By inducing a Raman transition using a pair of Gaussian and Laguerre-Gaussian laser beams, we realize a ^{87}Rb condensate whose orbital angular momentum (OAM) and its internal spin states are coupled. By varying the detuning and the coupling strength of the Raman transition, we experimentally map out the ground-state phase diagram of the system for the first time. The transitions between different phases feature a discontinuous jump of the OAM and the spin polarization, and hence are of first order. We demonstrate the hysteresis loop associated with such first-order phase transitions. The role of interatomic interaction is also elucidated. Our work paves the way to explore exotic quantum phases in the spin-orbital-angular-momentum coupled quantum gases.
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