  We demonstrate that the three-dimensional Skyrmion, which has remained
elusive so far, spontaneously appears as the ground state of $SU$(2) symmetric
Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge
field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon
squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we
find that the ground state continuously undergoes a change from a
three-dimensional to a one- or two-dimensional Skyrmion, which is identified by
estimating winding numbers and helicity. All of the emerged Skyrmions are
physically understandable with the concept of the helical modulation in a
unified way. These topological objects might potentially be realizable in
two-component BECs experimentally.
