Quantum Zeno effect for position measurement

[James MC]

Hello,

The quantum zeno effect is well understood and experimentally confirmed as regards polarization measurements (as discussed here). It's the quantum analogue of "the watched pot never boils" as it allows "continuous" measurement to inhibit certain state evolutions.

Does the effect (in principle) enable one to keep a particle confined to a particular spot simply via "continuous" position measurements?

Consider double slit experiment, we fire the electron towards the slits, but our goal is to prevent the electron from reaching the slits by continuously measuring the electron's position - is this in principle possible?

It seems that it is: "shooting" the electron out towards the slits suggests that position amplitude for electron rises (from zero) closer to the slit. So you can imagine that we measure position of electron just after it leaves the electron gun. High amp close to gun, low amp close to slits (at the "right after shooting" instant), so electron (at that instant) probably will collapse close to gun, far from slits. The quicker we make that measurement, the less chance we get collapse to region close to slits, far from gun. So now imagine that we make "continuous" position measurements of electron right as it leaves gun. In the limit there is no chance that the electron can move from point of measurement...

This seems quite odd (what happened to all that velocity??), but reasoning seems analogous to well-understood polarization case.

Would appreciate if someone could help enlighten me here. Thanks!

 

[mfb]

Does the effect (in principle) enable one to keep a particle confined to a particular spot simply via "continuous" position measurements?

I once read about an experiment doing this, but I am not sure if that was a real or just a theoretical experiment. As the position measurement is not like a polarizer (yes/no decision), you have to use a discrete lattice of allowed positions, and measure the position of the particle in this lattice so often that it cannot tunnel towards a different point between measurements.

Consider double slit experiment, we fire the electron towards the slits, but our goal is to prevent the electron from reaching the slits by continuously measuring the electron's position - is this in principle possible?

I don't think that will lead to anything like the quantum zeno effect.

It seems that it is: "shooting" the electron out towards the slits suggests that position amplitude for electron rises (from zero) closer to the slit.

No.

 

[James MC]

I once read about an experiment doing this, but I am not sure if that was a real or just a theoretical experiment. As the position measurement is not like a polarizer (yes/no decision), you have to use a discrete lattice of allowed positions, and measure the position of the particle in this lattice so often that it cannot tunnel towards a different point between measurements.

Yes, that is the idea. If you can recall it, I would be very interested to read about the experiment. I imagine it was a theoretical experiment. For even the polarizer case is merely theoretical. We can approach QZE by increasing number of polarization measurements, but we can never actually inhibit state evolution with 100% probability.

I don't think that will lead to anything like the quantum zeno effect.

But why do you say this? The measurement induced inhibition of state transition from being positioned within discrete lattice A to being positioned within discrete lattice B seems not in principle any different from measurement induced inhibition of state transition from being horizontal to being vertical. What is the difference?

Confused as to why you said no at the end. Isn't that just standard dynamics? Electron's wave function for position must evolve somehow, after we shoot the electron towards the slits.

 

[mfb]

But why do you say this?

I think your description of what should happen makes no sense. A double-slit experiment is not a two-state system.

If you measure the position of the particle all the time, you don't get interference, of course. But that is obvious - and you do not need continuous measurements, a measurement at the slits is sufficient.

 

[James MC]

I think your description of what should happen makes no sense. A double-slit experiment is not a two-state system.

If you measure the position of the particle all the time, you don't get interference, of course. But that is obvious - and you do not need continuous measurements, a measurement at the slits is sufficient.

No, you need to send many particles through the double slit set up to get an interference pattern on the back screen. Sending a single particle will only give you a single hit on the back screen.

My question is just whether continuous measurement of the one particle will prevent any result on the back screen.

As I've argued, reasoning in polarization case seems to straightforwardly pass over: firing an electron at the back screen will yield no result (with 100% certainty) if one continually measures the position of the particle.

