  We theoretically study an interacting few-body system of Rashba spin-orbit
coupled two-component Bose gases confined in a harmonic trapping potential. We
solve the interacting Hamiltonian at large Rashba coupling strengths using
Exact Diagonalization scheme, and obtain the ground state phase diagram for a
range of interatomic interactions and particle numbers. At small particle
numbers, we observe that the bosons condense to an array of topological states
with n+1/2 quantum angular momentum vortex configurations, where n = 0, 1, 2,
3... At large particle numbers, we observe two distinct regimes: at weaker
interaction strengths, we obtain ground states with topological and symmetry
properties that are consistent with mean-field theory computations; at stronger
interaction strengths, we report the emergence of strongly correlated ground
states.
