  Bose Einstein condensates of spin-1 atoms are known to exist in two different
phases, both having spontaneously broken spin-rotation symmetry, a
ferromagnetic and a polar condensate. Here we show that in two spatial
dimensions it is possible to achieve a quantum phase transition from a polar
condensate into a singlet phase symmetric under rotations in spin space. This
can be done by using particle density as a tuning parameter. Starting from the
polar phase at high density the system can be tuned into a strong-coupling
intermediate-density point where the phase transition into a symmetric phase
takes place. By further reducing the particle density the symmetric phase can
be continuously deformed into a Bose-Einstein condensate of singlet atomic
pairs. We calculate the region of the parameter space where such a molecular
phase is stable against collapse.
