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I was reading a sciencenews.org post about three photons being entangled. My question here is, why is the chance of producing an entangled pair once in a billion times? Isn't every particle produced in pairs, each of them being entangled to the other one formed in the pair? So shouldn't every photon that is produced, have an entangled photon? Why is the probability so low?

Shouldn't entanglement happen immediately during the production of the particle?

Note Since I am a little new to this topic, a little background of entanglement would be appreciated as I might be wrong in my conceptualization.

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rahulgarg12342
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  • Most optical emission processes only produce a single photon. Where did you read that particles are formed in pairs? Are you thinking about pair production processes in high energy physics? Those are not the same as the atomic processes, which produce single photons and entangled photon pairs. Most atomic light sources use the decay of one atomic state into another one, which typically emits one photon. Entangled photon pairs are mostly converted from a single photon with higher energy in a downconversion process, which splits the energy of the incoming photon in a non-linear crystal. – CuriousOne Sep 18 '14 at 11:08
  • Oh that is pretty helpful! So you are right. I did get confused between the two then. So does pair production, happen only in situations where there is a lot of energy? – rahulgarg12342 Sep 18 '14 at 11:11
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    Pair production is usually used as a name for the process which creates charged, massive matter-antimatter pairs. The minimal energy for that is approx. 1MeV, because electrons and positrons have rest masses of 511keV. Other charged particles have higher rest mass, and thus higher pair production threshold. – CuriousOne Sep 18 '14 at 11:17

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As was pointed out in the comments most photons are produced individually from deexcitation of electrons from higher energy orbitals, where they had been pushed by heat ( as with heat filament lamps) to lower ones.

Since I am a little new to this topic, a little background of entanglement would be appreciated as I might be wrong in my conceptualization.

When talking of photons the quantum mechanical framework is involved. In quantum mechanics the production of a photon follows solutions of the quantum mechanical equations for the boundary conditions of the problem. The confusing word ( in mty opinion) "entanglement" for any state that is in the quantum mecanical framework means that there exists one solution whose phases and amplitudes are completely known, and dependent on the boundary conditions of the problem at hand.

For two particles to be entangled it means they have been produced at the same time connected by a single interaction so that the phases and amplitudes are correlated for the two. This happens in the lasing process where laser light is formed where the phases are deliberately "entangled" for many photons and the phenomenon of coherent laser beams is achieved.

Ordinary light though, which emerges from incoherent processes by individual interactions is built up by zillions of photons. It can be forced into coherence when passed through a narrow slit , displaying the characteristics of a coherent point source. That is why in double slit experiments a first single slit commensurate with the wavelength is used in order to create a coherent point source and see the interference patterns clearly. It is not that the individual photons are interacting with each other, but that the boundary conditions impose an order in their relative phases that creates coherent phenomena. Coherence is a separate phenomenon from "entanglement" due to the production wave function, though both display a knowledge of phases between photons.

The probability of producing a photon goes like (1/137) each "entangled" ( i.e. contiguous interaction producing another photon) is multiplied by this small number so to get three photons produced within on solution of the boundary conditions of the filament of a lamp becomes this number to the cube, a very small number. In the case of lasers this is overcome by the smart choice of crystals and atoms and the boundary conditions that are imposed to create chain reactions of interactions which then have known phases and are "entangled".

Hope this helps.

anna v
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  • It is concluded from your answer that a laser beam is composed of entangled photons. Is it true? Then why do we use nonlinear crystals for if the laser photons are already entangled? Doesn't entanglement imply shared superposition? – ScienceJournalist01 Apr 29 '16 at 09:42
  • @QuantumJournalist as I state in my answer, "entangled" is a fancy word for "common quantum mechanical solution". Laser photons are then "entangled". I am not familiar with the use of nonlinear crystals and the optics thereof. From the article in wikipedia I gather that it is the manipulation of laser beams, https://en.wikipedia.org/wiki/Nonlinear_optics ,not generation of laser beams, so new quantum mechanical boundary problems. – anna v Apr 29 '16 at 10:21
  • Entangled means they do not manifest wave properties when considered separately. Laser photons manifest interference separately. What is true is that laser photons have identical wavefunctions that add up to a single separable macroscopic wavefunction but they manifest their wave properties separately. If you measure one laser photon, the wavefunctions of the rest will not collapse, like for entangled photons – ScienceJournalist01 Apr 29 '16 at 10:44
  • @QuantumJournalist I do not know your definition. Collapse is another hadwavint term . A wavefunction is not a balloon. If you interact with one photon the collective wavefunction of that photon will be different by that interaction. Furthermore the interaction can tell you about the polarization of therest of the beam , you do not have to interact with all photons. – anna v Apr 29 '16 at 11:09
  • You do not know about collapsing the wavefunction of a laser because a laser is in a single state, not in a superposition of states. – ScienceJournalist01 Apr 29 '16 at 15:37
  • Instead of two photons having HH or VV like for a laser beam with the individual photons having a H or V polarization, for entangled photons you have the HV + VH/sqrt(2) for the whole beam and no definite state for each photon. The collective polarization HH can be written as the product state H x H, while HV+VH/sqrt(2) cannot be written as a product state. – ScienceJournalist01 Apr 29 '16 at 15:44
  • @QuantumJournalist collapse is synonymous "with picking up one instance of a quantum mechanical probability distribution". All wavefunctions squared are QM probability distributions . Let us stop this here as we have different vocabularies. – anna v Apr 29 '16 at 17:17
  • I suggest you read https://www.quora.com/Are-Bose-Einstein-condensates-separable-or-entangled-systems and https://www.quora.com/If-a-Cooper-pair-is-an-entangled-system-is-a-BEC-of-Cooper-pairs-also-an-entangled-system which are questions about this topic answered by experts – ScienceJournalist01 Apr 29 '16 at 17:51
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No, but a mercury lamp does. Each mercury and calcium atom emits two indistinguishable photons out of a single atom, instead of one, like the rest of the atoms. The photons emitted by a single atom at the same time are entangled.

Do not expect entangled photons out of atoms that emit a single photon at the time. Also the mercury lamp must not have a fluorescent coating as this destroys the entanglement

Nonlinear crystals absorb one input photon and produce two indistinguishable daughter photons, each one in a superposition of states. (H+V)/sqrt(2) means a superposition of vertical and horizontal polarizations.

Read https://en.wikipedia.org/wiki/Quantum_entanglement#Methods_of_creating_entanglement

Although all the particles of a BEC are in a single quantum state, they are not entangled, but rather the macroscopic wavefunction can be separated as a product state

https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equation

I suggest you read https://www.quora.com/If-a-Cooper-pair-is-an-entangled-system-is-a-BEC-of-Cooper-pairs-also-an-entangled-system and https://www.quora.com/Are-Bose-Einstein-condensates-separable-or-entangled-systems which are questions about this topic answered by experts. They also answered us there that lasers are not composed of entangled photons.

ScienceJournalist01
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