Are photons from atomic cascade directly entangled?

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zonde
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As far as I know first entanglement experiment used polarization entangled photons from atomic cascade. As I understand atomic cascade produces entangled photons from two electrons that emit photons by falling from the same orbital to the same lower orbital (so they have the same spin).
Now it seems that each photon from pair is entangled with it's electron. So can we consider two photons directly entangled?
Naively it would seem more reasonable to view it differently: if we measure polarization of one photon it should "collapse" spin of the electron that emitted it. This electron in turn "collapses" the spin of other electron in the same orbital and that in turn "collapses" polarization state of other photon.
 
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DrChinese
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zonde
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zonde,

Here is a link to the article: http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.47.460

I see the photons as having opposite spins due to transition of atom (one electron) dropping down to the ground state. So I don't think your description quite matches.
Thanks a lot for the link.
They were using calcium transition ##4p^2\:^1S_0 - 4s4p\:^1P_1 - 4s^2\:^1S_0##. Ground state for calcium is when both it's valence electrons are in 4s orbital (that is written as 4s2). Excited state with two electrons in 4p orbital is written as 4p2 and excited state with only one electron in 4p orbital would be written as 4s14p1 that I suppose is abbreviated to 4s4p.
So it seems to match my description. I am however puzzled why two (sort of identical) transitions have different energies.
 
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DrChinese
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Yes, here they use the same cascade. They just pump it differently, less efficiently.
So I guess there are 2 electrons - spin entangled in their excited shell, that drop to the lower shell where they are still entangled. In doing so they flip their spin and emit a photon - which is entangled with the electron due to conservation of spin.

I guess it gets a little fuzzy for me here because it doesn't seem right that all 4 particles are now entangled on spin basis such that a read of one's spin tells you the spin of 3 others. I guess the electrons that are back in the ground state are now indistinguishable so that it is only the 2 photons that are net effectively entangled.

I hadn't really looked at the details of the Ca cascade before. Good stuff. You hear more about the Aspect experiments but those by the earlier pioneers are pretty amazing too.
 
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jfizzix
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As far as I know first entanglement experiment used polarization entangled photons from atomic cascade. As I understand atomic cascade produces entangled photons from two electrons that emit photons by falling from the same orbital to the same lower orbital (so they have the same spin).
Now it seems that each photon from pair is entangled with it's electron. So can we consider two photons directly entangled?
Naively it would seem more reasonable to view it differently: if we measure polarization of one photon it should "collapse" spin of the electron that emitted it. This electron in turn "collapses" the spin of other electron in the same orbital and that in turn "collapses" polarization state of other photon.
As far as I know, the cascade is a transition of a single electron down two levels, which then causes two photons to be emitted.
However, this two-photon transition can occur two different ways, because there are two intermediate p-orbitals the electron could be in between the initial 3s orbital and the 1s final orbital.
way 1:
3s -> 2p_1 -> 1s
way 2:
3s -> 2p_-1 -> 1s

In way 1, the first photon emitted is right-circularly polarized, and the second is left-circularly polarized
In way 2, the photons emitted have the opposite polarization

Since both of these two-level transitions lead the electron to the same final state, the transition amplitude for the cascade is a superposition of both possible trajectories.

As a result, the polarization state of the emitted pair of photons is an entangled superposition of opposing polarizations
 
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zonde
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I guess it gets a little fuzzy for me here because it doesn't seem right that all 4 particles are now entangled on spin basis such that a read of one's spin tells you the spin of 3 others. I guess the electrons that are back in the ground state are now indistinguishable so that it is only the 2 photons that are net effectively entangled.
Yes, for me too it does not seem right that 4 particles are entangled that way. Maybe there is additional variable that says how polarization of photon and spin of electron is related (and is the same for both photon-electron pairs). In that case there would be additional degrees of freedom for entangled quartet.
 
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zonde
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As far as I know, the cascade is a transition of a single electron down two levels, which then causes two photons to be emitted.
Thanks to two links given by DrChinese that describe actual experiments we can talk about particular transitions used in these experiments. And in both experiments decay of excited state is the same: two electrons from 4p orbital drop to 4s orbital.
 
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jfizzix
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Thanks to two links given by DrChinese that describe actual experiments we can talk about particular transitions used in these experiments. And in both experiments decay of excited state is the same: two electrons from 4p orbital drop to 4s orbital.
Ah. Looks like I picked up a fine bouquet of oopsie daisies.
 

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