I researched the question, and didn't find any absolute answer to whether BEC is more dense than normal matter. They keep describing it as a new "state" of matter. Here is one example:
"Just as there is a maximum threshold of energy above which atomic matter as we know it can't exist, there is a minimum threshold of energy below which atoms no longer behave in the ways we expect. Atoms become excited when their energy increases. In an analogous way, atoms become "de-excited" when their energy decreases. As atoms approach absolute zero, they become sluggish and ultimately condense into an additional physical state called a
Bose Einstein Condensate (BEC). Consider a balloon filled with steam, the gaseous state of water. Cool it down to room temperature and it will contain a small puddle of water inside it. Put it in a freezer and that water will solidify into ice. It's easy to visualize the atoms in steam moving around fast and bumping into each other, or atoms sliding around one another in liquid water, but there is no visible motion within a block of ice. Yet, undetectable to our eyes, there is. As the water freezes into ice, the atoms get close enough and slow down enough to form attractive chemical bonds with each other. In the case of water ice, they create a three-dimensional lattice. The type of bond arrangement depends on the kinds of atoms involved. No matter what the solid material is, the bonds hold the atoms more or less in place but they don't stop the atoms from jiggling about, like a runner jogging in place. This jiggling or oscillating motion, averaged over the material, is what we perceive as its heat or temperature. Lets say we cool our balloon down much further inside a special box that removes energy. The oscillations, on average, will slow down. Eventually, the ice will theoretically get so cold that the atoms no longer oscillate at all. At this point it has reached
absolute zero, a temperature measured as - 273.15°C or - 459°F or 0K. I say theoretically because it is not possible in practice to remove all the energy from a system (we are treating our balloon as a physical system). Scientists are finding ways to get very close to absolute zero, and as they do, matter begins to act very strangely. In theory, the ice in our balloon could transform from a solid into a BEC, and when it does it will exhibit some very interesting properties." from this
site.
, I think they are describing the density of the original gas - which from Wikipedia is described as having to be "about one-hundred-thousandth the density of normal air" for a BEC
