Orbis non sufficit
Sunday, May 28, 2006
Quantum Entanglement:
The bell-state quantum eraser
This is an extract from my third quantum mechanics assignment for this semester, it talks about an experiment called "the bell-state quantum eraser" which demonstrates the phenomena of quantum entanglement, among other things. Quantum entanglement is fricken amazing, the entire reason I study physics is to learn about things like this and to try and understand the implications that have on reality. Reality is a tricky thing.
I'm not sure how much of it anyone will understand, but hopefully you'll get the general idea.
"...the concept of quantum entanglement. This refers to a phenomena whereby two or more quantum systems cannot be described without reference to each other, even though they may be spatially separated. This allows information about one system to be determined by making measurements on the others. A spectacular example of this is an experiment called the ‘bell-state quantum eraser’. In this experiment a beam of light is passed through a special type of crystal (BBO) that can split a photon into a pair of lower energy photons with orthogonal linear polarisations, say x and y. These photons are entangled because by measuring the polarisation of one photon we know with certainty what the polarisation of the other is. A diagram of the experimental setup is included left. The photons are emitted slowly so that we can be sure there are only the two entangled photons passing through the apparatus at any one time, and can thus identify the pairs as they reach the detectors. Consider first the setup without the polariser in front of detector 2 or the quarter wave plates in front of the slits. The entangled photons each travel along separate paths, we shall call them p1 and p2, towards the detectors D1 and D2. The p1 photons pass through the double slit and form an interference pattern as is expected. Next we place the quarter wave plates in front of each slit. These plates will alter the polarisation of the light so that photons going through one slit will be circularly polarised in one direction and those going through the other slit will have the opposite polarisation. Not only this, but if our initial photon was linearly polarised in the other direction (say y instead of x) then it would emerge from the quarter wave-plates with the opposite circular polarisations to the first situation. So in order to determine which slit the photon has travelled through, we need to know the initial linear polarisation AND the final circular polarisation. We can determine the final circular polarisation of a photon at detector 1 and by measuring the polarisation of its entangled partner at detector 2 we can determine its initial linear polarisation. Both pieces of information are required to determine which slit the photon has travelled through.
Next we add the polariser in front of detector 2, oriented to admit light that is a combination of the two possible polarisations. It is now no longer possible to determine the initial polarisation of the p2 photons, and so determine the initial polarisation of the p1 photons. We now no longer have the two pieces of information required to determine which slit a path 1 photon has travelled through, and so the interference pattern re-emerges. We have done this without doing anything at all to the path 2 photons, and so demonstrated the entangled nature of the photon pairs.
To make it even stranger, we can move detector 2 backwards so that we detect photons at detector 1 first, and we remove the polariser. Now the photons hit the screen and the interference pattern has been destroyed, before their pair photon has even had a chance to pass through a polariser or not and hit detector 2. Somehow the photons ‘know’ that the polariser isn't there before we have even had a chance to find out which slit they had passed though. The mere possibility that we could know seems to destroy the pattern.
Even more strangely we could have the polariser in place while the p1 photons are hitting the screen and then take it away after they've formed their pattern, but before their entangled partners reach the polariser and detector 2, and we would find that there was no interference pattern. This is where it gets too strange for me to consider further, but the point is that spatial and temporal separations of the detectors theoretically have no impact on the result of the experiment, which is the truly amazing aspect of quantum entanglement."
References:
http://encyclopedia.thefreedictionary.com/measurement+problem
http://encyclopedia.thefreedictionary.com/quantum%20decoherence
http://www.qubit.org/library/intros/entang/index.html
http://www.joot.com/dave/writings/articles/entanglement/spookiness.shtml
http://en.wikipedia.org/wiki/Quantum_entanglement
http://grad.physics.sunysb.edu/~amarch/ (diagram)
http://en.wikipedia.org/wiki/Polarisation
The bell-state quantum eraser
This is an extract from my third quantum mechanics assignment for this semester, it talks about an experiment called "the bell-state quantum eraser" which demonstrates the phenomena of quantum entanglement, among other things. Quantum entanglement is fricken amazing, the entire reason I study physics is to learn about things like this and to try and understand the implications that have on reality. Reality is a tricky thing.
I'm not sure how much of it anyone will understand, but hopefully you'll get the general idea.
