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How do scientists entangle photons? One documentary I watched said that scientists can transport a single photon by entangling 2 other photons and somehow they are able to "teleport" them. How is it possible? How do you synthetically entangle photons?

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First,

Quantum Mechanics teaches us that when two particles are emitted simultaneously or quasi-simultaneously by the same entity, they are entangled.

There are many techniques and one of them is by Bremsstrahlung - radiation emitted by a charged particle that is being deflected (slowed) by another charged particle.

As an example of experiment that uses this kind of technique see intercontinental quantum liaisons between entangled electrons in ion traps of thermoluminescent crystals were they used entangled X ray photons and traped them in electrons that moved from valence band to conduction band by absorbing one of the entangled photon.

One photon was absorbed in a crystal, the other one in another crystal spatially separated from the first one.

In the experiments presented, the radiation is due to a beam of high energy electron aimed at a target of Tungsten

You wanted to know about "how do they entangle" but I also included details from all the steps that occured in the experiment, even if not all steps involve producing of entangled photons.

And just one more note about thermoluminscence:

Thermoluminescence occurs in crystals that contains imperfections, or impurity atoms, or atoms of doping. Such crystals have the property of storing the effect of the irradiation with X-rays or gamma rays. This storage can last for years and is used for geological and archeological dating with natural or pottery type materials. Artificial crystals are used for thermoluminescent dosimetry (TLD) to determine the exposure to ionizing radiations. When the crystals are heated, the energy is released in the form of light. In the reported experiment, dosimetry type crystals have been used.

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