Slow Light and Quantum Interference

If you’ve ever dabbled in learning about theoretical physics, as I have, you will enjoy an excellent book by Brian Greene called The Fabric of the Cosmos. It’s the first book that has explained how time and space are related by Einstein’s theory of general relativity in such a way that I now feel that I actually understand the concept. It’s quite amazing, and I’m pretty sure that if I could properly follow the math, it’d be even more amazing. There’s something that I still can’t wrap my mind around though: the particle/wave duality of things.

Double-slit experiment results. Image by Patrick Edwin Moran

Double-slit experiment results. Image by Patrick Edwin Moran

You’re probably familiar with the famous double-slit experiment that demonstrates the wave nature of quantum particles. The weirdest part about this is that if you set up the experiement so that only a single particle (or quantum) is emitted at a time, it somehow manages to pass through both slits and interfere with itself.

There’s more. Lots more. Waaay too much for me to cover. But the thing that I really just don’t get is why does this happen? As far as I can work out, no one else knows, either. It’s a central mystery of the universe, though there’s been a bunch of progress lately with M-theory.

I feel like I nearly get it though, which is why it’s so frustrating. It’s like I’m missing something really obvious here. If you can explain it, I’d love to hear from you. If you can explain it without me needing to dig out Shrödinger’s equation, so much the better.

Time Travel?

Greene describes a more complicated experiment called a delayed-choice quantum eraser, which is designed to test, among other things, the Heisenberg uncertainty principle. Briefly put, the Heisenberg uncertainty principle states that you can’t know both the position and velocity of a particle (for fields/waves, you can’t know both the value of the field at a given point and its rate of change).

It’s related to the double-slit experiment, because if you introduce a detector after the two slits that lets you know which slit the particle went through (known as which-path information), the interference pattern disappears. Knowing where the particle was disrupts the experiment. A quantum-eraser is a device that erases this knowledge. If you put a quantum-eraser into the experiment after the detector, you lose the information you gathered, and the interference pattern re-appears. Which is bizarre.

In the complex delayed-choice experiment described in the book, you can set up a kind of maze for photons after the choice has been made so that the erasure doesn’t happen until after the choice of which path to take has already been made. The distance between the choice-point and the detection/erasure point can be arbitrarily large; light years, even. Which means that the detection part that would cause the interference pattern to appear or disappear wouldn’t happen until years after the original measurements were made.

So if you were able to somehow send the which-path measurements to the remote detectors, you’d be able to predict the future, but only if you could send that information faster than the speed of light. Which is impossible. Or is it?

Various researchers have recently managed to slow light down. In 2004, using a semi-conductor of some kind, researchers at UC Berkeley got it down as slow as 9.7 km/s.

This made me wonder: what if you could use one of these slow-light things as part of the delayed-choice experiment? What if, instead of a light-second meaning the remote detectors had to be thousands of kilometers away, they could be only 9.7 kilometres away? That’s starting to get into the realm of the feasible. With equipment that could measure faster, maybe you’d only need 1/2 second of distance, or 1/4 second? Now we’re only talking about a distance of a couple of kilometres. The LIGO gravity-wave detector has tubes 4 kilometres long.

Would you then be able to detect the photons at one end, and, using ordinary fibre-optics with light travelling at full-speed for communication, tell the remote end (a mere 2 km away) what had happened before the idler-photons arrived, thus predicting what they would do? What would this do to the interference patterns?

My guess is that this isn’t possible because the materials used for slowing the light down would interact with the photons themselves, thus rendering the experiment invalid.

Still, it was a neat idea. :)

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