"...the concept of quantum entanglement. This refers to a phenomena whereby two or more quantum systems cannot be described without reference to each other, even though they may be spatially separated. This allows information about one system to be determined by making measurements on the others. A spectacular example of this is an experiment called the ‘bell-state quantum eraser’. In this experiment a beam of light is passed through a special type of crystal (BBO) that can split a photon into a pair of lower energy photons with orthogonal linear polarisations, say x and y. These photons are entangled because by measuring the polarisation of one photon we know with certainty what the polarisation of the other is. A diagram of the experimental setup is included left. The photons are emitted slowly so that we can be sure there are only the two entangled photons passing through the apparatus at any one time, and can thus identify the pairs as they reach the detectors. Consider first the setup without the polariser in front of detector 2 or the quarter wave plates in front of the slits. The entangled photons each travel along separate paths, we shall call them p1 and p2, towards the detectors D1 and D2. The p1 photons pass through the double slit and form an interference pattern as is expected. Next we place the quarter wave plates in front of each slit. These plates will alter the polarisation of the light so that photons going through one slit will be circularly polarised in one direction and those going through the other slit will have the opposite polarisation. Not only this, but if our initial photon was linearly polarised in the other direction (say y instead of x) then it would emerge from the quarter wave-plates with the opposite circular polarisations to the first situation. So in order to determine which slit the photon has travelled through, we need to know the initial linear polarisation AND the final circular polarisation. We can determine the final circular polarisation of a photon at detector 1 and by measuring the polarisation of its entangled partner at detector 2 we can determine its initial linear polarisation. Both pieces of information are required to determine which slit the photon has travelled through.
Next we add the polariser in front of detector 2, oriented to admit light that is a combination of the two possible polarisations. It is now no longer possible to determine the initial polarisation of the p2 photons, and so determine the initial polarisation of the p1 photons. We now no longer have the two pieces of information required to determine which slit a path 1 photon has travelled through, and so the interference pattern re-emerges. We have done this without doing anything at all to the path 2 photons, and so demonstrated the entangled nature of the photon pairs.
To make it even stranger, we can move detector 2 backwards so that we detect photons at detector 1 first, and we remove the polariser. Now the photons hit the screen and the interference pattern has been destroyed, before their pair photon has even had a chance to pass through a polariser or not and hit detector 2. Somehow the photons ‘know’ that the polariser isn't there before we have even had a chance to find out which slit they had passed though. The mere possibility that we could know seems to destroy the pattern.
Even more strangely we could have the polariser in place while the p1 photons are hitting the screen and then take it away after they've formed their pattern, but before their entangled partners reach the polariser and detector 2, and we would find that there was no interference pattern. This is where it gets too strange for me to consider further, but the point is that spatial and temporal separations of the detectors theoretically have no impact on the result of the experiment, which is the truly amazing aspect of quantum entanglement."
References:
http://encyclopedia.thefreedictionary.com/measurement+problem
http://encyclopedia.thefreedictionary.com/quantum%20decoherence
http://www.qubit.org/library/intros/entang/index.html
http://www.joot.com/dave/writings/articles/entanglement/spookiness.shtml
http://en.wikipedia.org/wiki/Quantum_entanglement
http://grad.physics.sunysb.edu/~amarch/ (diagram)
http://en.wikipedia.org/wiki/Polarisation
Monday, May 22, 2006
Weird
Wow, I actually don't have anything that has to be done right away at the moment. Sure, there's stuff I COULD be doing, but there's nothing won't get done if I don't do it now. Weird (considering that I'm at uni, I procrastinate plenty at home). Guess it's that time of semester. First exam will be friday next week, people don't really hand out assignments this late, and most of them were due last week. Only have two left to do. Unless I also have a math's one that I'm not aware of, which is possible. That would suck. I should find out about that soon though.
I've been playing a fair bit of 'super smash brothers melee' recently. It's a pretty cool game, there's something about the super smash brothers games that makes me enjoy them a lot more than other fighting games. There are many things that set it apart, but the main things I'd have to say that make it rock are the simplicity of the controls, the interesting terrain on which you fight and the items. Of course fighting with the cartoony nintendo characters is amusing too. Other fighting games you need to play frequently and for a fair while before you can actually remember enough of the combos and crap to be any good at them. Super smash brothers anyone can play right away, but it still has many subtleties, particularly with timing, that make a huge difference once you start getting more pro at it.
Anyway I think we shall have to have a super-smash bro's night sometime, perhaps with some halo 2 thrown in for good measure. It's been too long. Might have to wait till after exams, but that isn't too much of a wait.
Wow, I actually don't have anything that has to be done right away at the moment. Sure, there's stuff I COULD be doing, but there's nothing won't get done if I don't do it now. Weird (considering that I'm at uni, I procrastinate plenty at home). Guess it's that time of semester. First exam will be friday next week, people don't really hand out assignments this late, and most of them were due last week. Only have two left to do. Unless I also have a math's one that I'm not aware of, which is possible. That would suck. I should find out about that soon though.
I've been playing a fair bit of 'super smash brothers melee' recently. It's a pretty cool game, there's something about the super smash brothers games that makes me enjoy them a lot more than other fighting games. There are many things that set it apart, but the main things I'd have to say that make it rock are the simplicity of the controls, the interesting terrain on which you fight and the items. Of course fighting with the cartoony nintendo characters is amusing too. Other fighting games you need to play frequently and for a fair while before you can actually remember enough of the combos and crap to be any good at them. Super smash brothers anyone can play right away, but it still has many subtleties, particularly with timing, that make a huge difference once you start getting more pro at it.
