Understanding the Measurement and Interaction of Electrons: A Beginner's Guide

[zonde]

That's a good question. I'm not 100% sure, but the reason must be that the energy gap between the used phonon mode to the next excited state is very large and thus that even at room temperature the probability for transitions is very low. Perhaps you find the detailed answer in the Science article:

https://people.phys.ethz.ch/~reimk/Media/Science-2011-Lee-1253-6.pdf

It seems that phonons used in the experiment are of much higher frequency than that of thermal vibrations. And these phonons are relatively stable because of specific structure of crystal ("bulk vibration consisting of two counter-oscillating sublattices within the diamond structure.")

On the first glance the experiment seems to show rather bizarre effect - phonon shared by two distant diamonds. But on the second glance it seems that experiment is consistent with explanation that there are two polarization entangled phonons in crystals.

 

[bhobba]

Ok. Do you know how did they manage to achieve the entaglement in conditions that aren't cold and isolated?

No.

Thanks
Bill

 

[durant35]

It seems that phonons used in the experiment are of much higher frequency than that of thermal vibrations. And these phonons are relatively stable because of specific structure of crystal ("bulk vibration consisting of two counter-oscillating sublattices within the diamond structure.")

On the first glance the experiment seems to show rather bizarre effect - phonon shared by two distant diamonds. But on the second glance it seems that experiment is consistent with explanation that there are two polarization entangled phonons in crystals.

But how did they manage to cross paths of the two diamonds, I've red that electron paths had something to do about it.

 

[zonde]

But how did they manage to cross paths of the two diamonds, I've red that electron paths had something to do about it.

They didn't of course.
First they shine a pump laser pulse on both diamonds. A photon splits in phonon and redder photon than the rest of pump photons. They collect these redder photons from both crystals and analyze them together using two polarization beam splitters and half wave plate. After short time they shine second pulse on diamonds and phonon combines with one pump photon and creates bluer photon. These are collected and analyzed together in separate channel using two PBSes and wave plates.

 

[durant35]

But is that a vibration of a diamond per se or a state where the phonon is spread as a wave in both diamonds?

 

[zonde]

But is that a vibration of a diamond per se or a state where the phonon is spread as a wave in both diamonds?

For me it seems that this experiment is consistent with explanation that there is phonon in each diamond but they are polarization entangled.
Idea that there is single phonon spread over both diamonds seems bizarre. Say where is the energy of phonon then?

 

[durant35]

For me it seems that this experiment is consistent with explanation that there is phonon in each diamond but they are polarization entangled.
Idea that there is single phonon spread over both diamonds seems bizarre. Say where is the energy of phonon then?

What is polarization entaglement and how is it obtainable in two objects spread by distance which wavefunctions don't cross paths? I have much less understanding than you about this topic so I hope you can help me with it and with my lack of knowledge. Thank you.

 

[zonde]

What is polarization entaglement and how is it obtainable in two objects spread by distance which wavefunctions don't cross paths? I have much less understanding than you about this topic so I hope you can help me with it and with my lack of knowledge. Thank you.

Let's first find out how much do you know about polarization of light. Do you know how to get polarized light, say as described here: https://en.wikipedia.org/wiki/Polarizer ?

 

[durant35]

Okay, I've red it. I think I understand the basics. Can you continue please?

 

[zonde]

Generally we speak about photon polarization entanglement. Usually polarization entangled photons are produce using parametric down-conversion in specific arrangements.
Polarization entangled photons have a property that when you measure polarization of one photon from the pair the other one is certain to have the same polarization (or opposite depending on entanglement type) even when two measurements are performed at distant places.

 

[durant35]

Generally we speak about photon polarization entanglement. Usually polarization entangled photons are produce using parametric down-conversion in specific arrangements.
Polarization entangled photons have a property that when you measure polarization of one photon from the pair the other one is certain to have the same polarization (or opposite depending on entanglement type) even when two measurements are performed at distant places.

Okay, thanks for the explanation. But one thing are photons and other are relatively big diamonds which are quite localized unlike photons. How is entaglement by polarization obtainable for this kind of an object?

 

[zonde]

Okay, thanks for the explanation. But one thing are photons and other are relatively big diamonds which are quite localized unlike photons. How is entaglement by polarization obtainable for this kind of an object?

Diamonds or rather phonons are not measured directly but rather first converted into photons and then photon polarization is measured, simply stated.

