Quantum tunnelling - what is real?

[Jilang]

Is it correct that that the wavefunction of a particle is well defined in the classically forbidden region? This would seem to suggest that there would be a chance of finding it there. But I think that is not allowed. Have any experiments actually discovered particles in the barrier or do they just find them coming out the other side?

 

[tom.stoer]

Is it correct that that the wavefunction of a particle is well defined in the classically forbidden region?

Yes

This would seem to suggest that there would be a chance of finding it there.

In principle - yes

But I think that is not allowed.

Why?

Have any experiments actually discovered particles in the barrier or do they just find them coming out the other side?

I think this is impossible practically b/c the barrier is too small to contain a measuring device. Look at the applications section in http://en.wikipedia.org/wiki/Quantum_tunnelling

 

[Jilang]

Thanks Tom, I didn't think it was allowed as it is classically forbidden so even if there was a method of detecting it, it would not be possible. Are there any quantum barriers that would be sufficiently large to allow detection or are they all really tiny?

 

[ZapperZ]

Is it correct that that the wavefunction of a particle is well defined in the classically forbidden region? This would seem to suggest that there would be a chance of finding it there. But I think that is not allowed. Have any experiments actually discovered particles in the barrier or do they just find them coming out the other side?

What if I put, say, atoms in with magnetic moment in the barrier itself when electrons are tunneling across it. And what if these electrons came from the superconducting supercurrent?

Such an experiment has been done way back in the 70s and 80s, and showed that the presence of such magnetic moments can increase the inelastic scattering of these electrons as they tunnel through the barrier[1].

Look, quantum tunneling may sound "weird" or "unfamiliar". However, please be aware that we know it so well, its validity is no longer questioned, so much so that we are using it in the study of other things (STM, tunnel diodes, etc.. etc.).

Zz.

[1] J.R. Kirtley and D.J. Scalapino, Phys. Rev. Lett. v.65, p.798 (1990).

 

[tom.stoer]

I think what is questioned is not the effect, but the mathematics regarding a non-vanishing wave function inside the barrier. Of course this sounds natural mathematically I is a valid question to ask for an experiment to measure this non-vanishing probability inside the barrier. Unfortunately all effects I am aware of are not able to look into the barrier.

 

[Jilang]

What if I put, say, atoms in with magnetic moment in the barrier itself when electrons are tunneling across it. And what if these electrons came from the superconducting supercurrent?

Such an experiment has been done way back in the 70s and 80s, and showed that the presence of such magnetic moments can increase the inelastic scattering of these electrons as they tunnel through the barrier.

Look, quantum tunneling may sound "weird" or "unfamiliar". However, please be aware that we know it so well, its validity is no longer questioned, so much so that we are using it in the study of other things (STM, tunnel diodes, etc.. etc.).

Zz.

Thanks Zz I don't find the idea of tunnelling weird, just the idea of being able to detect them inside the barrier. Has this actually been possible? I just don't know and have been unable to find this out so far.

 

[ZapperZ]

I think what is questioned is not the effect, but the mathematics regarding a non-vanishing wave function inside the barrier. Of course this sounds natural mathematically I is a valid question to ask for an experiment to measure this non-vanishing probability inside the barrier. Unfortunately all effects I am aware of are not able to look into the barrier.

I don't understand this. We can PROBE what's going on in the barrier, the same way we probe what's going on inside any material that we study.

Without changing the barrier height and width/shape (which is all the parameters that we care about in this tunneling phenomena), can we do something inside the barrier to see if the particle does interact with something inside the barrier? We can. In a superconductor tunneling experiment, we can include, say, magnetic barrier in which the barrier topology doesn't change, but magnetic fluctuation inside the barrier can be present. And when we do that, it definitely changes the tunneling current and spectrum. In fact, certain type of barriers will induce inelastic scattering inside the barrier itself!

So have I "seen" what's going on inside the barrier to sufficiently conclude that, for example, the electron did pass through the barrier? If I have a theoretical description that can accurately describe the tunneling spectra, is that a convincing description of what's going on inside the barrier?

