Light is not matter at all. It is packets of energy. Energy is 'related' to matter by E=mc^2, but that does not mean that it IS matter. You can develop an equation showing how wood is related to heat. But that does not mean that wood IS heat.
The Bose-Einstein condensate is a 5th state of matter that occurs very near to absolute zero, when the atoms themselves lose their defining boundaries and sort of coexist or partially collapse in their spaces. The space of the electron clouds of one atom will 'sort of' share much of its space with other atoms. That means that the atoms sort of condense with respect ot each other, hence the term "condensate". So it is not, um, condensed milk, but condensed atoms.
Maybe the electrons lose their energy to such a degree that they are not, well, as if 'everywhere at once', and so other electrons can intrude. Normally electrons in atoms are more or less everywhere at once in their respective electron clouds, and other electrons cannot easily intrude into this space. That is what normally gives atoms their size.
it is important to grasp just how much space there is in an atom. There is an analogy that if the nucleus of a hydrogen atom was the size of a marble (I suppose this must be an international standard marble! :-) ), then the tiny electron would zing around within a space that is 2 km in diameter!