Anyway I think we shall have to have a super-smash bro's night sometime, perhaps with some halo 2 thrown in for good measure. It's been too long. Might have to wait till after exams, but that isn't too much of a wait.
Friday, May 12, 2006
It's all happening again!
Well, I havn't done anything about those photos since that last blog post, been too busy with things like differential geometry and topology. Its been pretty crazy, and I don't have a whole lot of confidence in my answers to the assignment questions, but it's an interesting subject and I wish I understood it better. I'm thinking that I'll try and jam some more maths units into my course somehow, ones that deal with some of this stuff some more, maybe from a more basic level. There's one I have in mind for next semester, MTH3132 - Analysis and Geometry, looks pretty cool. I don't quite meet the prerequisites, but hopefully I can convince them to let me do it anyway since I''ll have done this special topic. The other thing is that I'll be overloading again if I do it, which isn't so much fun, but I can't really see another way to do these cool maths subjects without doing something drastic like dropping engineering, which I don't really want to do. It's starting to feel like year 12 again though, in which I did 7 3/4 sequences instead of the usual 5, maximum of 6. Your head asplode!
dx^dx = 0 apparantly (and thats a wedge, not a power symbol).
Oh yeah, the string ensemble with the orchestra is up and running now, so we rock out and play music every wednesday now which is pretty cool. Err, don't seem to have a lot else to say, havn't been doing a lot besides uni work, playing music and doing martial arts recently. I played a fair bit of super smash brothers melee last weekend though, that amused me. Also have been reading things on wikipedia like this. Went to see MI3 last week sometime, it was quite good. Managed to leave scotty behind due to certain communications difficulties. Movies to see that I can think of off the top of my head include The DaVinci Code and X-Men 3.
Gotta get around to putting up my whiteboard, it's been leaning against my bedroom wall for at least a month I'd say. I have a lot of things to write on it too, just gotta figure out how to mount it on the wall without wrecking the plaster or the paint too much.
Well, I havn't done anything about those photos since that last blog post, been too busy with things like differential geometry and topology. Its been pretty crazy, and I don't have a whole lot of confidence in my answers to the assignment questions, but it's an interesting subject and I wish I understood it better. I'm thinking that I'll try and jam some more maths units into my course somehow, ones that deal with some of this stuff some more, maybe from a more basic level. There's one I have in mind for next semester, MTH3132 - Analysis and Geometry, looks pretty cool. I don't quite meet the prerequisites, but hopefully I can convince them to let me do it anyway since I''ll have done this special topic. The other thing is that I'll be overloading again if I do it, which isn't so much fun, but I can't really see another way to do these cool maths subjects without doing something drastic like dropping engineering, which I don't really want to do. It's starting to feel like year 12 again though, in which I did 7 3/4 sequences instead of the usual 5, maximum of 6. Your head asplode!
dx^dx = 0 apparantly (and thats a wedge, not a power symbol).
Oh yeah, the string ensemble with the orchestra is up and running now, so we rock out and play music every wednesday now which is pretty cool. Err, don't seem to have a lot else to say, havn't been doing a lot besides uni work, playing music and doing martial arts recently. I played a fair bit of super smash brothers melee last weekend though, that amused me. Also have been reading things on wikipedia like this. Went to see MI3 last week sometime, it was quite good. Managed to leave scotty behind due to certain communications difficulties. Movies to see that I can think of off the top of my head include The DaVinci Code and X-Men 3.
Gotta get around to putting up my whiteboard, it's been leaning against my bedroom wall for at least a month I'd say. I have a lot of things to write on it too, just gotta figure out how to mount it on the wall without wrecking the plaster or the paint too much.
Monday, May 01, 2006
Photos
I've been thinking recently that I really do quite a lot of stuff, but due to my lack of a camera of any kind and my not entirely fantastic memory I tend to forget a whole bunch of it. Of coure I don't forget the main points, but there's a lot of little things that just get lost without things like photos to remind you of them.
However, I note that a reasonable amount of the cool things that I do are with the rest of you guys, so consequently you have a lot of the photos which I am going to need :p.
I thought of this a while ago and figured I'd just look at your ringo accounts or whatever whenever I was interested, but I should have realised that I'd never bother if it wasn't more convinient than that. So, I shall be beginning my project to collate all such photos into one place, so that I don't forget the little things.
I've been thinking recently that I really do quite a lot of stuff, but due to my lack of a camera of any kind and my not entirely fantastic memory I tend to forget a whole bunch of it. Of coure I don't forget the main points, but there's a lot of little things that just get lost without things like photos to remind you of them.
However, I note that a reasonable amount of the cool things that I do are with the rest of you guys, so consequently you have a lot of the photos which I am going to need :p.
I thought of this a while ago and figured I'd just look at your ringo accounts or whatever whenever I was interested, but I should have realised that I'd never bother if it wasn't more convinient than that. So, I shall be beginning my project to collate all such photos into one place, so that I don't forget the little things.