Please note that there are a couple of very old papers by Bardeen and Harrison that set up the tunneling matrix element inside the barrier itself for a superconducting tunneling phenomenon. I can dig up my old, dusty thesis and find those citations for you if you want them.

Zz.

 

[Maui]

Are there any quantum barriers that would be sufficiently large to allow detection or are they all really tiny?

Detectors tend to kill quantum behavior, so it will likely not detect anything. Mind you how the interaction with the barrier isn't collapsing or decohering the tunneling particle's wavefunction.

 

[Jilang]

I don't understand this. We can PROBE what's going on in the barrier, the same way we probe what's going on inside any material ..

So have I "seen" what's going on inside the barrier to sufficiently conclude that, for example, the electron did pass through the barrier? If I have a theoretical description that can accurately describe the tunneling spectra, is that a convincing description of what's going on inside the barrier?

I am happy that they go through the barrier, but there seems to be some uncertainty as to how long they actually spend in there. My question is more about whether you could actually in principle devise an experiment to detect them inside it.

 

[tom.stoer]

ZapperZ, I don't think that we disagree on the tunneling effect. All I am saying is that I don't know / are not familiar with experiments measuring the wave function inside the barrier. So if you say that there are experiments where the barrier is large enough to look inside experimentally, then everything is fine.

 

[Jilang]

Detectors tend to kill quantum behavior, so it will likely not detect anything. Mind you how the interaction with the barrier isn't collapsing or decohering the tunneling particle's wavefunction.

Thanks Maui, but I can't quite make sense of your second sentence. If you are saying there should be an interaction with the barrier that is not necessarily true as the barrier is not like a wall. It might be just a potential gradient of some kind.

 

[Maui]

Thanks Maui, but I can't quite make sense of your second sentence. If you are saying there should be an interaction with the barrier that is not necessarily true as the barrier is not like a wall. It might be just a potential gradient of some kind.

Not really. Quantum tunneling has been a practical hurdle for quite some time in processor designs and the barrier's intended purpose is to really be a wall:

"Gate thickness, another important dimension, is reduced to as little as 1.2 nm (Intel). Only a few atoms insulate the "switch" part of the transistor, causing charge to flow through it. This undesired effect, leakage, is caused by quantum tunneling. The new chemistry of high-k gate dielectrics must be combined with existing techniques including substrate bias and multiple threshold voltages to prevent leakage from prohibitively consuming power."

http://en.wikipedia.org/wiki/65_nanometerThe point was both environmentally induced decoherence and interactions cause collapse do not seem to be on solid footing.

 

[Nugatory]

Thanks Tom, I didn't think it was allowed as it is classically forbidden so even if there was a method of detecting it, it would not be possible.

It's possible. The total energy of the system (particle plus detector) has to be conserved, but in the interaction between detector and particle, energy can be transferred to the particle allowing a measurement that localizes the particle in the classically forbidden region.

 

[ZapperZ]

ZapperZ, I don't think that we disagree on the tunneling effect. All I am saying is that I don't know / are not familiar with experiments measuring the wave function inside the barrier. So if you say that there are experiments where the barrier is large enough to look inside experimentally, then everything is fine.

Do you know of any experiment that "measures the wave function" anywhere?

Zz.

 

[tom.stoer]

Not ψ, but |ψ|, e.g. in interference experiments.

 

[ZapperZ]

Not ψ, but |ψ|, e.g. in interference experiments.

How do interference experiments measure that?

Zz.

 

[tom.stoer]

ZZ, this is silly.

You measure e.g. individual particles on screens, in detectors etc. and you derive |ψ| from the measured intensity, distribution etc. This is known since more than a century.

The only question is how to construct a measuring device which can be located in the barrier and which could do something similar. It's about observing an effect which appears in the forbidden region, not outside.

The only technical problem I see is the size and the material of the barrier.

 

[Jilang]

It's possible. The total energy of the system (particle plus detector) has to be conserved, but in the interaction between detector and particle, energy can be transferred to the particle allowing a measurement that localizes the particle in the classically forbidden region.

