Wednesday, May 17, 2006

Quantum awesomeness part deux

So I've been preparing for exams this week, but I promised a second half to the quantum mechanics post, and a second half you shall have. When we last saw our intrepid photons, they were allowing us to "see" an obstruction 25% of the time, by coming out the dark port instead of the light port. Fifty percent of the time, however, they blew everything up. Suffice to say, these are not ideal odds. Can we find some way to improve them?

Here's where the quantum Zeno effect comes in. As you might guess, this is named after the Greek philosopher who was constantly making arrows get stuck in flight, keeping Achilles from overtaking the tortoise, and in various other ways ascertaining that it's not possible for anything to get anywhere. As you know if you took any sort of pre-Socratic philosophy course, Zeno is hard to refute logically; it's difficult to argue against the idea that an arrow in flight isn't going anywhere because at each individual instant it's stationary, or that in order to get from point A to point B, you have to cover half the distance, then half the remaining distance, then half the remaining distance, ad infinitum. The best way to refute it, in fact, is simply to point out that this isn't what happens. But with quantum particles, this kind of logic holds much more sway -- remeber, if it's logically necessary that a particle be doing something, it does it.

So in order to make a photon bend to your will, all you need is to make it logically necessary that it be doing what you want it to do. How to do that? Well, first it's important to establish that light can be either horizontally polarized or vertically polarized (the light waves oscillate either side-to-side or up-and-down). You can set up your photon detector (like D-light and D-dark in the earlier experiment) behind a horizontal or vertical polarizer, which will transmit similarly polarized light but absorb perpendicular light. Thus, if you shoot a horizontally polarized photon at a detector, you'll detect it, but if you interpolate a vertical polarizer, it'll be absorbed (vertical polarizers transmit vertical light and absorb horizontal light) and you won't see it at all.

Now imagine that before the detector, you place something that rotates the polarization of light 90 degrees (see image, once again ganked from this SciAm reprint). Now, when the photon gets to the detector, it's vertically polarized, it doesn't get absorbed, and you can detect it again. Replace the vertical polarizer with a horizontal polarizer, and the photon disappears again -- it starts out horizontally polarized, but by the time it reaches the end it's been rotated to vertical, and the horizontal polarizer absorbs it. So far so good. Now suppose that instead of one rotator that rotates the polarization 90 degrees, you have six rotators that do 15 degrees each. Same end effect -- a horizontally polarized photon will be vertically polarized by the time it reaches the polarizer, and it will get absorbed.

Here's where it gets awesome. In between each of the six rotators, we put another horizontal polarizer. When the photon goes through the first rotator, it's only rotated 15 degrees, so it's still pretty horizontal; this means that it has a low chance of being absorbed by the first polarizer. A 6.7% chance, in fact -- SciAm says it's determined by the square of the sine of the rotating angle, and who am I to argue? The important thing here is that the chance is small, and as the angle gets smaller, the chance of absorption decreases too. Accordingly, it has a 94.3% chance of passing through the polarizer -- and if it passes through, it must be horizontally polarized, because horizontal polarizers only transmit horizontally polarized light. When the photon goes through the next rotator, then, it is again only rotated 15 degrees off of horizontal. This means that if the photon makes it through all six rotators and all six polarizers, it is still horizontally polarized -- even though it's gone through 90 degrees worth of rotation. There's only a two-thirds chance of this occurring, because each polarizer represents some small chance of absorption, but as we increase the number of rotators and polarizers, that chance goes up (because the rotation angle, and thus the chance of absorption, goes down).

So what happens when we integrate this experiment with the earlier one, where we were detecting obstructions? Well, imagine that instead of sending photons through a regular beam splitter, you send them through a polarizing beam splitter -- it transmits horizontally polarized light and reflects vertically polarized light. When the photon is released, it first goes through a rotator, then into the beam splitter; the beam splitter sends horizontally polarized light one way and vertically polarized light the other way, then they both bounce off mirrors, recombine at the beam splitter, and go on. It's pretty much like the setup we saw in the last post. If you keep the photon in the system for several cycles, though -- six cycles if it's a 15 degree rotator, for instance, or 12 if it's a 7.5 degree rotator -- then you'll end up with a photon of the opposite polarization. It's exactly like sending it through six (or twelve) rotators in a row. As with the other "seeing in the dark" experiment, you don't have to know or care whether the photon got sent down the vertical path or the horizontal path or a little bit of each. The likelihood is that it probably did both -- doesn't matter, though. What matters is that you put one horizontally polarized photon in and get one vertically polarized photon out.

What happens, though, if there's an obstruction in the vertical-polarization path path? Well, it's almost exactly like interleaving the polarizers with the rotators. Horizontally polarized photon enters, gets rotated 15 degrees (say), and hits the polarizing beam splitter. It has a 6.7% chance of the beam splitter considering it to be vertical and reflecting it, just as it previously had a 6.7% chance of the polarizer considering it to be vertical and absorbing it. If the photon is reflected, it'll hit the obstruction and be absorbed (or exploded, depending on how demonstrative you want to get). If not, it will be transmitted, going on the horizontal-polarization path -- but if it does this, it must be horizontal, because only horizontally polarized light would be transmitted instead of reflected. So you get a quantum Zeno effect: the photon, despite being repeatedly rotated, either gets absorbed or remains horizontally polarized. And there's only a 6.7% chance of the former each time, and less if the angles are smaller and the cycles more frequent.

After the requisite number of cycles, you let the photon out and check under its tail. If it's vertically polarized, there's no obstruction, because there was no Zeno effect; the photon got rotated a total of 90 degrees, and its polarization is a total of 90 degrees off from what it was before. If it's still horizontally polarized, though, it was still rotated a total of 90 degrees, but its polarization is exactly what it was before -- Zeno effect. This means there must be an obstruction, since you only get this effect when there's a chance of the photon not making it through. The photon you're detecting never touched the obstruction, or you wouldn't be detecting it (it would be absorbed/exploded). But the obstruction must be there, or the polarization would have changed. So again, you can "see" something that no light has ever touched, but this time you can get your effectiveness damn close to 100% just by decreasing the angle of rotation and increasing the number of times that the photon cycles. With every decrease, there's a higher chance that the photon makes it through even when there's an obstruction -- but if it makes it through without changing polarization, the obstruction must be there.

So what's so awesome about all this? Well, the implications of being able to see something without light touching it are pretty amazing... you could develop, for instance, less invasive internal photography. Practical applications are pretty remote at this point, of course, but think about the philosophical ones -- it's hard to get your head around how quantum particles work, even with a totally surface-level layperson's explanation like the one I've given, and according to a large percentage of Real Quantum Physicists my description is probably 90 degrees rotated from reality. But dude, we can see something without light touching it. That is, not to put too fine a point on it, pretty rad.

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