How to Teach Physics to Your Dog (15 page)

The quantum Zeno effect uses the active nature of quantum measurement to prevent a quantum object (like an atom) from
moving from one state to another, by making repeated measurements. If we measure the atom a very short time after the transition starts, it will most likely be found in the initial state. The act of measuring the atom projects it back into the initial state, as we saw in
chapter 3
, and the transition starts over.

If we keep measuring the state of the atom, we keep putting it back where it started. The atom is in a predicament reminiscent of Zeno’s paradox—taking an infinite number of steps toward some goal, but never getting there.
*
As the old saying has it, a watched pot never boils, at least as long as it’s a quantum pot.

This is dramatically different from classical physics. Measuring the state of a classical object does not change the state—if a pot of water is 50% of the way to boiling when the measurement is made, it’s still 50% of the way to boiling after the measurement. The quantum Zeno effect works only because of the active nature of quantum measurement—the water in a quantum pot is either boiling or not boiling. If you find that it isn’t boiling, you need to start over, as if you had never heated it.

The definitive quantum Zeno effect experiment was done in 1990 by Wayne Itano in Dave Wineland’s group at NIST in Colorado, using beryllium ions. Ions are just atoms with one electron removed, and like all atoms, they have a collection of allowed energy states, which they move between by absorbing or emitting light. Itano’s experiment collected a few thousand beryllium ions, and made them move slowly from one state to another by exposing them to microwaves.

Left unmeasured, the ions took 256 milliseconds to complete the transition from State 1 to State 2.
^†
Their state during this
process was described by a wavefunction with two parts, corresponding to the probability of finding the atom in State 1 and State 2. At the start of the experiment, the atoms were 100% in State 1, and at the end, they were 100% in State 2. In between, the probability of State 2 steadily increased, while the probability of State 1 steadily decreased.

The experimenters measured the state of the ions using an ultraviolet laser with its frequency chosen so that an ion in State 1 would happily absorb light, while ions in State 2 would not absorb any light. Ions in State 1 absorbed photons from the laser and re-emitted them a few nanoseconds later, making a bright spot on a camera pointed at the ions. Ions in State 2, on the other hand, produced no light when illuminated by the laser. The total amount of light reaching the camera, then, was a direct measurement of the number of ions in State 1.

To demonstrate the quantum Zeno effect, the NIST group trapped a large number of ions, all in State 1. Then they turned on the microwaves, waited 256 milliseconds, and pulsed on the laser. None of the ions produced any light, indicating that 100% of the sample had moved to State 2, as expected. Then they repeated the experiment, with two laser pulses: one after 128 ms (halfway through the move to State 2), and one after 256 ms. In this case, they saw half as much light after 256 ms, indicating that only 50% of the sample had made the transition to State 2.

The decreased probability is explained by the quantum Zeno effect. The laser pulse halfway through measured the state of the ions. Many of them were found in State 1, and the measurement destroyed the State 2 part of the wavefunction. These atoms were now 100% in State 1, so the transition had to start over, with the probability of State 2 increasing slowly. After another 128 ms, the probability of finding the ions in State 2 was only 50%.

The probability of moving from State 1 to State 2 decreased further with more measurements. With four pulses (at 64, 128, 192, and 256 ms), only 35% of the atoms made the transition.

With eight pulses, only 19% made the transition. With a total of 64 laser pulses over the full experimental interval (one every 4 ms), fewer than 1% of the atoms made the transition. All of these probabilities were in excellent agreement with the theoretical predictions of the quantum Zeno effect, as shown in the figure below.

“So, when you make a measurement, the ion absorbs a photon, and that collapses the wavefunction?”

“Actually, the ion doesn’t need to absorb a photon at all. The Wineland group repeated the experiment starting with the ion in State 2. In that case, the ion starts out in the ‘dark’ state, and doesn’t absorb any photons during the measurements. They still got the same result—the probability of making the transition from State 2 to State 1 decreased with more measurements, exactly as predicted.”

The probability of making a transition from one state to another in the quantum Zeno effect experiment done by the Wineland group (W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland,
Phys. Rev.
A 41, 2295–2300 [1990], modified and reprinted with permission). Black bars are the theoretical prediction, gray bars are the experimental result, with error bars showing the experimental uncertainty. The probability of changing states decreases as the number of measurements increases, whether the ions start in State 1 or State 2.

“Wait, not absorbing a photon is the same as absorbing a photon?”

“When it comes to thinking of the photons as measurement tools, yes. It’s just like the treat in two boxes—if you open one of the boxes, and find it empty, you know the treat has to be in the other box. That determines the state of the treat just as if you opened the box and found a treat there.”

“It’s not as much fun, though, because I don’t get the treat.”

“Yes, well, your life is very difficult.”

The quantum Zeno effect does not depend on a particular interpretation of quantum mechanics. It’s easier to discuss what’s going on using the Copenhagen language of wavefunction collapse, but we can equally well describe it in terms of the many-worlds interpretation. In the many-worlds picture, new branches of the wavefunction appear at each measurement step, but we are more likely to perceive the higher probability branch. The probability of seeing a state change is the same in both interpretations.