Thanks for this. I think you are saying that to detect it you need to give it enough energy to climb up above the barrier so in that sense it's not still in there. This article discusses an experiment like that
http://cds.cern.ch/record/386067/files/9904098.pdf
It's quite amusing as by the end they seem to have talked themselves out of it actually performing it. One issue appears to be that the disturbance created will destroy any information you are likely to receive. Perhaps it's one of those situations where the uncertainty principle wins every time so there is no way even in principle to devise such an experiment?

 

[tom.stoer]

Perhaps it's one of those situations where the uncertainty principle wins every time so there is no way even in principle to devise such an experiment?

I don't think so. I think it's a technical problem.

 

[ZapperZ]

ZZ, this is silly.

You measure e.g. individual particles on screens, in detectors etc. and you derive |ψ| from the measured intensity, distribution etc. This is known since more than a century.

The only question is how to construct a measuring device which can be located in the barrier and which could do something similar. It's about observing an effect which appears in the forbidden region, not outside.

The only technical problem I see is the size and the material of the barrier.

It is not silly. I'm trying to find your "threshold" in what you consider to be a sufficient level of information that you can actually deduce for the validity of your |ψ|.

Now first of all, note that interference measurements were known LONG before QM came along. If it is such an obvious experiment that shows such a description, we would have had QM from the very beginning. So already the interference experiment is NOT an obvious observation.

Secondly, do you get the full information about your ψ from interference experiment? I will argue that you do not! You lose information about position time evolution, and you also lose information not only along the longitudinal direction, but also the direction parallel to the slits. You also can only make inference about the phase of the wavefunction. In other words, the interference experiment may give you SOME info, but not a complete info about the wavefunction.

Thirdly, note what you had to do. You compared the results of experiments to the theoretical formulation, and thus, deduced the validity of that formulation. How is this different than what I had stated earlier? I mentioned about the theoretical description of the phenomenon. I even mentioned about Bardeen/Harrison's setup of matrix element in the barrier (W.A. Harrison,Phys. Rev.123, 85 (1961)). The Kirtley/Scalapino paper that I cited showed the physics of introducing magnetic impurities inside the barrier itself, and its description was used in the tunneling spectroscopy analysis. This is no different than your argument of what you can get out of the interference experiment!

So what's different, and why the unusual requirement that one must have some detector of some kind inside the barrier? We do different experiments for different things based on what Nature allows.

Zz.

 

[Jilang]

I don't think so. I think it's a technical problem.

Tom, thank you for your input and opinion. You seem to understand the question I am asking. I have been reading how the momentum ends up being complex in the barrier. Does that mean that the normal idea of a particle needs to be abandoned altogether in that region?

 

[George Jones]

Tom, thank you for your input and opinion. You seem to understand the question I am asking. I have been reading how the momentum ends up being complex in the barrier. Does that mean that the normal idea of a particle needs to be abandoned altogether in that region?

What do mean by complex? Do you mean the the wave number $k$ is imaginary in the classically forbidden region (say $x>0$)? In this case, write $k = i \kappa$ where $\kappa$ is real. Then

$$e^{i\left(kx - \omega t\right)} = e^{ikx}e^{i\omega t} = e^{-\kappa x} e^{i \omega t}.$$

The probability density then is

$$\left| e^{-\kappa x} e^{i \omega t} \right|^2 = e^{-2\kappa x}$$

Thus, probability density decays exponentially; the deeper into the classically forbidden region, the smaller the chance of finding the particle.

 

[George Jones]

Aha! You mean

$$-i\hbar \frac{d}{dx} e^{-\kappa x} = i \kappa e^{-\kappa x}!$$

See section 5.2 of

http://arxiv.org/abs/quant-ph/0103153

 

[Jilang]

What do mean by complex? Do you mean the the wave number $k$ is imaginary in the classically forbidden region (say $x>0$)? In this case, write $k = i \kappa$ where $\kappa$ is real. Then

$$e^{i\left(kx - \omega t\right)} = e^{ikx}e^{i\omega t} = e^{-\kappa x} e^{i \omega t}.$$

The probability density then is

$$\left| e^{-\kappa x} e^{i \omega t} \right|^2 = e^{-2\kappa x}$$

Thus, probability density decays exponentially; the deeper into the classically forbidden region, the smaller the chance of finding the particle.

