Freezing Coherent Field Growth in a Cavity by the Quantum Zeno Effect

ResearchBlogging.orgWhen 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. Deléglise, 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

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I second that "...well?"

Don't tease us readers like that! I need to geek out my coworkers, daggum it! :)

By G Barnett (not verified) on 19 Dec 2008 #permalink

A physicist and a mathematician (both male, because it's an old sexist joke) both answer an ad for a psychology study. The mathematician is called in firast, and showed into a room containing a bed with a gorgeous naked woman on it. He's told to sit in a chair on the wall opposite the bed.

The experimenters tell him that he's going to sit in the chair, and every five minutes, the chair will move forward through half of the remaining distance to the bed. When he reaches the bed, he can do whatever he wants with the woman in the bed.

"What!?!" he says, indignantly. "I'll never get there-- what kind of sick joke is this?" He storms out angrily.

Then the bring the physicist in. They sit him down in the chair, and explain the experiment to him. He reacts basically like a wolf in a Warner Brothers cartoon-- eyes bugging out, tongue lolling, steam from the ears, etc.

The psychologists running the experiment are surprised by the intensity of the reaction. "Don't you realize that you'll never make it all the way to the bed?" they ask.

"Sure," he says, "but I'll get close enough for all practical purposes." order to get out of bed on a Monday morning, I have to get halfway up first, then halfway more up then halfway more...
No wonder I'm late for work.

But now I have the perfect excuse! "Sorry, boss, it's that old Quantum Zeno effect, I'm sure you'll understand!"

Just for the record, here's a link to Sean's delightful old explanation of quantum interrogation with puppies! (Which for obvious reasons I always mistakenly remember as having been written by you and Emmy.)

What always bothered me about Zeno's Paradox was that philosophers seem to assume, for no good reason, that A) an infinite number of tasks cannot be done, regardless of the time required for each task, and B) that going half a given distance takes as long as going the full distance.

Clearly, neither of this things are the case.

The default confusion here is between:
(1) the [Classical? Ancient?] Zeno's Paradox [actually, Zeno gives several paradoxes about motion, about which Peter Lynds in New Zealand drew controversy in 2003 with the publication of a physics paper about time, mechanics and Zeno's paradoxes]
(2) the Quantum Zeno Paradox.

To quote from [ now-vanished page, whose cached version I used]:

"... the quantum Zeno paradox [is] an odd mathematical result that is being debated to this day. Assuming an unstable quantum state, intuition would dictate that eventually, the system will irreversibly decay in certain amount of time, defined as the Zeno time. However if the system is measured in a period shorter than the Zeno time, then the wave function of the system will repeatedly collapse before decay. In effect, constant measurements of the system will actually prevent its collapse! Even more mysterious, if the time interval between measurements is longer than the Zeno time, the decay rate of the system will increase, leading to what is termed the anti-Zeno effect."

More formally, to cite:

Phys. Rev. A 41, 2295 - 2300 (1990)
Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland
Time and Frequency Division, National Institute of Standards Technology, Boulder, Colorado 80303

Received 12 October 1989

"The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two 9Be+ ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations."


Phys. Rev. Lett. 87, 040402 (2001) [4 pages]
Observation of the Quantum Zeno and Anti-Zeno Effects in an Unstable System

M. C. Fischer, B. Gutiérrez-Medina, and M. G. Raizen
Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1081

Received 30 March 2001; published 10 July 2001

"We report the first observation of the quantum Zeno and anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong nonexponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of nonexponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system."

Now that readers have refreshed their memories of this, the posting by Chad is crystal clear.

you can use the renormalization group to solve zeno's paradox.

say you need to cross a room with length scale L. you rescale the problem to length scale L'=2L.

now in the renormalized statement of zeon's paradox if you need to cross a room of length L', you first need to go 1/2L'.

since 1/2L'=L, this means you have just crossed the room, avoiding the paradox.

I think this is closely related to quantum tunneling where they can push photons faster than the speed of light by decreasing the distance between two plates to molecular distances.