  A method is suggested to obtain solutions of the various quantum optical
Hamiltonians in the framework of the asymptotic iteration method. We extend the
notion of asymptotic iteration method to solve the 2 \times 2 matrix
Hamiltonians. On a particular case, eigenvalues of the Rabi and Rashba
Hamiltonians are computed. The method presented here reproduces a number of
earlier results in a natural way as well as leads to a novel findings. Possible
generalizations of the method are also suggested.