Thank you Mr Jones, I am happy with how an imaginary momentum leads to an exponential decay of the wavefunction but less clear about what it means for the velocity. If the momentum is imaginary is the velocity also?

 

[phion]

You can see the consequences of quantum tunneling today in damn near anything with an IC; [bipolar] transistors, diodes, thyristors, MOSFET, CMOS, and more recently TFET.

Device physicists are starting to take advantage of thinner barriers to induce the quantum tunneling affect and control the the flow of current by keeping the energy high, switching on or off according to the likelihood of of electrons materializing on the other side of a barrier.

I believe the barrier-lowering strategy is still the most widely used current control mechanism, though there is a voltage problem that introduces a physical limit which arises from the fact that electrons and holes are constantly in motion due to their thermal energy.

I'd be willing to bet that these new junctions play a big role in the next 12-18 months of "shrink" in the transistor industry.

 

[Jilang]

You can see the consequences of quantum tunneling today in damn near anything with an IC; [bipolar] transistors, diodes, thyristors, MOSFET, CMOS, and more recently TFET.

Device physicists are starting to take advantage of thinner barriers to induce the quantum tunneling affect and control the the flow of current by keeping the energy high, switching on or off according to the likelihood of of electrons materializing on the other side of a barrier.

I believe the barrier-lowering strategy is still the most widely used current control mechanism, though there is a voltage problem that introduces a physical limit which arises from the fact that electrons and holes are constantly in motion due to their thermal energy.

I'd be willing to bet that these new junctions play a big role in the next 12-18 months of "shrink" in the transistor industry.

Phion, thanks for your feedback. Quantum tunnelling is a fascinating subject. Whilst it is mathematically well understood I am struggling to find good experimental data as to what is actually occurring. To what extent for example might a better understanding of tunnelling lead to insights into the spooky action at a distance etc?

 

[ZapperZ]

Phion, thanks for your feedback. Quantum tunnelling is a fascinating subject. Whilst it is mathematically well understood I am struggling to find good experimental data as to what is actually occurring. To what extent for example might a better understanding of tunnelling lead to insights into the spooky action at a distance etc?

Did you even read the Harrison paper that I cited in one of my post?

Zz.

 

[Jilang]

Did you even read the Harrison paper that I cited in one of my post?

Zz.

Sorry no. I looked back through the posts and although you mention Kirtley/ Scalapino pg 798, Harrison only gets a mention in post #20 to Tom. I went to Harrison's website but nothing seems to go back to 1961. Do you have a good link to it?

 

[ZapperZ]

Sorry no. I looked back through the posts and although you mention Kirtley/ Scalapino pg 798, Harrison only gets a mention in post #20 to Tom. I went to Harrison's website but nothing seems to go back to 1961. Do you have a good link to it?

This:

Thirdly, note what you had to do. You compared the results of experiments to the theoretical formulation, and thus, deduced the validity of that formulation. How is this different than what I had stated earlier? I mentioned about the theoretical description of the phenomenon. I even mentioned about Bardeen/Harrison's setup of matrix element in the barrier (W.A. Harrison,Phys. Rev.123, 85 (1961)). The Kirtley/Scalapino paper that I cited showed the physics of introducing magnetic impurities inside the barrier itself, and its description was used in the tunneling spectroscopy analysis. This is no different than your argument of what you can get out of the interference experiment!

Zz.

 

[Jilang]

This:



Zz.

That link does not work. You may have mentioned previously it in another thread, but not this one before #20. Is there a link somewhere for it somewhere else? Thanks.

 

[ZapperZ]

That link does not work. You may have mentioned previously it in another thread, but not this one before #20. Is there a link somewhere for it somewhere else? Thanks.

