  The recent report on the realization of a Bose-Einstein condensate of G-wave
molecule made up of bound pairs of Cesium bosons is a surprise. These molecules
are created at the G-wave resonance at 19.87G, where the severe three-body loss
usually associated with these resonance are found to be reduced significantly
when the density of the gas is reduced in a quasi 2D setting. The G-wave
molecules produced through this resonance have non-zero angular momentum
projections, resulting in the first BEC with a macroscopic intrinsic angular
momentum. Here, we show that this intrinsic angular momentum will lead to many
new quantum effects. They include a splitting of collective modes in the
absence of vortices, an orientation dependent energy shift due to the moment of
inertia of the molecules, and a contribution to angular momentum in non-uniform
magnetic fields different from that of the Berry phase current. The intrinsic
angular momentum also provides a way to probe the half vortices, excitations
that are unique to molecular condensates of bosons. The wavefunction giving
rise to the intrinsic angular momentum can also be mapped out from the noise
correlation.
