When I saw ZapperZ’s post about this paper (arxiv version, expensive journal version) from the group of Serge Haroche in Paris, I thought it might be something I would need to incorporate into Chapter 5 of the book-in-progress. Happily, it’s much too technical to require extensive re-writing. Having taken the time to read it, though, I might as well make a ResearchBlogging post of it… (My comments will be based on the arxiv version, because it’s freely downloadable.)
So, “Freezing Coherent Field Growth in a Cavity by the Quantum Zeno Effect.” That’s quite a mouthful. What does it really mean? It means that they’ve used quantum measurement to prevent photons from collecting in the space between two highly reflective mirrors, even as they pump more photons in.
The Quantum Zeno Effect is named in analogy with Zeno’s Paradoxes, which purport to show that motion is impossible. The most famous version is a proof that it takes an infinite amount of time to cross a room, because you first need to go half of the distance across the room, and then half the remaining distance, then half of the remaining remaining distance, and so on. This is much more troubling to philosophers and mathematicians than physicists, leading to a very slightly off-color joke.
The quantum version of Zeno’s paradox is the Quantum Zeno Effect, which uses the active nature of measurement to prevent a quantum system from changing states. A more colorful name for it is the “watched pot effect,” which does a slightly better job of capturing what’s going on: you have a system that is moving from one state to another, but you stop that state change by repeatedly measuring the state. Each time you make a measurement, there’s a very high probability of finding the system in the initial state, and when you do that, the whole process has to start over. A watched pot will never boil, provided it’s a quantum pot, because each time you find it in the not-boiling state, the boiling process starts over as if you had never heated it at all.
The “pot” in this experiment is a microwave cavity consisting of two niobium mirrors positioned facing one another. They use a pulsed microwave source to shoot a few photons at a time into the cavity, and once the photons are there, they bounce back and forth between the mirrors for better than a tenth of a second (the lifetime is 0.13 s). That may not seem like a lot, but it’s an awful lot of bounces before the photon leaks out through one of the mirrors.
In a preliminary experiment, they looked at the build-up of photons in the cavity as they repeatedly pulsed on the microwave source. The result showed a steady build-up of photons, as shown in the red dots of the figure below (Figure 3 of the paper):
To invoke the Quantum Zeno Effect, they measured the number of microwave photons in the cavity in between each of the microwave pulses. Of course, to do that, they needed a way to know how many photons they had in the cavity, which they did using rubidium atoms prepared in a highly excited (“Rydberg”) energy level.
Their measurement scheme was pretty ingenious. To do a real Quantum Zeno Effect measurement, they needed a way to know how many photons were in the cavity without absorbing any of them, which would change the number for non-quantum reasons. They managed this by basically putting the experimental cavity in the middle of an atomic clock.
The rubidium atoms were directed into a beam that passed through the middle of the experimental cavity. Right before they got there, though, they were excited into a superposition of two energy states. This superposition state undergoes a periodic oscillation with some phase, and if you repeat the excitation procedure a little while later, and then look at the state of the atoms, you’ll see different results depending on how much time has elapsed. If you catch the atoms at just the right time in the oscillation, they’ll all end up excited to the higher-energy state of the two, and if you catch them at just the wrong time, they’ll all be put back in the lower energy state. This is essentially Ramsey interferometry, which is the basis for modern atomic clocks.
You can also change the result by sticking something in the middle that changes the phase of the oscillation, like, for instance, a microwave cavity with some number of photons in it. The atoms don’t absorb any of the photons (if you choose the frequency and states correctly), but they do interact with the photons, and that interaction causes a measurable shift in the oscillation.
In the experiment presented here, they arranged it so that they could distinguish between states of up to eight photons, based on the shift in the oscillation of the atoms. Figure 2 of the paper demonstrates this ability to tell apart the various photon states, and determine exactly how many photons were in the cavity at any given time.
For the Quantum Zeno experiment, then, they set up their source and cavity, and repeatedly pulsed on the microwave source. Between pulses, they sent atoms through the cavity, and measured the number of photons. This measurement, according to quantum mechanics, projects the cavity into one of the possible photon number states (0, 1, 2, 3, 4, 5, 6, 7, or 8 photons in the cavity), with 0 being the most likely outcome. The process of injecting photons into the cavity then has to start over, whereupon the next measurement sets it back to 0 again, and so on.
By repeating the measurements over and over, they were able to dramatically inhibit the buildup of photons in the cavity. Without measurements, they had 2 photons in the cavity after 50 pulses. With measurements, that number dropped to just over 0.1 photons (meaning, very roughly, that one time in ten they measured one photon in the cavity). The results with measurements between pulses are shown as the blue points in the figure above. The experimental results agree very nicely with a theoretical model of the process, shown by the lines in the lower figure. (The dashed line is a very simple idealized model, the solid line is a more sophisticated simulation of the experiment.)
This isn’t actually good for anything, but it’s a neat demonstration of the weirdness of quantum mechanics. It’s another demonstration of the weird role played by measurement in quantum mechanics.
(Incidentally, the fact that this post mentions quantum measurement is not license to start posting tendentious comments about decoherence. Those go in their allotted thread— any attempts to resume the argument here will be summarily deleted.)
J. Bernu, S. DelÃ©glise, C. Sayrin, S. Kuhr, I. Dotsenko, M. Brune, J. M. Raimond, S. Haroche (2008). Freezing Coherent Field Growth in a Cavity by the Quantum Zeno Effect Physical Review Letters, 101 (18) DOI: 10.1103/PhysRevLett.101.180402