There's no link. You will have to find access to Phys. Rev. papers.

Zz.

 

[George Jones]

That link does not work.

ZapperZ ddn't give a link! He gave a reference to an journal, W.A. Harrison,Phys. Rev.123, 85 (1961)! In this instant internet age, have we forgotten what this means!

If you are a student, you probably have a number of ways that you can access this.

1) Go to your university library, and find a (bound) hardcopy, and, if it looks interesting, photocopy it, or scan it.

2) Go to your library, and, on a library computer, get a pdf file of the article using PROLA (Physical Review Online Archive).

3) You may be able to get articles at home using PROLA and your university account.

[edit]Zz was faster[/edit]

 

[Jilang]

ZapperZ ddn't give a link! He gave a reference to an journal, W.A. Harrison,Phys. Rev.123, 85 (1961)! In this instant internet age, have we forgotten what this means!

If you are a student, you probably have a number of ways that you can access this.

1) Go to your university library, and find a (bound) hardcopy, and, if it looks interesting, photocopy it, or scan it.

2) Go to your library, and, on a library computer, get a pdf file of the article using PROLA (Physical Review Online Archive).

3) You may be able to get articles at home using PROLA and your university account.

[edit]Zz was faster[/edit]

Thanks Mr Jones for your helpful advice (as always!). I found the site and created an account there, but I am not a student so would have to buy it. I don't live near a library either. Having read read the abstract I am not that much interested in how to calculate the wavefunction which is what it says it about, so am going to pass. Thanks again.

 

[ZapperZ]

Thanks Mr Jones for your helpful advice (as always!). I found the site and created an account there, but I am not a student so would have to buy it. I don't live near a library either. Having read read the abstract I am not that much interested in how to calculate the wavefunction which is what it says it about, so am going to pass. Thanks again.

But this is where the DETAILS are, and I thought that's what you're asking. Harrison (and the subsequent Bardeen's paper) gave explicit details of the description inside the barrier! That is what is means by such a calculation. If you bother to read it, you'll also notice the presence of the group velocity of the tunneling particle, which something that I had a very intimate knowledge of because I had to model that inside the barrier itself to match the experimental tunneling spectra as part of my doctoral work.

It is when you match experiment with the theoretical description are you able to make a convincing argument of the validity of ANY description, and this is what can be done regarding "what is going on" inside the barrier!

But besides this, there is a more general issue here, which is the "leakage" of the wavefunction inside a classically-forbidden region. There are many other phenomena beyond just tunneling where this is applicable, including the famous superconducting proximity effect. Here, we also can't "see" what is going on inside the "barrier" other than measuring the surface resistivity (did the superconducting order parameter actually leaked into a non-superconducting region?). But the theoretical description produced such accurate measurements of what you should get if this were to happen, that this phenomenon is a done deal as far as establishing its validity.

So to me, this question really isn't about "what's going on inside the barrier". But rather, it is more on the reflection ON YOU on what really is your criteria of what you accept to be valid. There have been NO detectors put inside a tunneling barrier to detect the tunneling particle. Period. However, does that make the theoretical picture of what we have invalid and untested? Does that fact that we have OTHER experimental observations, of which the entire result produced a consistent result that agreed with such a picture, completely irrelevant to you?

Zz.

 

[Jilang]

So to me, this question really isn't about "what's going on inside the barrier". But rather, it is more on the reflection ON YOU on what really is your criteria of what you accept to be valid. There have been NO detectors put inside a tunneling barrier to detect the tunneling particle. Period. However, does that make the theoretical picture of what we have invalid and untested? Does that fact that we have OTHER experimental observations, of which the entire result produced a consistent result that agreed with such a picture, completely irrelevant to you?

Zz.

I don't know how you got the impression that that I am questioning the validity of any experiment. I am becoming more inclined to believe that you did not really grasp the direction of my initial question. You state that no detectors have been out inside a tunnelling barrier to detect the tunnelling particle. That is useful information thank you. But would it be ever possible to? I am now thinking probably not.