Quantum entanglement between fermions

In summary: Let's not discuss Slater determinants and wave functions but fermionic Fock states. A twp-particle state is described by|1,1\rangle = b_\mu^\dagger b_\nu^\dagger|0\rangle|0\rangle = b_\mu^\dagger\right)^2|0\rangle = 0|1,1\rangle = -|1,1\rangle
  • #1
limarodessa
51
0
Hi all

Can you help me?

Can the quantum entanglement exist between fermions which never interacted each other?

For example – if this states of fermions are described by Slater determinant

Does exist some papers from scientific journals about this theme?

Thank you in advance for answer
 
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  • #2
Er.. back up a bit. When you already have a fermionic state described by Slater determinant, aren't there already 2 or more interacting fermions that have to have their spins aligned "just right" to produce the anti-symmetric state?

Zz.
 
  • #3
ZapperZ said:
When you already have a fermionic state described by Slater determinant, aren't there already 2 or more interacting fermions that have to have their spins aligned "just right" to produce the anti-symmetric state?

Zz.

So, if fermions had no interacted their states cannot be described by Slater determinant ?
 
  • #4
limarodessa said:
So, if fermions had no interacted their states cannot be described by Slater determinant ?

Is there any sense of using the Slater determinant for ONE fermion?

Zz.
 
  • #5
ZapperZ said:
Is there any sense of using the Slater determinant for ONE fermion?

Zz.

There may be several fermions. But can we use the Slater determinant for fermions which never interacted each other ?
 
  • #6
limarodessa said:
There may be several fermions. But can we use the Slater determinant for fermions which never interacted each other ?

I don't think you understand what the Slater determinant is for. Why do you think you use the Slater determinant?

If I have non-interacting fermions, I don't have to use the Slater determinant. How the total wavefunction really is for all these non-interacting particles is irrelevant, because they don't "sense" each other. But when they do, the fermionic statistics will kick in. By definition, they are now interacting with each other because now, the total wavefunction for all the particles involved must be antisymmetric.

Zz.
 
  • #7
ZapperZ said:
If I have non-interacting fermions, I don't have to use the Slater determinant.
Zz.

Thanks
 
  • #8
ZapperZ said:
How the total wavefunction really is for all these non-interacting particles is irrelevant, because they don't "sense" each other. But when they do, the fermionic statistics will kick in. By definition, they are now interacting with each other because now, the total wavefunction for all the particles involved must be antisymmetric.

Zz.

Well. But what you can say about this ? :

http://www.springerlink.com/content/mt368h1295458112/

'...It is then shown that a non-interacting collection of fermions at zero temperature can be entangled in spin...'
 
  • #10
ZapperZ said:
If I have non-interacting fermions, I don't have to use the Slater determinant. How the total wavefunction really is for all these non-interacting particles is irrelevant, because they don't "sense" each other. But when they do, the fermionic statistics will kick in. By definition, they are now interacting with each other because now, the total wavefunction for all the particles involved must be antisymmetric.
Sorry, but I disagree.

Let's not discuss Slater determinants and wave functions but fermionic Fock states. A twp-particle state is described by

[tex]|1,1\rangle = b_\mu^\dagger b_\nu^\dagger|0\rangle[/tex]

Each fermionic creation operators create a single fermion; the two indices indicate that there are several quantum numbers, e.g. a spin; they must be different otherwise the resulting stet is exactly zero

[tex]b_\mu^\dagger b_\mu^\dagger|0\rangle = \left(b_\mu^\dagger\right)^2|0\rangle = 0[/tex]

Now if you interchange the two operators you get a minus sign

[tex]b_\nu^\dagger b_\mu^\dagger|0\rangle = -|1,1\rangle[/tex]

This is exactly what the we need in order to achieve a totally antisymmetric state; we do not have explicit antisymmetrization, the fermionic commutation relation already takes this into account.

It is important that we did not specify how the two fermions would interact. We didn't specify a Hamiltonian at all. That means that antisymmetrization comes prior to interaction; it must always be implemented for fermions - even for free = non-interacting fermions. Or let's say it the other way round: antisymmetrization and entanglement is not to be confused with interaction.
 
  • #11
Er... read again the logic of the question. ...if this states of fermions are described by Slater determinant..., meaning you START with states that have been regulated by it!

Zz.
 
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  • #12
The definition of the Slater determinant (http://en.wikipedia.org/wiki/Slater_determinant) is independent on whether the identical fermions interact or not. A multi-electron state can be constructed with the Slater determinant, but the electrons could very well be free. The state of the 2 electrons in ionized helium atom for which the electrostatic interaction b/w the electrons can be neglected (thus one being kept in the atom and the other thrown to kilometers away) is still described by an antisymmetric 2-particle wavefunction, because the 2 electrons are identical fermions.

Anyways, the one of the articles quoted by the initiator of the thread (http://www.springerlink.com/content/mt368h1295458112/) pretty much answers his question.
 
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  • #13
ZapperZ said:
Er... read again the logic of the question. ...if this states of fermions are described by Slater determinant..., meaning you START with states that have been regulated by it!

Zz.
If you want to talk about multi-fermion-states then they must always be constructed using antisymmetrization[/U]; whether you do that using a Slater determinant for wave functions or via Fock states doesn't matter. If you don't antisymmetrize you shouldn't call these babies "fermions".
And it has nothing to do with interaction.
 
  • #14

1. What is quantum entanglement between fermions?

Quantum entanglement between fermions refers to a phenomenon in quantum mechanics where two or more fermions, which are particles with half-integer spin, become entangled or connected in a way that their properties are dependent on each other regardless of the distance between them. This phenomenon is also known as "spooky action at a distance" and is a fundamental aspect of quantum mechanics.

2. How does quantum entanglement between fermions occur?

Quantum entanglement between fermions occurs when two or more fermions interact with each other and become correlated in a way that their properties cannot be described independently. This can happen through processes such as particle collisions or through the creation of pairs of fermions with opposite spin. Once entangled, the fermions will share a single quantum state, even if they are physically separated.

3. What are some potential applications of quantum entanglement between fermions?

Quantum entanglement between fermions has potential applications in quantum computing, cryptography, and communication. It can also be used for quantum teleportation, where the quantum state of one particle is transferred to another particle without physically moving it. Additionally, studying entanglement between fermions can also help us better understand the fundamental principles of quantum mechanics.

4. Can quantum entanglement between fermions be observed in real-life scenarios?

Yes, quantum entanglement between fermions has been observed in various experiments, including the famous Bell test experiments. These experiments have shown that entangled particles can exhibit correlated behavior that cannot be explained by classical physics. However, due to the delicate nature of entanglement, it is challenging to observe in everyday scenarios.

5. Is quantum entanglement between fermions instantaneous?

No, quantum entanglement between fermions does not occur instantaneously. While the entangled particles may exhibit correlated behavior, information cannot be transmitted faster than the speed of light. This means that even though the particles may appear to be connected regardless of distance, there is still a speed limit for any communication or transfer of information between them.

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