 

[durant35]

Okay, now that makes much more sense. Could this experiment be obtaniable in some other circumstances or diamonds are specific because of their specific structure?

 

[durant35]

I reworked the experiment in my mind and I think I understand a bit of it. Do photons exhibit similar behavior while passing through other bodies that are already vibrating (like our bodies) so that they put them in a state of vibrating and non vibrating?

 

[vanhees71]

Ok. Do you know how did they manage to achieve the entaglement in conditions that aren't cold and isolated?

A free source of the paper is

https://www.researchgate.net/profile/Xian-Min_Jin/publication/51855622_Entangling_Macroscopic_Diamonds_at_Room_Temperature/links/00463519f66babe7f6000000.pdf

 

[durant35]

A free source of the paper is

https://www.researchgate.net/profile/Xian-Min_Jin/publication/51855622_Entangling_Macroscopic_Diamonds_at_Room_Temperature/links/00463519f66babe7f6000000.pdf

You've just made my day harder :P Because there are many mentioned examples of macro entaglement and I don't understand how are they achieved.
Why the diamond experiment is/isn't obtainable in other objects like our bodies?

 

[mfb]

All the excited states have to be well isolated from the environment. This is possible (for fractions of a second) in nice clean crystals like diamond, it is not possible in human bodies.
There is some evidence that very brief quantum effects are relevant in photosynthesis (e.g. this news), but those states are (a) on the level of a few molecules and (b) extremely short-living.

 

[durant35]

What about macroscopic light and entaglement?

 

[durant35]

Why doesn't the excited state spread to the environment that observes it so it also becomes excited?

 

[mfb]

Why doesn't the excited state spread to the environment that observes it so it also becomes excited?

That question does not make sense.

And what is "macroscopic light"? Light does not have a size.

 

[durant35]

That question does not make sense.

And what is "macroscopic light"? Light does not have a size.

The word 'spread' has the same meaning as the evolution of superpositions which ultimately result in the Schrodinger's cat. By that I mean, concretely in the case of diamonds we mentioned, does the air that surrounds one of the diamonds get in some kind of superposition depending on its interaction with the diamond that is 'vibrating and non vibrating'.

Also I need a conclusion about decoherence, does it produce an eigenstate? So a cat is hypotethically in a superposition of dead and alive and after a few fragments of time it decoheres and it becomes either dead or alive, just one of those two states.

 

[mfb]

does the air that surrounds one of the diamonds get in some kind of superposition depending on its interaction with the diamond that is 'vibrating and non vibrating'.

No, interaction with the air would lead to decoherence.

Also I need a conclusion about decoherence, does it produce an eigenstate?

An eigenstate of what? Of something that is measured: yes.

 

[durant35]

No, interaction with the air would lead to decoherence.An eigenstate of what? Of something that is measured: yes.

I read that decoherence leads to transition from a superposition state to a mixed state, but a mixed state per se implies an eigenstate as an outcome, right? That is one concrete result, like the 'cat is dead' after the decoherence proc.ess

 

[durant35]

Also, because of the environment, we are never in superposed states, right? So for instance my cat is always alive when I see it on everyday basis, there's no superposition. I read a document from a physicist Zurek which claims that decoherence saves us, but decoherence isn't instanteneous so do we everyday objects have superposed properties despite decoherence not being instanteneous?

 

[mfb]

Also, because of the environment, we are never in superposed states, right?

Right.

I read a document from a physicist Zurek which claims that decoherence saves us, but decoherence isn't instanteneous so do we everyday objects have superposed properties despite decoherence not being instanteneous?

Decoherence happens so fast, you never get something that could be seen as relevant superposition for macroscopic properties - measuring those would need some time as well.

 

[durant35]

Right.Decoherence happens so fast, you never get something that could be seen as relevant superposition for macroscopic properties - measuring those would need some time as well.

Im sorry mr mfb but I don't get it precisely, is it that we are not in a superposition a definite fact or the decoherence process kills the superpositions occurring rapidly but for a small period of time we are in one.
I can't shake my head over it, but I constantly have this thought of people being in a superposition of dead and alive for fragments of seconds without external cause but we cannot see it. Tell me please how does decoherence solve this bizarre idea?

 

[bhobba]

Im sorry mr mfb but I don't get it precisely, is it that we are not in a superposition a definite fact or the decoherence process kills the superpositions occurring rapidly but for a small period of time we are in one.
I can't shake my head over it, but I constantly have this thought of people being in a superposition of dead and alive for fragments of seconds without external cause but we cannot see it. Tell me please how does decoherence solve this bizarre idea?

