Mechanical Robot Fish

The Mixed-Up Thoughts of Michael Francis Booth

Attempting to Understand the Quantum Zeno Effect

Following a link from Brad Delong, who is mightily confused, I found a paraphrase of the new Nature paper on the so-called “Quantum Zeno Effect”:

The “Quantum Zeno Effect” takes its name from Zeno’s paradoxes, which argue that motion ought to be impossible, because to cover any given distance requires you to first move half the distance, then half the remaining distance, then half again, and so on ad infinitum. Each of those distances should require a finite time to move, and there are infinitely many steps, so you should never get anywhere. The paradox fails, of course, but in the quantum world, it can be made surprisingly real, thanks to the nature of quantum measurement. Consider the case of an atom placed into an excited state with a finite lifetime. After some period of time, say one second, there is a 50% probability that the atom has spontaneously decayed to the ground state. If you do a measurement that determines the state of the atom, you have a 50% chance of finding it in the excited state, and a 50% chance of finding it in the ground state. “Big deal,” you say, but here’s the key: after you make that measurement, the atom is 100% in whichever state you measured. A second measurement a short time later is guaranteed to find the same result as the first. So, imagine a different experiment– rather than waiting until the results are 50/50, make the measurement a much shorter time after the excitation– a tenth of a second, say. The probability that the atom has already decayed is really, really small– 0.002%– so you’re really likely to find it in the excited state, after which the atom is entirely in the excited state again, and the decay clock starts over. Then mesaure it again, and again, and again, waiting a tenth of a second each time. After ten measurements, you’re one second past the original excitation, and the probability of finding the particle in the excited state is almost 100% (99.98%, give or take). If you keep making measurements at short intervals, you can keep the atom in the excited state basically forever. The cool thing is, you can do this sort of thing with passive measurements. You don’t have to bounce a photon off the atom to prove that it’s in the excited state– instead, you can send in a photon that will only be absorbed by a ground-state atom, and see what happens. If it isn’t absorbed (and it most likely won’t be), that’s just as effective at keeping the atom in the excited state as if you’d done something more active to detect the excited-state atom.

In reponse to an interesting but flawed thought experiment in the comments, I was compelled to indulge in some good old physics-grad-student handwaving:

The Quantum Zeno Effect is different. The excited atom is not merely being “watched” – it is being probed with photons, which come close enough to interact with it. (If they didn’t, they wouldn’t tell us anything or have any effect whatsoever.) Then those photons periodically interact with the rest of the universe – well, with the detector and the experimenter, anyway, but the difference is moot: a few extra zeros at the end of an inconceivably large number. Such an experiment can no longer be approximated as “a scientist watches an atom, waiting for decay”; it’s now “a scientist periodically observes a system, which consists of an atom and a bunch of interacting photons, and looks for decay”. To put this more poetically: the experimenter is not watching the atom from several feet away; rather, he or she is constantly touching the atom with a beam of photons and feeling for the moment when it decays. This is a profoundly nifty experiment, because as you gradually add more and more significant interactions between the atom and a much larger system (the photons, and through them, the rest of the universe), you begin to see the gradual emergence of classical behavior. Classical mechanics is what quantum mechanics looks like when there are so many interacting particles that all the really weird states (e.g. the states in which the cat is in a superposition of the meowing-state and the sleeping-state) are so statistically unlikely that they are never seen; all we ever see is a superposition of the uncountably-vast number of really boring, essentially indistinguishable states in which the cat is only doing one thing at a time, obeying Newton’s laws like a good little citizen. According to classical mechanics, excited atoms shouldn’t ever emit a photon: to do so would require a miraculous “quantum leap”. Because the Quantum Zeno experiment is not 100% efficient (see above) we can’t reach such a pseudo-classical situation, in which the excited state would last forever. But we can get a lot closer.

I think there’s a decent chance that I have this right, but I’m not putting money on it. I may have to break down and actually read the Nature paper…