both paths. If they were the same distance or the difference is exactly a multiple of the wavelength then the photon causes a reaction with the detector. It can do this because it is a particle not a wave. If the distance is a odd multiple of half a wavelength then nothing happens. If the distance is between these two extremes then a smaller reaction happens. Hence you get an interference pattern of a number of lines.

Please note that I said both that the photon is a particle and a wave. Both statements are correct. I also said that the photon goes through both slits at the same time. This is only a theory not a fact. It is the only way we can explain this interference pattern. If you put detectors on the slits to find out which slit the photon went through the interference pattern will go away.

To understand Quantum theory one thing you must reject is common sense.

[Ziggurat]

Originally Posted by rjh01

This is not quite right. The photon goes through both slits (how good is that a single photon goes though two different paths. It can do this because it is a wave not a particle). It then travels to the photon detector.

None of that contradicts anything I said. But if the photon you send at both slits is a VERY short pulse, short enough that the two parts do not overlap in space and time at the detector due to path length differences, then it will not interfere with itself. The photon must be longer than any path length difference in order for any interference to occur. And if it's longer than the path length difference, then you cannot use arrival time to determine which path it took.

[alexi_drago]

Originally Posted by ctamblyn

Indeed, any measurement that could reveal which path the particle took will wash away the interference. This is most definitely one of my favourite experiments in physics.

Can it be measured with electrons?

[Ziggurat]

Originally Posted by alexi_drago

Can it be measured with electrons?

Yes. The basic effect (wave interference) behind the 2-slit experiment is also the principle behind diffraction, which can be done with x-rays, neutrons, electrons, and even helium atoms.

[alexi_drago]

Originally Posted by Ziggurat

Yes. The basic effect (wave interference) behind the 2-slit experiment is also the principle behind diffraction, which can be done with x-rays, neutrons, electrons, and even helium atoms.

And is it possible to know the velocity and time taken from emmision to detection for any of those? or is that where the fact that making measurements affects the conditions messes everything up?

[temporalillusion]

Haven't they observed interference with Carbon-60 molecules (buckyballs)?

[rjh01]

Originally Posted by Ziggurat

None of that contradicts anything I said. But if the photon you send at both slits is a VERY short pulse, short enough that the two parts do not overlap in space and time at the detector due to path length differences, then it will not interfere with itself. The photon must be longer than any path length difference in order for any interference to occur. And if it's longer than the path length difference, then you cannot use arrival time to determine which path it took.

Wikipedia says it better than I can.

Quote:

The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. The pattern of interference remains the same, as can be seen if many photons are emitted one at a time and recorded on the same sheet of photographic film. The clear implication is that something with a wavelike nature passes simultaneously through both slits and interferes with itself — even though there is only one photon present. (The experiment works with electrons, atoms, and even some molecules too.)

Source http://en.wikipedia.org/wiki/Double-slit_experiment

Bolding on both quotes is mine. I cannot see how the two bolded statements can both be right.

[ctamblyn]

Originally Posted by rjh01

Bolding on both quotes is mine. I cannot see how the two bolded statements can both be right.

The two situations are not the same. In the Wikipedia case the photon has a well-defined wavelength. In the other case the photon has a sharply-defined position (when created) which implies a spread of wavelengths, due to Heisenberg, causing the interference pattern to become smeared. Have a look for Heisenberg's uncertainty principle on wiki - I'd post a link but I'm not allowed yet :-(

Ugh, it's 2.30 in the morning. Time to get some rest. My apologies if this post is utter rubbish.

[MattusMaximus]

Originally Posted by temporalillusion

Haven't they observed interference with Carbon-60 molecules (buckyballs)?

Yes.

[Andrew Wiggin]

Originally Posted by rjh01

To understand Quantum theory one thing you must reject is common sense.

I'd say more that to understand quantum theory you have to reject the idea that the fundamental particles behave like very very small billiard balls. We all know how billiard balls work, and somehow when we extend those rules to particles we end up completely boggled, as the very very small has its own set of rules.

A

[rjh01]

Originally Posted by ctamblyn

The two situations are not the same. In the Wikipedia case the photon has a well-defined wavelength. In the other case the photon has a sharply-defined position (when created) which implies a spread of wavelengths, due to Heisenberg, causing the interference pattern to become smeared. Have a look for Heisenberg's uncertainty principle on wiki - I'd post a link but I'm not allowed yet :-(

Ugh, it's 2.30 in the morning. Time to get some rest. My apologies if this post is utter rubbish.

No, a photon of light can only have one wavelength. This can be known.

The Uncertainty principle says

Quote:

In quantum mechanics, the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.