We can use the quantum Zeno effect to dramatically reduce the chance of a system changing states, simply by measuring it many times. We can never make the probability of transition exactly zero—there’s always a small chance that it will change in spite of the measurements—but we can make it very small, demonstrating the power of quantum measurement.

“Humans are so silly. If you want to stop the transition, wouldn’t it be easier to just turn off the microwaves?”

“Well, sure, but the point is to demonstrate that the quantum Zeno effect is real. It’s not interesting because it can stop ions from changing states; it’s interesting because of what it tells us about quantum physics.”

“Yeah, but what good is it? Can it do anything useful?”

“Well, you can use it to detect objects without having them absorb any light.”

“Objects . . . like bunnies?”

“Sure, hypothetically.”

“Oooh! I like the sound of that!”

The quantum Zeno effect can be exploited to do some amazing things. A collaboration between the University of Innsbruck and Los Alamos National Laboratory has demonstrated that it’s possible to use light to detect the presence of an absorbing object
without having it absorb any photons,
by using the quantum Zeno effect to stop a photon moving from one place to another.

We start with a photon on the left-hand side of the apparatus, bouncing back and forth between two mirrors. There is a small chance of the photon leaking through the central mirror, so over time the photon will shift into the right-hand side of the apparatus. If there is an absorbing object (a bunny, say) on the right-hand side, though, it will prevent the photon from moving, through the quantum Zeno effect.

In the future, this technique may be used to study the properties of quantum systems that are too fragile to survive absorbing even a single photon.

Here’s a simplified version of this quantum interrogation experiment: imagine that we have a single photon bouncing back and forth between two perfect mirrors. Halfway between those two, we insert a third mirror that’s not quite perfect.

The wavefunction for this system has two pieces, one corresponding to finding the photon in the left half of the apparatus, and the other corresponding to finding the photon in the right half. If we start the experiment with a single photon in the left half, we find that over time, it will slowly move into the right half. Each time the photon hits the imperfect central mirror, there’s a small chance that it goes through, so the left-side piece of the wavefunction gets a little smaller, and the right-side piece gets bigger. Eventually, the left-side piece is reduced to zero, and there is a 100% chance of finding the photon on the right side. Then the process reverses itself. The photon will slowly “slosh” back and forth between the two sides of the apparatus, just as the ions in the NIST experiment moved between State 1 and State 2.

We can trigger the quantum Zeno effect by adding a device to measure the position of the photon, such as a bunny in the right half of the apparatus. Each time the photon hits the central mirror, the bunny measures whether the photon passed through the mirror: being very skittish, the bunny will run away if it detects even a single photon on the right side.

The “sloshing” that happens in the no-bunny case is blocked by the quantum Zeno effect when the bunny is present. If the photon does pass through the mirror, the bunny absorbs it and flees. The photon no longer exists, so its wavefunction is zero, and nothing changes after that. If it doesn’t make it through, the photon is definitely on the left-hand side, and the wavefunction is put back in the initial photon-on-the-left state, and everything starts over.

The quantum Zeno effect lets us do what any dog wants to: determine whether there’s a bunny in the apparatus without scaring it off. We start with a photon on the left side, wait long enough for it to move over to the right side, and then look at the left side of the apparatus. If there’s no photon there, there’s no bunny on the right, either because the bunny absorbed the photon and ran off, or because there never was a bunny and the photon has “sloshed” over to the right. If the photon is still in the left-hand side of the apparatus, we know that not only was there a bunny, but it is still there, and has not absorbed even a single photon of light.

There is always a chance that the photon will make it through and scare the bunny away, but we can make this chance as low as we like, by decreasing the probability that the photon will leak through the mirror. We’ll have to wait longer to complete the measurement, as the time required for the photon to “slosh” into the right side will increase, but the chances of successfully detecting the bunny improve dramatically. If the photon needs to bounce back and forth on the left-hand side 100 times before it “sloshes” to the right, the probability of detecting a bunny
without scaring it off
is 98.8%. If you repeated the experiment 1,000 times, only 12 bunnies would be scared off.

“Oooh! So, all I need to do is get some big mirrors . . .”

“No. You are not setting this experiment up in the backyard.”

“But I can use the quantum Zeno effect to sneak up on the bunnies . . .”

“No. Just . . . No. You are not putting great big mirrors across the yard, and that’s final.”

“Awww . . .”

Quantum interrogation hasn’t been used to catch bunnies, but it has been demonstrated experimentally using polarized photons, by physicists in Innsbruck, Los Alamos, and Illinois.
Quantum interrogation allows you to do some incredible things—taking pictures of objects without ever bouncing light off them, for example. This probably isn’t useful for spy purposes (unless you can somehow get your enemies to obligingly store their secrets between two mirrors), but it might be essential for probing fragile quantum systems like large collections of atoms in superposition states that can’t survive the absorption of a photon.