Every pure state is in a superposition and in an infinite number of different ways. You need to specify superposition of position.

What's going on here in the Macro world is, without going into the technical details, we have as a result of decoherence states get converted to mixed state of position. Such mixed states can be considered to be in a definite position rather than a superposition.

Thanks
Bill

 

[durant35]

Every pure state is in a superposition and in an infinite number of different ways. You need to specify superposition of position.

What's going on here in the Macro world is, without going into the technical details, we have as a result of decoherence states get converted to mixed state of position. Such mixed states can be considered to be in a definite position rather than a superposition.

Thanks
Bill

So basically those small superpositions of location can be considered an exact position for all purposes, and the macroscopic properties like dead or alive are definite despite the uncertainty and there are no superpositions of those properties?

 

[zonde]

I can't shake my head over it, but I constantly have this thought of people being in a superposition of dead and alive for fragments of seconds without external cause but we cannot see it. Tell me please how does decoherence solve this bizarre idea?

You can meaningfully speak about superposition of dead an alive only if the two can be viewed as basically the same quantum state (technically, as states in the same Hilbert space) differing only by complex phase factor. And I don't think this is possible.

 

[bhobba]

So basically those small superpositions of location can be considered an exact position for all purposes, and the macroscopic properties like dead or alive are definite despite the uncertainty and there are no superpositions of those properties?

As I have mentioned to you a few times its next to impossible explain this linguistically. You must go into the math.

However what you said is not correct. What happens is a general state gets converted to a mixed state in the position basis. This can be interpreted as having a definite position but the position it has isn't known, but has a certain probability.

Here is what a mixed state is about. A pure state is written as |u><u|. These are the states the principle of superposition applies to which is the |u> forms a vector space. A mixed state is a generalisation of a pure state. Imagine you are presented with states |bi><bi| to observe with probability pi. It turns out such a state is mathematically ∑pi |bi><bi|. Now what decoherence does in most practical cases (technically its the Hamiltonian has radial symmetry) is it converts a state to ∑pi |bi><bi| where the |bi><bi| are states of definite position. This means you can interpret this as the system being in state |bi><bi| with probability pi. However while you can interpret it that way it was not prepared the way I told you a mixed state was prepared ie some process randomly presenting a state. There is no way to tell the difference - but it was not prepared that way. That's why its called apparent collapse. If it was prepared that way - ie randomly presenting an actual state - than it would be actual collapse.

Thanks
Bill

 

[durant35]

I think I understand it in principle but I don't understand how to practically employ it in practice and how does the classical world emerge from it, with definite macroscopic properties and not superpositions. The fact that decoherence isn't instanteneous seems to always leave room for a macro superposition without any reason and that's what makes it bizarre and gives me anxiety.

As I have mentioned to you a few times its next to impossible explain this linguistically. You must go into the math.

However what you said is not correct. What happens is a general state gets converted to a mixed state in the position basis. This can be interpreted as having a definite position but the position it has isn't known, but has a certain probability.

Here is what a mixed state is about. A pure state is written as |u><u|. These are the states the principle of superposition applies to which is the |u> forms a vector space. A mixed state is a generalisation of a pure state. Imagine you are presented with states |bi><bi| to observe with probability pi. It turns out such a state is mathematically ∑pi |bi><bi|. Now what decoherence does in most practical cases (technically its the Hamiltonian has radial symmetry) is it converts a state to ∑pi |bi><bi| where the |bi><bi| are states of definite position. This means you can interpret this as the system being in state |bi><bi| with probability pi. However while you can interpret it that way it was not prepared the way I told you a mixed state was prepared ie some process randomly presenting a state. There is no way to tell the difference - but it was not prepared that way. That's why its called apparent collapse. If it was prepared that way - ie randomly presenting an actual state - than it would be actual collapse.

Thanks
Bill

 

[bhobba]

I think I understand it in principle but I don't understand how to practically employ it in practice and how does the classical world emerge from it, with definite macroscopic properties and not superpositions..

That part is simple.

The macro world has definite position. Since after decoherence the mixed state is equivalent to having a definite position everything is fine.

Thanks
Bill

 

[durant35]

Thanks. So if it has a definite position does this imply that it has classical properties (like being alive) which evolve classically?

That part is simple.

The macro world has definite position. Since after decoherence the mixed state is equivalent to having a definite position everything is fine.

