Phase transitions of spin-orbit coupled Bose-Einstein Condensate in an external trap potential

Recently, the experimental realization of artificial magnetic fields using laser beams in a Rb87 Bose-Einstein condensate provides a valuable opportunity to investigate the rich physics of atomic gases in the presence of external Abelian and Non-Abelian gauge fields. We investigate the ground state properties of two-component BECs with Rashba spin-orbit coupling in the presence of external trapping potential. In the presence of density-density interaction between particles, the competitions among interaction, spin-orbit coupling and trap potential results in phase transitions of the ground states from a spiral spin-density wave state to a skyrmion type spin texture with rotational symmetry. We numerically solve the Gross-Pitaevskii equation and plot the phase diagram. The corresponding physics with asymmetrical Rashba coupling is also discussed.