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From what I understood, when creating Bose–Einstein condensate, electrons are reduced energy levels (transition to other electron shells). Would stripping an atom of electrons have a similar effect as lowering electron energy states?

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No.

To reach the BEC you need to increase phase-space density, which involves losing energy (to get colder) and losing entropy (a BEC is a coherent state with zero entropy).

The energy refers to the motional energy of the atoms in the BEC. You want to slow them down. Regardless of the internal electronic state (in principle), provided it adds up to a bosonic state.

The electrons change state when they interact with light. Lasers are shone onto the atoms as part of the cooling mechanisms.

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