Thanks
Bill

 

[bhobba]

Thanks. So if it has a definite position does this imply that it has classical properties (like being alive) which evolve classically?

I am not into biology - my thing is physics using math. But I would say - yes.

Thanks
Bill

 

[durant35]

Thanks.

So let me try to conclude all of this. The system evolves from a superposition to a mixed state, but the nature observes only one state of the macro object with a definite position while other is information in the environment. So for instance the photons measure ' the cat is alive' state and the 'cat is dead' state doesn't stop existing but it is 'contained' as information in reality, and that's why it is just an apparent collapse but it is sufficient because environment only measures a definite state which for macroscopic objects then evolves classically as you mentioned in one of your previous posts.

I am not into biology - my thing is physics using math. But I would say - yes.

Thanks
Bill

 

[Bruno81]

Thanks.

So let me try to conclude all of this. The system evolves from a superposition to a mixed state, but the nature observes only one state of the macro object with a definite position while other is information in the environment. So for instance the photons measure ' the cat is alive' state and the 'cat is dead' state doesn't stop existing but it is 'contained' as information in reality, and that's why it is just an apparent collapse but it is sufficient because environment only measures a definite state which for macroscopic objects then evolves classically as you mentioned in one of your previous posts.

Nobody knows how qm connects to the classical macro world. Don't take everything for granted, as there is no higher authority on this particular subject. While we struggle to understand nature and reality, keep your expectations low and humble... if there is no classical reality existing at all times in 3 D space, there is likely lots' of room for revisions of our basic notions. Physicists used to think all of Nature was deterministic and all mysteries concerning our existence resided in the low entropy of the Big Bang(basically they thought we evolved in the only possible way given how the initial conditions were 14 billion years ago). Now we have enough eveidence that this point is almost worthless due determinism arising from indeterminism(see double slit experiement with single photons/electrons). It's more into the philosophy side of things as physicists find few or no practical aspects to these developments. If you stick around and ask the right questions, you'll see the issue in full detail.

 

[vanhees71]

To the contrary! It's pretty well known, how the "classical world" emerges from the quantum world via "coarse graining", i.e., noting that the macroscopic observables are much coarser than any microscopic resolution, and a classical state ("point in phase space") is in reality an average over many quantum states.

E.g., the fundamental quantum many-body equations for the evolution of the single-particle Wigner function, the socalled Kadanoff-Baym Equations go over into the (semi-)classical Boltzmann(-Uehling-Uhlenbeck) equations after the gradient expansion. Into that approximation goes the assumption that the macroscopic variables vary much slower in space and time than the rapid oscillations of the microscopic degrees of freedom, i.e., the macroscopic observables are given by an average over macroscopic small but microscopic large phase-space regions and times. For a pedagogic introduction into that subject, see Landau-Lifshitz, vol. X or

W. Cassing. From Kadanoff-Baym dynamics to off-shell parton transport. Eur. Phys. J. ST, 168:3–87, 2009.
http://dx.doi.org/10.1140/epjst
http://arxiv.org/abs/arXiv:0808.0715

 

[Bruno81]

Coarse graining is not an official interpretation hence it can't explain why a certain coarse graining and not another is actualised. And even if it, which it doesn't, it woud have tension with Bell and a host of experiments(double slit, DCQE, etc).

 

[vanhees71]

What do you mean by "official interpretation"? It's not an interpretation at all but a mathematical approximation method to derive semi-classical transport equations from quantum many-body theory.

 

[bhobba]

Coarse graining is not an official interpretation

I think its fundamental to Decoherent Histories. In that interpretation QM is the stochastic theory of coarse grained histories..

Thanka
Bill

 

[Bruno81]

So it doesn't explain how a classical world emerges, doesn't explain single outcomes but instead provides a mathematical approximation method to derive semi-classical transport equations from quantum many-body theory. I wil look into this in more detail.

 

[durant35]

What do you mean by "official interpretation"? It's not an interpretation at all but a mathematical approximation method to derive semi-classical transport equations from quantum many-body theory.

So no macroscopic superpositions are allowed, the classical world is as we see it in a definite state all the time?

 

[mfb]

Yes, especially if you "see" it (i. e. it interacts with light).

 

[durant35]

Yes, especially if you "see" it (i. e. it interacts with light).

Glad to hear that, that finally washes away some of my anxiety regarding this. I know QM is weird but to have a classical, definite state and properties of macroscopic objects at any instant which we can combine with special and general relativity is a sign of relief.