This seems very odd to me. So I'm wondering if there's a problem in the argument. So far I don't see one. Maybe there's an issue with position measurements not being a matter of "this property" versus "that property" (two-state system). But I don't see what that issue could be.

 

[mfb]

No, you need to send many particles through the double slit set up to get an interference pattern on the back screen. Sending a single particle will only give you a single hit on the back screen.

Sure, but many single hits form an interference pattern.

My question is just whether continuous measurement of the one particle will prevent any result on the back screen.

It will not. You do not destroy the particle.

As I've argued, reasoning in polarization case seems to straightforwardly pass over: firing an electron at the back screen will yield no result (with 100% certainty) if one continually measures the position of the particle.

No, the electron does not vanish.

This seems very odd to me.

Good. It seems odd as it is wrong.

 

[James MC]

Sure, but many single hits form an interference pattern.

Yes but interference patterns are not relevant to the present theoretical experiment. All we need is a single particle, shot in the direction of a detection screen, such that the particle's wave function spreads as soon as it is shot from the particle gun.

We also need a mechanism for continuous measurement, to be applied before particle can reach detection screen. This requires a measurement device that would, if applied once (or a few times), allow the particle to still reach the screen. Continuous measurement is just the theoretical possibility of applying that measurement infinitely fast again and again. Here a thin conducting wire loop will do the job. As the electron passes through the loop, the current in the wire loop becomes correlated with the position of the electron. Electron still reaches screen. We can now imagine we have many, many conducting loops that the electron is shot through. Now we consider the (merely) theoretical possibility of an infinite number of wire-loop measurements applied at the same spot or region. This would continually collapse electron to that spot, so that it would never leave that spot to give a result on the back screen... unless you have an argument to the contrary.

It will not. You do not destroy the particle.

No, the electron does not vanish.

Of course the electron will neither vanish nor be destroyed: we can't continually measure the position of something that doesn't exist. The point is not that the electron vanishes, but that it never shows up on the detection screen if we are continuously measuring its position before it can get to that screen. If we stop collapsing its wave function then it will make it to the detection screen.

Good. It seems odd as it is wrong.

I want to see an argument for why it's wrong. To do this, you need to at least say what breaks the apparent symmetry between the polarization case, and the position case. At one point you said that polarization is a two-state measurement (vertical versus horizontal) whereas position measurement is more complex. But you never said why that would break the symmetry and prevent QZE for position.

 

[king vitamin]

Unless I'm confused, it sounds like you're simply confining the electron after it leaves the gun so that you know where it is, and since it's trapped it can't go anywhere (including the screen).

Here's a quantum Zeno experiment for the positions of atoms in an optical lattice (I think it's the first of it's type):
http://arxiv.org/abs/quant-ph/0104035

 

[mfb]

@James MC: "Infinite position measurements" with infinite precision do not work, not even in theory. You can add a trapping lattice to the electron track, of course, but then you do not have a "beam" any more even if you do not measure the position.

 

[strangerep]

The quantum zeno effect is well understood and experimentally confirmed [...]

Whenever I see papers claiming to have experimentally demonstrated QZE, I check the references to see whether this paper of Ballentine's is even mentioned:

L. E. Ballentine, "Comment on 'Quantum Zeno effect",
Phys. Rev. A., v43, no9, (1991), p5165.

In this paper, Ballentine refutes the claims in an earlier paper by Itano et al in which experimental confirmation of QZE by wave function collapse was claimed. He does this by a more careful analysis of the dynamics involved between system and apparatus. In reply to Ballentine's comment, Itano et al then seemed to step back from their previous claims.

The paper you linked to in the other thread neglects to reference the above, afaict, which makes me dubious about how thorough the author's literature searches have been.

Ballentine also provides a useful section about QZE in this textbook, well worth studying.

However... this point of view remains controversial. Here is an older thread where differing views were expressed. It also contains further references which I alluded to above.

https://www.physicsforums.com/showthread.php?t=546523