  Theoretical study is presented for a spinor Bose-Einstein condensate, whose
two components are coupled by copropagating Raman beams with different orbital
angular momenta. The investigation is focused on the behavior of the ground
state of this condensate, depending on the atom-light coupling strength. By
analyzing the ground state, we have identified a number of quantum phases,
which reflect the symmetries of the effective Hamiltonian and are characterized
by the specific structure of the wave function. In addition to the well-known
stripe, polarized and zero-momentum phases, our results show that the system
can support phases, whose wave function contains a complex vortex molecule.
Such molecule plays an important role in the continuous phase transitions of
the system. The predicted behavior of vortex-molecule phases can be examined in
cold-atom experiments using currently existing techniques.
