In quantum entanglement is the entanglement between a pair of entangled photons broken if one of the pair induces stimulated emission? That is one of the pair generates a third photon.
Normally stimulated emission may be a rare event, except in a medium where hf
Neil, please describe the experiment. It is not clear how exactly your entangled pair of photons produces a 3rd photon.
Stimulated emission can take place in a medium of excited atoms. So, please give details of the experimental arrangement.
In principle, the entanglement should not be broken as long as you don't bring the particles in contact with a classical detector. But, depending on the bodies met by the photons during their flight, the entanglement may become a 3-photons entanglement, or, may be totally decohered if the photons pass through complicated objects with a huge number of particles.
Dear Sofia,
If you're working in a regime where kT >> hf there are a multitude of energy levels very close together, down at microwave frequencies. That medium could be any medium that is transparent to microwaves say polyethylene. The mean number of photons in a mode is just 1/( exp(hf/kT) -1), so emission comprises 50% spontaneous and 50% stimulated. It is the thermal regime as opposed to the quantum regime (where hf>kT) but energy packets are still hf, but just smaller amounts of energy.
So one of these low frequency photons (from the entangled pair of low frequency photons) interacts with the medium so to undergo stimulated emission, thereby producing the 3rd photon.
The thought is that as one of the entangled photons has interacted the entanglement might be lost. The question would be, is all lost with a broken entangled pair, or can something be reconciled with perhaps use of the third photon?
(It has to do with how entanglement experiments might be designed in the thermal region.)
Does this make things any clearer?
many thanks,
Neil
Dear Neil,
I understand, what you drive at. Just take into account that the photon that you pass through the medium has to have the same energy, or more, than the excitation energy of the atoms in the medium.
Anyway, assume that the initial form of the entanglement of two particles A and B, is,
(1) |ψ0> = (1/√2) ( |1;a>A |1;b>B + |1;c>A |1;d>B),
where 1 indicates that there is one particle and a, b, c, d, indicate values of some observable. When the particle B passes through the medium, the result of the stimulated emission is going to be
(2) |ψstim> = (1/√2) { |1;a>A [ exp(iα) |1;b>B + q1 exp(iα1) |2;b>B + q2 exp(iα2) |3;b>B + . . .] + |1;c>A [ exp(iβ) |1;d>B + q1 exp(iβ1) |2;d>B + q2 exp(iβ2) |3;d>B + . . . ] }.
What does this give you? The state (2) is not a cloning of the state (1).
Dear Sofia,
thank you for your response, i guess if entanglement is broken between the two photons, there are perhaps two options:
1) If one of a pair of entangled photons stimulates a third photon, then it may be possible to process the data from all three is some way, as the entanglement may then have 'spread' to all three photons? It there are no others involved where else could the information have gone?
2) try to minimise any stimulated emission in the system by having the minimal of materials which interact with the beam, before the photons enter the analyser?
This perhaps seems a bit wacky, but it's all i could think of at the moment.
many thanks,
Neil
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