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What if we cool carbon atoms to a few degrees above absolute zero to make it bose condensate....since there will be few degrees of freedom and enough isolation from outside forces or thermal interferance, I predict that the atoms will become entangled...Am I on the right path or what do you think?...

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Every Bose-Einstein condensate is in a highly entangled state, it doesn't matter what is made up of. For more info: read this paper here

However, I am not sure if carbon atoms will become a condensate at few degrees above absolute zero. The temperature has to be much closer to zero. Maybe there are other parameters like pressure and volume that would allow this but yeah that shouldn't make any difference as far as your question is concerned.

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