The Bose-Einstein (BE) condensate is said to be a new state of matter which is fundamentally different from solid. liquid or gas. What are some of these properties which separate it from ordinary phases of matter? Are these properties only theoretically conjectured or has been measured? In particular, it is too cold to be a gas but why is it not a solid or a liquid? Is it hard or soft? Has rigidity or fluidity?
A Bose Einstein condensate is a superfluid, which is fundamentally different from an ordinary liquid or gas. Superfluidity manifests itself in a variety of ways, most notably in the way the system responds to rotation. A superfluid vannot rotate as a rigid body, but has to form quantized line defects, vortices. This has been seen in experiment, see http://jilawww.colorado.edu/bec/CornellGroup/gallery/index.html .
Superfluidity was previously seen in liquid helium. Helium is a gas at room temperature and pressure, which liquifies at about 4K, and becomes superfluid at 2.2K. Under high pressure helium solidifies, and at very (very) low pressure it forms a superfluid when cooled from the gas phase.
In BEC the system is a gas at high temperature, and then condenses into the superfluid state without an intervening liquid phase. In most systems that are studied experimentally the BEC is quite stable, but typically the true ground state is a solid which is many orders of magnitude more dense than the BEC. The BEC behaves like a gas in the sense that it is quite compressible (you can make sound waves, or excite monopole oscillations). However, as a superfluid it flows like an ideal fluid.